APPENDIX A ACI Building Code Requirements for Thin Shells and Folded Plates*

Since concrete is the basic, most common material for the construction of thin shells, the requirements of such specific codes as those of the American Concrete Institute must be followed. Unfortunately, for many years these codes did not address in specific terms the unique problems related to thin shells, so that in the absence of special provisions only the common rules on concrete structures could in general be followed. One major result has been a great thickness for shells being imposed by minimum cover requirements for steel reinforcement. Naturally, code requirements vary from country to country, so that although ACI restrictions were enforced in the United States, shells only three-quarters of an inch thick were legally possible in Mexico, as demonstrated by the numerous thin shells there by Felix Candela. The ACI's design provisions for shells and folded plates are covered in Chapter 19 of its code. These include such major topics as definitions, criteria for structural and model analysis, reinforcement, prestressing, and construction. In separating the supporting members of a thin shell structure from its whole, the code explicitly specifies that Chapter 19's provisions apply only on the thin shell portion of the structure. The edge beams, columns, footings, and other supporting members are covered by other chapters in the code. Naturally, thin shell designs should also be controlled by the rest of the code, except for provisions that may conflict with those in Chapter 19.

*From Building Code Requirements for Reinforced Concrete (ACI 318-89). The full text of Chapter 19 and its Commentary are reprinted with the permission of the American Concrete Institute, Detroit.

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19.0-NOTATION Ec = modulus of elasticity of concrete, psi (see 8.5.1) Fe = specified compressive strength of concrete, psi = square root of specified compressive strength of concrete, psi = specified yield strength of nonprestressed re- inforcement, psi = thickness of shell or folded plate, in. = develop length, in. = strength reduction factor (see 9.3) 19.1 Scope and Definitions

This code and commentary provides building code information on the design, analysis, and construction of concrete thin shells and folded plates. The process began in 1964 with the pub• lication of a practice and commentary by ACI Committee 334,19.1 and continued with the in• clusion of Chapter 19 in ACI Building Code ACI 318-71 and in later editions. The current revision reflects additional experience in de• sign, analysis, and construction gained since the earlier publications, and was influenced by the publication of the "Recommendations for Concrete Shells and Folded Plates" of the In• ternational Association for Shell and Spatial Structures (lASS) in 1979.19.2 Since Chapter 19 applies to concrete thin shells and folded plates of all shapes, extensive discussion of their design, analysis, and con• struction in the commentary is not possible. Ad• ditional information can be obtained from the references listed at the end of this chapter, which are provided for the assistance of the designer. They are not an official part of the code. The designer is responsible for their in• terpretation and use. Particular emphasis on de• velopments and practice in the United States is given in "Concrete Thin Shells," ACI SP_28. 19-3

19.1.1 Provisions of Chapter 19 shall apply to R 19 .1.1 Chapter 19 is intended to apply to thin shell and folded plate concrete structures, thin shells and folded plate concrete structures including ribs and edge members. in building construction. Discussion of the ap• plication of thin shells in special structures such as cooling towers and circular prestressed con• crete tanks may be found in the reports of ACI• ASCE Committee 33419.4 and ACI Committee 344. 19.5

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19.1.2 All provisions of this code not specifi• cally excluded, and not in conflict with provi• sions of Chapter 19 shall apply to thin-shell structures.

19.1.3 Thin shells: three-dimensional spatial R 19.1. 3 Common types of thin shells are structures made up of one or more curved slabs domes (surfaces of revolution), 19.3. 19.6-19.9 cy• or folded plates whose thicknesses are small lindrical shells, 19.3. 19.6. 19.8. 19.10-19.15 conoids, compared to their other dimensions. Thin shells 19.6. 19.16-19.18 elliptical paraboloids, 19.6. 19.19 hy• are characterized by their three-dimensional perbolic paraboloids, 19.3. 19.6. 19.8. 19.19-19.28 and load-carrying behavior which is determined by groin vauIts.19.3. 19.19. 19.29. 19.30 Considerable in• the geometry of their forms, by the manner in formation on the experience gained in the de• which they are supported, and by the nature of sign, analysis and construction of these shells the applied load. may be found in the cited references. Less experience is available regarding other shell types or shapes, including free-form shells. However, a number of these have been success• fully built. Thin shell elements are slabs or plates with thicknesses less than one-fifth the transverse width and less than one-twentieth the radius of curvature on span lengths.

19.1.4 Folded plates: a special class of shell R19.1.4 Folded plates may be prismatic,19.3. structures formed by joining flat, thin slabs 19.6. 19.31-33 nonprismatic,19.34 or faceted. The along their edges so as to create a three-dimen• first two types, which are the most common, sional spatial structure. consist generally of planar thin slabs joined along their longitudinal edges to form a beam• like structure spanning between supports. Fac• eted folded plates, which are much less com• mon, are made up of triangular and/or poly• gonal planar thin slabs joined along their edges to form three-dimensional spatial structures similar to continuously curved thin shells such as domes or other shell forms. Only limited ex• perience is available on the design, analysis, and construction of faceted folded plates.

19.1.5 Ribbed shells: spatial structures with R19.1.5 Ribbed shells I9.3. 19.35. 19.36 generally material placed primarily along certain pre• have been used for larger spans where the in• ferred rib lines, with the area between the ribs creased thickness of the curved slab alone be• filled with thin slabs or left open. comes excessive or uneconomical. Ribbed shells also have been used because of the construction techniques employed and to enhance the aes• thetic impact of the completed structure.

19.1.6 Auxiliary members: ribs or edge beams R 19.1.6 Most thin shell structures require ribs which serve to strengthen, stiffen, and/or sup• or edge beams at their boundaries to carry the port the shell; usually, auxiliary members act shell boundary forces, to assist in transmitting jointly with the shell. them to the supporting structure, and to accom• modate the increased amount of reinforcement in these areas.

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19.1.7 Elastic analysis: an analysis of defor• R 19.1. 7 Elastic analysis of thin shells and mations and internal forces based on equilib• folded plates means any method of structural rium, compatibility of strains, and assumed elas• analysis which is based on assumptions which tic behavior, and representing to suitable provide suitable approximations to the three• approximation the three-dimensional action of dimensional behavior of the structure. The the shell together with its auxiliary members. method must provide the internal forces and displacements needed in the design of the shell proper, the rib or edge members, and the sup• porting structure. Equilibrium of internal forces and external loads and compatibility of deformations must be satisfied. Methods of elastic analysis based on classical shell theory, simplified mathematical or analyti• cal models, or numerical solutions using finite e1ement,19.37 finite differences, or numerical in• tegration techniques, are described in the cited references. The choice of the method of analysis and the degree of accuracy required depend on certain critical factors. These include: the size of the structure, the geometry of the thin shell or folded plate, the manner in which the structure is supported, the nature of the applied load and, finally, the extent of personal or documented experience regarding the reliability of the given method of analysis in predicting the behavior of the specific type of shell or folded plate.

19.1.8 Inelastic analysis: an analysis of defor• R19.1.8 Inelastic analysis of thin shells and mations and internal forces based on equilib• folded plates means a refined method of analy• rium, nonlinear stress-strain relations for con• sis based on the specific nonlinear material crete and reinforcement, consideration of properties, nonlinear behavior due to the crack• cracking and time dependent effects, and com• ing of concrete, and time dependent effects patibility of strains. The analysis shall represent such as creep, shrinkage, temperature, and load to suitable approximation the three-dimen• history. These effects are incorporated in order sional action of the shell together with its auxil• to trace the response and crack propagation of a iary members. reinforced concrete shell through the elastic, inelastic and ultimate ranges. Such analyses usu• ally require incremental loading and iterative procedures to converge on solutions which sat• isfy both equilibrium and strain compatibil• ity.19.38 Analysis of this type generally requires extensive computer time.

19.1.9 Experimental analysis: an analysis pro• cedure based on the measurement of deforma• tions and/or strains of the structure or its model; experimental analysis is based on either elastic or inelastic behavior.

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19.2 Analysis and Design

19.2.1 Elastic behavior shall be an accepted R19.2.1 For types of shell structures where basis for determining internal forces, and dis• experience, tests, and analyses have shown that placements, of thin shells. This behavior may be the structure can sustain reasonable overloads established by computations based on an analy• without undergoing brittle failure, elastic analy• sis of the uncracked concrete structure in which sis is a generally acceptable procedure. The de• the material is assumed linearly elastic, homoge• signer may assume that reinforced concrete is neous, and isotropic. Poisson's ratio of concrete ideally elastic, homogeneous, and isotropic, may be assumed equal to zero. having identical properties in all directions. Poisson's ratio may be assumed equal to zero since in concrete shells the three-dimensional effects of Poisson's ratio are not very signifi• cant. In shells of unusual size, shape, or com• plexity, the analysis should consider behavior through the elastic, cracking, inelastic, and fac• tored load. For unusual shell types, it is important to verify that the elastic behavior is not terminated by a brittle failure.

19.2.2 Inelastic analyses may be used where it R19.2.2 Inelastic analysis procedures will gen• can be shown that such methods provide a safe erally require extensive use of computer proce• basis for design. dures. Several references indicate possible solu• tion methods.19.~8-19.40

19.2.3 Equilibrium checks of internal resist• ances and external loads shall be made to en• sure consistency of results.

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19.2.4 Experimental or numerical analysis R19.2.4 A wide range of numerical analysis procedures may be used where it can be shown procedures is available. The designer must en• that such procedures provide a safe basis for sure that the method selected is appropriate. design. The finite element method can be used to sat• isfy displacement compatibility and boundary conditions. It does not necessarily satisfy overall or local equilibrium with sufficient accuracy un• less a fine enough finite element mesh size is used. Other computational techniques include finite difference and numerical integration methods. Experimental analysis of elastic models has been used as a substitute for an ana• lytical solution of a complex shell structure. Ex• perimental analysis of reinforced micro-con• crete models through the elastic, cracking, inelastic, and ultimate ranges should be consid• ered for shells of unusual size, shape, complex• ity, or importance. For model analysis, only those portions of the structure which affect significantly the items under study need be simulated. Every attempt should be made to ensure that the experiments reveal the quantitative behavior of the proto• type structure. Similarly, wind tunnel tests of a scaled-down model do not necessarily provide usable results and should be conducted by a recognized ex• pert in wind tunnel testing of structural models. 19.41

19.2.5 Approximate methods of analysis not R19.2.5 In general, solutions that include satisfying compatibility of strains either within both membrane and bending effects and satisfy the shell or between the shell and auxiliary compatibility of strains and equilibriums are members may be used where it can be shown preferred. Approximate solutions which satisfy that such methods provide a safe basis for statics but not the compatibility of strains may design. be used only when extensive experience has proved that safe designs have resulted from their use. Such methods include beam-type analysis for barrel shells and folded plates hav• ing large ratios of span to either width or radius of curvature, simple membrane analysis for shells of revolution, and others in which the equations of equilibrium are satisfied, while the strain compatibility equations are not. However, in complex structures where sev• eral shells join together, or where shells join auxiliary members, a more accurate analysis should be used.

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19.2.6 In prestressed shells, the analysis must RI9.2.6 If the shell is prestressed, the analysis also consider behavior under loads induced must include its strength at factored loads as during prestressing, at cracking load, and at well as its adequacy under service loads, the factored load. Where prestressing tendons are load which causes cracking, and the behavior draped within a shell, design shall take into ac• under loads induced during prestressing. This count force components on the shell resulting was recommended in ACI 318R-77, 19.2.3, from tendon profile not lying in one plane. and was moved to the code for clarity. Axial forces due to draped prestressed tendons may not lie in one plane and due consideration must be given to the resulting force components. The effects of post-tensioning of supporting members on the shell must be taken into account.

19.2.7 The thickness h of a thin shell, and its RI9.2.7 In general, Chapter 19 assumes the reinforcement, shall be proportioned for the use of the strength design method of 8.1.1. On required strength and serviceability. All ele• this basis the thin shell's thickness and rein• ments shall be proportioned by the same forcement must be proportioned to satisfy the method, using either the strength design strength provisions of this code, so as to resist method of 8.1.1 or the alternate design method internal forces obtained from an analysis, an of 8.1.2. experimental model study, or a combination thereof. The thickness of the shell is often dic• tated not by the requirements of strength, but by the limitation of deflection of edge members, by the requirements of stability imposed by 19.2.8, or by the required reinforcement cover and the construction exigencies. The necessary thickness and reinforcement may be also provided by using the alternate design method prescribed in 8.1.2. The design method chosen shall be used consistently throughout the structure. If composite action is involved, the provi• sions of Chapter 17 must be satisfied. Chapter 16 applies if elements are precast. When shell or folded plate elements are precast and connected by cast-in-place segments, composite action must be considered.

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19.2.8 Shell design shall investigate and pre• R19.2.8 Thin shells, like other structures that clude the possibility of general or local insta• experience in-plane compressive forces, are bility. subject to buckling when the applied load reaches a critical value. Because of the surface• like geometry of shells, the problem of calculat• ing buckling load is complex. If one of the prin• cipal membrane forces is tensile, the shell is less likely to buckle than if both principal mem• brane forces were compressive. The kinds of membrane forces that develop in a shell depend on its initial shape and the manner in which the shell is supported and loaded. In some types of shells, post-buckling behavior must be consid• ered in determining safety against instability. 19.2 Investigation of thin shells for stability shall consider the effect of the following factors: (1) anticipated deviation of the geometry of the shell surface as built from the idealized, perfect geometry, (2) large deflections, (3) creep and shrinkage of concrete, (4) inelastic properties of materials, (5) cracking of concrete, (6) location, amount, and orientation of reinforcement, and (7) possible deformation of supporting ele• ments. For shells of moderate size, the smallest practical shell thickness used in reinforced con• crete construction is such that the danger of buckling is usually minimal and simplified anal• yses suffice. Practical measures to improve re• sistance to buckling successfully used in the past include the provision of two mats of rein• forcement - one near each outer surface of the shell, a local increase of shell curvatures, the use of ribbed shells, and the use of concrete with high tensile strength and low creep. A practical procedure for determining criti• cal buckling loads of shells is given in the lASS recommendations. 19.2 Some recommendations for buckling design of domes used in industrial applications are given in ACI Committee 344 Report.19.5 Approaches for other shells are con• tained in "Concrete Shell Buckling," ACI SP_67. 19,42

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19.2.9 Auxiliary members shall be designed RI9.2.9 Auxiliary members must be designed according to the applicable provisions of this in accord with the general provisions of the code. The design method selected for shell ele• code, using one of the two methods prescribed ments under 19.2.7 shall also be used for auxil• in 8.1, which is consistent with the design iary members. A portion of the shell equal to method of the shell elements. Portions of the the flange width specified in 8.10 may be as• shell may be utilized as flanges for transverse or sumed to act with the auxiliary member. In longitudinal frames or arch-frames and beams. such portions of the shell, the reinforcement Such flanges may be curved or sloping. Canti• perpendicular to the auxiliary member shall be lever action of the flanges must be investigated at least equal to that required for the flange of a in determining reinforcement in the flange per• T-beam by 8.10.5. pendicular to the longitudinal axis of the sup• porting member, as required by Chapter 8. In all cases, at least the minimum shrinkage and temperature reinforcement must be used. 19.3 Design Strength of Materials

19.3.1 Specified compressive strength of con• crete!,. at 28 days shall not be less than 3,000 psi.

19.3.2 Specified yield strength of nonpre• stressed reinforcement J, shall not exceed 60,000 psi.

19.4 Shell Reinforcement

19.4.1 Shell reinforcement shall be provided R19.4.1 At any point in a shell, two different to resist tensile stresses from internal membrane kinds of internal forces may occur simulta• forces, to resist bending and twisting moments, neously: those associated with membrane ac• to control shrinkage and temperature cracking, tion, and those associated with bending of the and as special reinforcement at shell bounda• shell. The membrane forces are assumed to act ries, load attachments, and shell openings. in the tangential plane midway between the sur• faces of the shell and are the two axial forces and the membrane shears. Flexural effects in• clude bending moments, twisting moments, and the associated transverse shears.

19.4.2 Membrane reinforcement shall be pro• R19.4.2 Membrane reinforcement should be vided in two or more directions in all parts of provided to carry the full calculated membrane the shell. tension forces with no tensile stress carried by concrete. Throughout the shell membrane re• inforcement must be provided in at least two approximately orthogonal directions. In high stress areas, a third layer of membrane rein• forcement may be utilized.

19.4.3 The area of shell reinforcement at any R19.4.3 Minimum membrane reinforcement section as measured in two orthogonal direc• corresponding to slab shrinkage and tempera• tions shall not be less than the slab shrinkage or ture reinforcement must be provided in at least temperature reinforcement required by 7.12. two approximately orthogonal directions even if the calculated membrane forces are compres• sive in one or more directions.

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19.4.4 Reinforcement required to resist shell R19.4.4 The requirement of ensuring membrane forces shall be provided so that the strength in every direction is based on safety design strength in every direction shall be at considerations. Any method of design which as• least equal to the component of the principal sures sufficient strength consistent with equilib• membrane forces in the same direction due to rium is considered acceptable. The direction of factored loads. the principal membrane tensile force at any point may sometimes vary depending on the direction, magnitudes, and combinations of the various applied loads. The magnitude of the internal membrane forces, acting at any point due to a specific load system, generally is calculated on the basis of an elastic theory in which the shell is assumed un• cracked. The computation of the required amount of reinforcement to resist the internal membrane forces has been traditionally based on the assumption that concrete cannot resist tension. A great many shell structures have been successfully designed and constructed over the years. This experience provides evi• dence of the adequacy of this approach. The associated deflections, and the possibility of cracking, should be investigated in the service• ability phase of the design. Where reinforcement is not placed in the direction of the principal tensile forces and where cracks at the service load level would be objectionable, the computation of reinforce• ment may have to be based on more refined approachesI9.43. 19.44 which consider the exis• tence of cracks. In the cracked state, the con• crete is assumed unable to resist either tension or shear. Thus, equilibrium is attained by means of tensile resisting forces in reinforce• ment and compressive resisting forces in concrete.

19.4.5 The area of shell tension reinforce• R19.4.5 The requirement that the tensile re• ment shall be limited so that the reinforcement inforcement yield before the concrete crushes is will yield before crushing of concrete in com• consistent with 10.3.3. In shells, initial crushing pression can take place. of the concrete is not likely to occur. However, it has been suggested that such crushing would occur in some portions of some shells where the principal membrane forces are approximately equal and opposite in sign. It can be shownl9.45 that a limit on the maximum amount of rein• forcement effective in resisting the principal tensile membrane force will insure that the crushing of concrete does not take place before the yielding of reinforcement. The limit sug• gested on the ratio of reinforcement in any por• tion of shell is the smaller of 0.6f'. J, or 2,400/ J,. These limits are the same as those used in ACI 318-77 but are expressed here in ratio form.

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19.4.6 In regions of high tension, membrane RI9.4.6 It is generally desirable for all shells reinforcement shall, if practical, be placed in and particularly important in regions of sub• the general directions of the principal tensile stantial tension that the directions of reinforce• membrane forces. Where this is not practical, it ment approximate the directions of the princi• is permitted to place membrane reinforcement pal tensile membrane forces. However, in some in two or more component directions. structures it is not always possible or practical for the reinforcement to follow the stress trajec• tories. For such cases, orthogonal component reinforcing is allowed.

19.4.7 If the direction of reinforcement varies RI9.4.7 When the directions of reinforce• more than I 0 deg from the direction of princi• ment deviate significantly (10 deg) from the di• pal tensile membrane force, the amount of rein• rections of the principal membrane forces, forcement may have to be increased to limit the higher strains in the shell must occur to develop width of possible cracks at service load levels. the capacity of reinforcement. 19.44 This might lead to the development of unacceptably wide cracks. The crack width should be estimated and controlled if necessary. Permissible crack widths for service loads under different environmental conditions are given in the report of ACI Committee 224.19.46 Crack width can be limited by an increase in the amount of reinforcement used, by reducing the stress at the service load level, by providing re• inforcement in three or more directions in the plane of the shell, or by using closer spacing of smaller diameter bars rather than wider spaced larger bars.

19.4.8 Where the magnitude of the principal RI9.4.S The practice of concentrating tensile tensile membrane stress within the shell varies reinforcement in the regions of maximum ten• greatly over the area of the shell surface, rein• sile stress has led to a number of successful and forcement resisting the total tension is to be economical designs, primarily for long folded concentrated in the regions of largest tensile plates, long barrel vault shells, and for domes. stress where it can be shown that this provides a The requirement of providing the minimum re• safe basis for design. However, the ratio of shell inforcement in the remaining tensile zone is in• reinforcement in any portion of the tensile zone tended to control cracking. shall be not less than 0.0035 based on the over• all thickness of the shell.

19.4.9 Reinforcement required to resist shell RI9.4.9 The sign of bending moments may bending moments shall be proportioned with change rapidly from point to point of a shell. due regard to the simultaneous action of mem• For this reason, bending reinforcement, where brane axial forces at the same location. Where required, is to be placed near both outer sur• shell reinforcement is required in only one face faces of the shell. In many cases, the thickness to resist bending moments, equal amounts shall required to provide proper cover and spacing be placed near both surfaces of the shell even for the multiple layers of reinforcement may though a reversal of bending moments is not govern the design of the shell thickness. indicated by the analysis.

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19.4.10 Shell reinforcement in any direction RI9.4.10 The value of cp to be used is that shall not be spaced farther apart than 18 in. nor prescribed in 9.3.2.2(a) for axial tension. five times the shell thickness. Where the princi• pal membrane tensile stress on the gross con• crete area due to factored loads exceeds 4cp if. reinforcement shall not be spaced farther apart than three times the shell thickness.

19.4.11 Shell reinforcement at the junction of RI9.4.11 and RI9.4.12 On curved shell sur• the shell and supporting members or edge faces it is more difficult to control the alignment members shall be anchored in or extended of precut reinforcement. This must be consid• through such members in accordance with the ered to avoid insufficient splice and develop• requirements of Chapter 12, except that the ment lengths. Sections 19.4.11 and 19.4.12 minimum development length shall be 1.2t" but specify extra reinforcement length to maintain not less than 18 in. the minimum lengths on curved surfaces.

19.4.12 Splice development lengths of shell reinforcement shall be governed by the provi• sions of Chapter 12, except that the minimum splice length of tension bars shall be 1.2 times the value required by Chapter 12 but not less than 18 in. The number of splices in principal tensile reinforcement shall be kept to a practical minimum. Where splices are necessary they shall be staggered at least t" with not more than one-third of the reinforcement spliced at any section. 19.5 Construction

19.5.1 When removal of formwork is based on RI9.5.1 When early removal of forms is nec• a specific modulus of elasticity of concrete be• essary, the magnitude of the modulus of elastic• cause of stability or deflection considerations, ity at the time of proposed form removal must the value of the modulus of elasticity E. shall be be investigated in order to insure safety of the determined from flexural tests of field-cured shell with respect to buckling, and to restrict beam specimens. The number of test speci• deflections. 19.s. 19.47 The value of the modulus of mens, the dimensions of test beam specimens, elasticity E. must be obtained from a flexural and test procedures shall be specified by the test of field-cured specimens. It is not sufficient Engineer. to determine the modulus from the formula in 8.5.1, even if f. is determined for the field• cured specimen.

19.5.2 The Engineer shall specify the toler• RI9.5.2 In some types of shells, small local ances for the shape of the shell. If construction deviations from the theoretical geometry of the results in deviations from the shape greater shell can cause relatively large changes in local than the specified tolerances, an analysis of the stresses and in overall safety against instability. effect of the deviations shall be made and any These changes can result in local cracking and required remedial actions shall be taken to en• yielding which may make the structure unsafe sure safe behavior. or can greatly affect the critical load producing instability. The effect of such deviations should be evaluated and any necessary actions should be taken promptly.

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REFERENCES

19.1. ACI Committee 334, "Concrete Shell Structures-Practice and Commentary," (ACI 334.IR-64) (Revised 1982), ACI JOURNAL, Proceedings V. 61, No.9, Sept. 1964, pp. 1091- 1108. Also ACI Manual of Concrete Practice, Part 4. See also, Discussion, ACI JOURNAL, Proceedings V. 62, No.3, Part 2, Mar. 1965, pp. 1755-1765. 19.2. lASS Working Group No.5, "Recommendations for Reinforced Concrete Shells and Folded Plates," International Association for Shell and Spatial Structures, Madrid, 1979, 66 pp. 19.3. Concrete Thin Shells, SP-28, American Concrete Institute, Detroit, 1971, 424 pp. 19.4. ACI Committee 334, "Reinforced Concrete Cooling Tower Shells-Practice and Commentary," (ACI 334.2R-77) (Revised 1982), American Concrete Institute, Detroit, 1977, 10 pp. Also ACI Manual of Concrete Practice, Part 4. 19.5. ACI Committee 344, "Design and Construction of Circular Prestressed Concrete Structures," (ACI 344R-70) (Reaffirmed 1981), American Concrete Institute, Detroit, 1970, 16 pp. Also ACI Manual of Concrete Practice, Part 4. 19.6. Billington, David P., Thin Shell Concrete Structures, 2nd Edition, McGraw-Hill Book Co., New York, 1982,373 pp. 19.7. Ketchum, Milo S., "Design of Shell Structures-Short Shells and Domes of Revolution," Consulting Engineer, V. 17, No.1, July 1962. 19.8. Tedesko, Anton, "How Have Concrete Shell Structures Performed?," Bulletin, International Association for Shell and Spatial Structures (Madrid), No. 73, Aug. 1980, pp.3-13. 19.9. Christiansen, j. V., "The King County Multipurpose Domed Stadium," Proceedings, lASS World Congress on Space Enclosures (Montreal, 1976), Building Research Centre, Concordia University, Montreal, 1976, V. 2, pp. 11)49-1061. 19.10. "Design of Cylindrical Concrete Shell Roofs," Manual of Engineering Practice No. 31, American Society of Civil Engineers, New York, 1952, 1977. 19.11. Chinn,j., "Cylindrical Shell Analysis Simplified by Beam Method," ACIJoURNAL, Proceedings V. 55, No. 11, May 1959, pp. 1183-1192. Also, Discussion, ACIJoURNAL, Proceedings V. 55, No.6, Part 2, Dec. 1959, pp. 1583-1603. 19.12. Gibson, j. E., The Design of Shell Roofs, 3rd Edition, E. & F. Spon Limited, London, 1968, 300 pp. 19.13. Bryant, Anthony H., and Scrivener, John C., "Cylindrical Shell Roofs with Draped Prestressing," Proceedings, ASCE, V. 95, ST4, Apr. 1969, pp. 611-634. 19.14. Harris, Harry G., and White, Richard N., "Inelastic Behavior of RC Cylindrical Shells, Proceedings, ASCE, V. 98, ST7, July 1972, pp. 1633-1653. 19.15. Mast, Paul E., "Design and Construction of Northlight Barrel Shells," ACI JOURNAL, Proceedings, V. 59, No.4, Apr. 1962, pp. 481-525. Also, Discussion, ACI JOURNAL, Proceedings, V. 59, No. 12, Dec. 1962, pp. 1903-1910. 19.16. Hadid, H. A., and Chandra, R., "An Experimental Investigation of a Reinforced Mortar Parabolic Conoidal Shell," Bulletin, International Association for Shell and Spatial Structures (Madrid), No. 28, Dec. 1966, pp. 53 - 62. 19.17. Hadid, H. A., "Variational Methods for the Analysis of a Conoidal Shell," Bulletin, International Association for Shell and Spatial Structures (Madrid), No. 35, Sept. 1968, pp. 23-36. 19.18. Medwadowski, S. j., "Bending of Thin Shell Conical Frustum Segments," Proceedings, lASS Symposium on Simplified Calculation Methods (Brussels, 1961), North-Holland Publishing Company, Amsterdam, 1962. 19.19. Parme, Alfred L., "Hyperbolic Paraboloids and Other Shells of Double Curvature," Proceedings, ASCE, V. 82, ST5, Sept. 1956, pp. 1057-1081. Also, Discussion, V. 83, ST2, Mar. 1957. 19.20. Candela, Felix, "General Formulas for Membrane Stresses in Hyperbolic Paraboloidal Shells," ACIJoURNAL, Proceedings, V. 57, No.4, Oct. 1960, pp. 353-371.

355 ACI Building Code Requirements

19.21. Scordelis, Alexander C.; Ramirez, H. D.; and Ngo, D., "Membrane Stresses in Hyperbolic Paraboloid Shells Having an Arbitrary Quadrilateral Shape in Plan," ACI JOURNAL, Proceedings, V. 67, No. I,Jan. 1970, pp. 36-44. 19.22. Schnobrich, William C., "Analysis of Hipped Roof Hyperbolic Paraboloid Structures," Proceedings, ASCE, V. 98, ST7,July 1972, pp. 1575-1583. 19.23. Shaaban, Ahmed, and Ketchum, Milo S., "Design of Hipped Hypar Shells," Proceedings, ASCE, V. 102, STll, Nov. 1976, pp. 2151-2161. 19.24. Schnobrich, W. C.; Mohraz, B.; and Hoebel, J. L., "Influence of Edge Beam Properties on the Stress in Hyperbolic Paraboloid Shells," Proceedings, lASS International Colloquium on Progress of Shell Structures in the Last Ten Years and Its Future Development (Madrid, 1969), International Association for Shell and Spatial Structures, Madrid, 1970, V. 3. 19.25. Gioncu, V., "Stresses and Deflections in Umbrella Roof HP Shells," Bulletin, International Association for Shell and Spatial Structures (Madrid), No. 56, Dec. 1974, pp.31-38. 19.26. White, Richard N., "Reinforced Concrete Hyperbolic Paraboloid Shells," Proceedings, ASCE, V. 101, ST9, Sept. 1975, pp. 1961-1980. 19.27. Scordelis, Alexander C., and Ketchum, Mark A., "Structural Behavior and Design of Saddle HP Shells," Proceedings, lASS World Congress on Shell and Spatial Structures (Madrid, 1979), Laboratorio Central de Ensayo de Materiales de Construccion, Madrid, 1980, V. 2, pp. 4.239-4.254. 19.28. Tedesko, Anton, "Shell at Denver-Hyperbolic Paraboloidal Structure of Wide Span," ACIJoURNAL, Proceedings, V. 57, No.4, Oct. 1960, pp. 403-412. 19.29. Csonka, P., "Composite Sectorial Shells with Cantilevered Front Side," Bulletin, International Association for Shell and Spatial Structures (Madrid), No. 28, Dec. 1966, pp.25-36. 19.30. Scordelis, Alexander C., "Analysis and Design of HP Groined Vaults," Proceedings, lASS World Congress on Space Enclosures (Montreal, 1976), Building Research Centre, Concordia University, Montreal, 1976, pp. 561-568. 19.31. Pultar, Mustafa; Billington, David P., and Riera, Jorge D., "Folded Plates Continuous Over Flexible Supports," Proceedings, ASCE, V. 93, ST5, Oct. 1967, pp. 253-277 . . 19.32. Cheung, Yau-Kai, "Folded Plate Structure by the Finite Strip Method," Proceedings, ASCE, V. 95, STl2, Dec. 1969, pp. 2963-2979. 19.33. Klaiber, F. Wayne; Gutzwiller, MartinJ.; and Lee, Robert H., "Analytical and Model Studies of Prestressed Folded Plates," Proceedings, ASCE, V. 99, ST6, June 1973, pp. 1287-1307. 19.34. Johnson, Claude D., and Lee, Ti-Ta, "Long Nonprismatic Folded Plate Structures," Proceedings, ASCE, V. 94, ST6, June 1968, pp. 1457 -1484. 19.35. Esquillan, Nicholas, "The Shell Vault of the Exposition Palace, Paris," Proceedings, ASCE, V. 86, STl,Jan. 1960, pp. 41-70. 19.36. Esquillan, Nicholas, "Olympic Ice Stadium at Grenoble," ACI JOURNAL, Proceedings, V. 66, No.7, July 1969, pp. 513-521. 19.37. Ashwell, D. G., and Gallagher, R. H., Editors, Finite Elementsfor Thin Shells and Curved Members, John Wiley & Sons, London, 1976, 268 pp. 19.38. Lin, Cheng-Shung, and Scordelis, Alexander C., "Nonlinear Analysis of RC Shells of General Form," Proceedings, ASCE, V. 101, ST3, Mar. 1975, pp. 523-538. 19.39. Hand, Frank R.; Pecknold, David A.; and Schnobrich, William C., "Nonlinear Layered Analysis of RC Plates and Shells," Proceedings, ASCE, V. 99, ST7, July 1973, pp. 1491-1505. 19.40. Kabir, Ahmad F., and Scordelis, Alexander C., "Analysis of RC Shells for Time Dependent Effects," Bulletin, International Association for Shell and Spatial Structures (Madrid), No. 69, Apr. 1979, pp. 3-13. 19.41. Models for Concrete Structures, SP-24, American Concrete Institute, Detroit, 1970, 448 pp. 19.42. Concrete Shell Buckling, SP-67, American Concrete Institute, Detroit, 1981,234 pp. 19.43. Gupta, Ajaya K., "Membrane Reinforcement in Shells," Proceedings, ASCE, V. 107, STl, Jan. 1981, pp. 41-56.

356 Thin Shells and Folded Plates

19.44. Baumann, T., "On the Question of Multi-Directional Reinforcement of Plate and Shell Structure," Der Bauingenieur (Heidelberg), V. 97, No. 10,1972 (in German). 19.45. Fialkow, Morris N., "Ductility Requirements for Reinforced Concrete Cylindrical Shells and Folded Plate Structures," ACI JOURNAL, Proceedings, V. 77, No.2, Mar.-Apr. 1980, pp. 82-86. 19.46. ACI Committee 224, "Control of Cracking in Concrete Structures," (ACI 224R-80), American Concrete Institute, Detroit, 1980, 42 pp. Also ACI Manual of Concrete Practice, Part 3. 19.47. Tedesko, Anton, "Construction Aspects of Thin-Shell Structures," ACI JOURNAL, Proceedings, V. 49, No.6, Feb. 1953, pp. 505-520.

357 APPENDIX B Excerpts from The Engineering Index Annual 1989

The latest bibliographical references on shell structures are extremely significant to anyone interested in exploring this field in all its ramifications. It is essential to find access to the latest bibliographical data, especially for researchers outside the United States. The original source of the following reference material is The Engineering Index Annual 1989, a major publication that describes itself as "the world's first and most comprehensive collection of time-saving abstracts on engineering developments." This work, published annually since 1884, has been compiled by Engineering Information, Inc., a nonprofit organization. Because the list of publications in this field is quite extensive, it has been found necessary to give only the references to the 1989 Index. It should be kept in mind that for each group of publications published each year the Index classifies the various articles into different areas that may vary from year to year. In the 1989 Index, for instance, fifty-four subtitles were selected. The abstracts for the individual articles can be found within the Annual Index. The six-digit number at the beginning of each listing here is used to locate the abstract for that particular article. Any major research library should have the engineering indexes.

Reprinted with the permission of Engineering Information, Inc. The full text of most of articles referred to herein can be ordered directly from Engineering Information, Inc., 345 East 47 St., New York, NY 10016.

359 Excerpts from The Eneineerine Index Annual 1989

036954 Numerical Study of Axisymmetric transmit loads to the foundation. The article Waves in an Elastic Cylindrical Shell discusses the foundation requirements, cutting Partially Filled with a Viscous Liquid. This and assembling the triangular panels; setting paper is devoted to a study of the natural steel and applying concrete; interior and longitudinal-transverse waves in an elastic exterior finishes; and the costs and material cylindrical shell of the Kirchoff-Love type, quantities. filled with a viscous compressible liquid. Hurd, M.K. Caner Constr v 33 n 11 Nov 1988 4p. Direct numerical integration of the equations of motion is the basis of this study. Examples of the calculation of the eigenvalues of 036957 Transient Waves in Inhomogeneous natural and steady oscillations in this Anisotropic Elastic Shells. This paper formulation of the problem are discussed. For considers the problem of transient wave a shell with a viscous compressible liquid there propagation in linearly elastic Cosserat shells are an infinite number of modes with of constant thickness that may be anisotropic complex eigenvalues. The Wien effect is and inhomogeneous. The methods of rays and observed for the upper conical waves. 12 Refs. of singular wave curves are combined to find Nochkin, I.M. (Moscow Inst of Electronics and and integrate the transport equations Mechanical Engineering, Moscow, USSR); Pashkov, governing growth-decay behavior of the six LA.; Troyanovskii, I.E. Sov Appl Meek v 24 n 2 Aug possible wave modes. Conditions on material 1988 P 144-148. parameters and wave geometry are obtained for various different uncouplings of the wave modes. Some special cases of propagation 036955 Axisymmetric Problem of the conditions and of decay equations are worked Penetration of a Compressible Fluid by out in detail. (Author abstract) 9 Refs. Thin Elastic Spherical Shells. This article Cohen, H. (Univ of Manitoba, Winnipeg, Manit, describes the solution of a linear axisymmetric Can); Thomas, R.S.D. Acta Meek v 77 n 1-2 Apr problem concerning the penetration of a 1989 p 47-67. compressible fluid by thin elastic spherical shells. The problem is solved in four formulations with different boundary 036958 Elasto/Visco-Plastic Dynamic conditions on the free surface of the fluid. In Response ofAxisymmetrical Shells Under the first two formulations, the free surface is Mechanical and/or Thermal Loading. An assumed to be movable. However, its rise near analytical method for the e1asto/visco-plastic the penetrating shell is not considered in dynamic problems of axis ymmetricaI thin formulation 1 and is accounted for in shells subjected to mechanical and/or thermal formulation 2. In the other two formulations, loads is developed. The equations of motion the free surface is constrained by a rigid and the relations between the strains and shield in formulation 3 and by a deformable displacements are derived by extending shield in formulation 4. It is assumed that the Sanders' elastic shell theory. For the wetted surface of the shell is impermeable to constitutive relations, Perzyna's elasto/visco• the fluid and that the disturbances generated plastic equations including the temperature in the fluid by the shell decay at infinity. 6 Refs. effect are employed. The derived fundamental Kubenko, V.D. (Acad of Sciences of the Ukrainian equations are numerically solved by the finite SSR, Kiev, USSR); Gavrilenko, V.V. Sov Appl Meek difference method. As numerical examples, Oct 1988 p 374-384. the simply supported cylindrical shells made of mild steel are treated and the following two cases are analyzed: a nonuniform temperature 036956 Geodesic Dome of Polystyrene and cylinder subjected to impulsive internal Concrete. Structurally, the geodesic dome is a pressure, and an internal pressure cylinder space truss and is the strongest known subjected to impulsive thermal load. In both straight-line form enclosing space. It is cases the variations of displacements and efficient as well as strong; there is no straight• internal forces with time are discussed. line geometric form that requires less surface (Author abstract) skin to enclose a given amount of space than Tao, Katsumi (Toyohashi Univ of Technology, a geodesic dome. In the concrete and Toyohashi, jpn); Takezono, Shigeo; Taguchi, polystyrene dome described, folds in the Toshihiro; Hotada, Kazuo. ]SME Int] Ser 1 ]SME concrete shell replace the straight bars. The Int] Ser 1 v 32 v32 n3 n3 jul jul 1989 1989 P folds, however, act just as the bars would to 341-347.

360 Excerpts from The Eneineerine Index Annual 1989

ACOUSTIC WAVE EFFECTS Guseinov, I.G. (Acad of Sciences of the Azerbaidzhan SSR, Baku, USSR). Sov Appl Meek v 036959 Interaction of Unsteady Acoustic 24 n 2 Aug 1988 P 138 - 144. Waves with Plates and Hollow Shells in a Fluid. A method is developed for solving 036962 Soundproof Characteristics of coupled problems for the unsteady interaction Orthotropic Cylindrical Shells. This paper is of acoustic waves with plates and hollow concerned with the soundproof characteristics spherical or cylindrical shells in a fluid by of infinitely long, cylindrical sandwich shells applying double integral transforms and composed of orthotropic face layers and a investigating them simultaneously. Analytical honeycomb core. The shell is excited by solutions of unsteady hydroelastic problems axisymmetric acoustic waves traveling within are obtained for spherical and cylindrical the shell. To simplify the shell governing shells. These solutions can be used to study equations it is assumed that the facings resist transient processes and their effect on the only bending moments and the honeycomb stress and deformation of the structural core resists only transverse shear forces. The elements for a wide range of parameters of sound transmission loss for the shell wall, TL, the hydroelastic system. 15 Refs. is derived and calculated numerically for Kubenko, V.D. (Acad of Sciences of the Ukrainian various values of the physical parameters SSR, Kiev, USSR); Moseenkov, Yu. B. Sov Appl involved. (Author abstract) 11 Refs. In Meek v 23 n 10 Apr 1988 p 951-957. Japanese. Chonan, Seiji. Nippon Kikai Gakkai Ronbunsku A 036960 Investigation of Axisymmetric Hen v 54 n 505 Sep 1988 p 1684-1691. Electroacoustic Waves in a Cylindrical Sandwich Shell by Three-Dimensional and 036963 Soundproof Characteristics of Applied Theories. The power series method Cylindrical Sandwich Shells with a is utilized in the present paper to solve Honeycomb Core. An analysis is presented problems on axisymmetric electroacoustic for the soundproof characteristics of infinitely wave propagation in a cylindrical sandwich long sandwich cylindrical shells subjected to shell on the basis of the three-dimensional inner axisymmetric acoustic waves. To electroelasticity equations. Approximate simplify the shell equation it is assumed that dispersion dependences are obtained on the the core material resists only transverse shear basis of the theory of vibrations of forces and that the facings do not resist piezoceramic shells with finite shear stiffness transverse shear forces. Acoustic waves in the extended to the case of inhomogeneity over air surrounding the shell is denoted by the the thickness, and comparison of these Helmholtz equation. Sound transmission loss dependences with the exact solutions found TL is calculated for various values of the permits estimation of the limits of applied physical parameters of the core and the theory applicability. 6 Refs. facings. (Author abstract) 6 Refs. In Japanese. Shul'ga, N.A. (Acad of the Sciences of the Chonan, Seiji. Nippon Kikai Gakkai Ronbunshu C Ukrainian SSR, Kiev, USSR); Rudnitskii, S. 1.; Hen v 54 n 505 Sep 1988 p 2156-2163. Evseichik, Yu. B. Sov Appl Meek v 23 n 10 Apr 1988 p 1005-1011. 036964 Sound Insulation Characteristics of Finite Length Orthotropic Shells. An 036961 Action of Acoustic Waves on a analysis is presented of the acoustic Spherical Shell Filled by a Viscous, characteristics of orthotropic cylindrical shells Compressible Fluid. This paper considers excited by axisymmetric plane sound waves within the axisymmetric problem, the action traveling within the shells. The shell is of acoustic waves on a spherical shell, filled by exposed in a free field in the range of length a viscous compressible fluid. The limitations L, and is otherwise covered with an infinite for an imcompressible, viscous, and ideal fluid rigid baffle. The problem is studied on the follow from the results. The tangential and basis of a thick shell theory in which account bending stresses are shown as functions of the is taken of the effects of shear deformation angular coordinate at relatively high and rotatory inertia. The air outside the shell frequency when the shell is filled by air, oil, is described by the Helmholtz linear acoustic and kerosene. When the shell is filled by air, equation. The sound transmission loss the stresses created by the plane wave are through the shell wall, TL, is obtained and larger than for a shell filled by kerosene or calculated for various values of the physical oil. 8 Refs. parameters involved. (Author abstract) 10 Refs.

361 Excerpts from The Enaineerina Index Annual 1989

Chonan, s. (Tohoku Univ, Sendai, Jpn); Koriyama, cylindrical shells weakened by a curvilinear H.i Sound Vib v 126 n 3 Nov 8 1988 P 525-532. hole. A modified method of series expansion in a small parameter is proposed in this paper, 036965 Simplified Method for a which can be utilized in analyzing cylindrical Hydrodynamic Loading Prediction of an composite orthotropic shells weakened by Acoustic Wave. This paper discusses existing small and medium elliptical holes. 13 Refs. methods for the hydrodynamic loading Revenko, V.P. (Scientific-Production Organization, prediction on a circular cylindrical shell USSR). Sov Appl Meeh Oct 1988 p 368-373. subjected to an underwater weak shock wave. To this end, a new, special purpose finite 036968 Fourier Integral Representation of element program was developed. The new Curvilinear Influence Functions Applied to program treats the acoustic fluid medium by Surface Structures. The paper proposes the an equation which defines the incident application of curvilinear influence functions particle velocity in the fluid in the absence of represented by Fourier integrals to problems the structure. This is then coupled to the of surface structures. It investigates in detail structure to yield the total fluid loading. characteristic properties of such integrals. Tensile pressures are not allowed by Particular attention is called to differentiation restricting the water pressure to above of the integrals representing functions with ambient level. (Edited author abstract) 14 Refs. curvilinear discontinuities, as in this case their Moussouros, Minos (US Naval Surface Warfare distributional features are most visible. The Cent, Silver Spring, MD, USA). Am Soe Meeh Eng problem is illustrated by an example of an Pap Preprint - American Society of Mechanical infinite plate. (Author abstract) 12 Refs. Engineers, Houston, TX, USA, Jan 22-25 1989. Muc, A. (Technical Univ of Cracow, Cracow, Pol); Publ by American Soc of Mechanical Engineers Zielinski, A.P. Thin-Walled StTuct v 7 n 2 1989 P (ASME), New York, NY, USA, 1989 OCN12 18p. 85-98.

036966 Inelastic Response of an Infinite 036969 Co Shell Plate and Beam Elements Cylindrical Shell to Transient Acoustic Free From Their Deficiencies. The author Waves. The geometrically and constitutively proposes a generally applicable new nonlinear response of an infinite, circular, formulation which removes all shear and cylindrical shell submerged in an infinite fluid membrane locking mechanisms from the finite medium to a transverse, transient acoustic element equations of the structural Co shell, wave is analyzed. Circumferential Fourier plate, and beam elements. Employment. of full series solutions are obtained through the integration with the proposed formulatIon numerical integration of coupled ordinary eliminates also the zero energy modes problem, differential equations and convolution and!or softening effects, associated with the integrals. Numerical results are presented in use of the technique of reduced integration in the form of response histories, response Co plate and shell element applications. The snapshots, and iso-damage curves for incident formulation proposed is obtained through a waves of rectangular pressure profile. simple and cost effective scheme. (Edited Response solutions obtained with the first• author abstract) 52 Refs. order doubly asymptotic approximation are compared with their 'exact' counterparts. Briassoulis, Demetres (Agricultural Univ of Athens, (Edited author abstract) 25 Refs. Greece). Comput Methods Appl Meeh Eng v 72 n 3 Mar 1989 p 243-266. Geers, T.L. (Univ of Colorado, Boulder, CO, USA); Yen, C.-L. AMD Symp SeT ASME Appl Meek Div v 94 036970 Analysis of Simply-Supported 1988 Large-Scale Interaction Problems, Presented Laminated Circular Cylindrical Shell at the Winter Annual Meeting of the ASME, Roofs. An elasticity solution has been Chicago, IL, USA, Nov 27-Dec 21988. p 13-45. presented for the analysis of a laminated circular cylindrical shell roof with simply. supported edges, and the displacements and ANALYSIS stresses of the solution are expressed in terms of infinite series. A solution according to the 036967 Analysis of the Stress-Strain State of classical shell theory (CST) is also developed. a Nonshallow-Orthotropic Cylindrical Shell Computations are made for various ratios of with an Elliptical Hole. The method of midsurface radii to thicknesses and the results expansion in a series in a small parameter has of the CST have been examined in the light of been applied successfully in analyzing isotropic the elasticity solution results. (Author abstract)

362 Excerpts from The Ensineerins Index Annual 1989

Ren, J.G. (Changsha lnst of Technology, Hunan, coupled first order differential equations is China). Compos Struct v 11 n 4 1989 P 277 - 292. solved for each shell substructure using the Pade approximation for matrix 036971 Continuum-Based Stiffened exponentiation. The substructures are then Composite Shell Element for Geometrically joined by matching all of the displacement and Nonlinear Analysis. A continuum-based, force boundary variables. The strength of laminated, stiffened shell element is used to SSM from the substructure synthesis viewpoint investigate the static, geometrically nonlinear is demonstrated by analyzing several shell response of composite shells. The element is structures including a hermetic capsule and a developed from a three-dimensional continuum refrigeration compressor shell. In all element based on the incremental, total examples, finite element method (FEM) Lagrangian formulation. The Newton-Raphson predictions are used to support SSM results. method or modified Riks method is used to For the compressor shell, SSM results compare trace the nonlinear equilibrium path. A well with the limited experimental data. number of sample problems of un stiffened and (Edited author abstract) 58 Refs. stiffened shells are presented to show the Tavakoli, M.S. (Georgia lnst of Technology, accuracy of the present element and to Atlanta, GA, USA); Singh, R. ] Sound Vib v 130 n 1 investigate the nonlinear response of laminated Apr 8 1989 P 97 -123. composite plates and shells. (Author abstract) 28 Refs. 036974 Extending Life of LD Converter Liao, C.L. (Virginia Polytechnic lnst & State Univ, Vessel. At Kakogawa Works, all three LD Blacksburg, VA, USA); Reddy,J.N. AlAAJ v 27 n 1 converter vessels were renewed for 1987- Jan 1989p95-101. 1988 because of working limits caused by shell deformation. In renewing the vessels, an 036972 Accurate Rigid-Body Modes analytical method was developed to quantify Representation for a Nonlinear Curved deformation of the barrel shell, which is the Thin-Shell Element. For certain highly curved dominant factor in vessel life. Based on the shells, such as bellows, the formulation of a analytical results, an air jet cooling technique curved-shell finite element with curvilinear and steel plate were developed and applied to displacement components may fail to properly the new vessels. As a result, it is now possible model some rigid body modes, even with to extend the life of vessels using a high ratio either the explicit inclusion of rigid-body terms of MgO-C bricks. (Author abstract) 4 Refs. In or the use of high-order displacement Japanese. functions. It is suggested in this paper that the Kita, Ryuji; Nishikawa, Tsuneaki; Okazaki, rigid-body modes can be properly included if Toshiyuki; Mine, Takao; Nishijima, Akifumi; the Cartesian displacement components are Kawasaki, Hiroya. R&D Res Dev Kobe Steel Ltd v 39 used. A 48-degree-of-freedom (DOF) curved n 1 Jan 1989 p 61-64. thin-shell element is formulated, and both the curvilinear and the Cartesian forms are used 036975 Review on the Analysis of for this investigation. Examples of the Laminated Shells. Laminated shell structures nonlinear analyses of a bellows shell and a are increasingly being used in chemical, spherical cap are given to demonstrate the mechanical, marine and aerospace advantage of using the Cartesian formulation. applications. A significant amount of research Curved elements may also suffer from has been conducted in the past on studying membrane locking, which is caused by the the structural response of these structures. A inability of an element to bend without review of various investigations on the analysis stretching. (Edited author abstract) 53 Refs. of these shells is given here. Specifically, this Yang, T.Y. (Purdue Univ, West Lafayette, IN, review deals with the development of various USA); Kapania, Rakesh K.; Saigal, Sunil. AlAAJ v 27 theories for modeling the thick laminated n 2 Feb 1989 p 211-218. shells, including shear effects; analytical studies, development of various finite elements 036973 Eigensolutions of Joined/Hermetic to model these shells, including applications to Shell Structures Using the State Space tire modeling; buckling and post-buckling Method. A substructure synthesis method analysis of perfect and imperfect laminated based on state space mathematics is proposed shells; and vibration and dynamic response for the eigensolution of axisymmetric joined/ analysis of various laminated shells. (Author hermetic thin shell structures. In the state abstract) 157 Refs. space method (SSM), a system of eight Kapania, R.K. (Virginia Polytechnic Inst & State

363 Excerpts from The Enaineerina Index Annual 1989

Univ, Blacksburg, VA, USA). J Pressure Vessel in the form of elastically or rigidly fastened Tecknol Trans ASME v III n 2 May 1989 p 88-96. plates and shallow shells. We employ Timoshenko's theory of shells. The desired 036976 Geometrically Nonlinear Analysis of unknown functions are represented as series in Shallow Shells Using Higher Order Finite the coordinate functions, each of which may Elements. Based on K. Marguerre's shallow not necessarily satisfy the specified attachment shell theory, a family of higher-order finite conditions for the structure. We employ elements each consisting of 17 - 25 nodes and solution methods for problems of plates and with separate in-plane and bending shells based on the use of complete functionals displacement variables has been developed for and of the contour equation of the domain in the geometrically nonlinear analysis of shallow setting up the approximating function. (Edited shells subjected to lateral loads. A step• author abstract) 11 Refs. iteration Newton-Raphson scheme has been Serazutdinov, M.N. Meek Solids v 23 n 3 1988 P adopted in solving the final system of 136-14l. recurrent nonlinear equations. Several numerical examples, including a spherical cap 036979 Analysis of Simply Supported and a square shallow shell with surface in Orthotropic Cylindrical Shells Subject to double sine curves, are presented to Lateral Impact Loads. An analytic solution is demonstrate the versatility and convenience of given for the problem of simply-supported the use of higher-order elements in modelling orthotropic cylindrical shells subject to impact shallow shells and also the sufficient accuracy loading. The closed-form solution has not of the predictions made by the present been obtained previously. The analysis is based formulation in the context of geometrically on an expansion of the loads, displacement nonlinear analysis. (Author abstract) 13 Refs. and rotations in a double Fourier series which Chan, H.C. (Univ of Hong Kong, Hong Kong); satisfies the end boundary conditions of Chung, W.C. Comput Struct v 31 n 3 1989 P simple support. Each expansion is assumed to 329-338. be separable into a function of time and a function of position. By neglecting in-plane and rotary inertia the problem becomes a 036977 Nonlinear Analysis of Shell second order ordinary differential equation in Structures by Degenerated Isoparametric time for the Fourier coefficients of the radial Shell Element. Two rotation strategies deflection. For a given loading impulse the termed the finite rotation method and the solution can be found by invoking the mixed rotation method are proposed to described the rotation of the shell normal and convolution integral. The results show that four rotation strategies in the literature are for impact by a heavy mass, the solution is equivalent to that obtained by an approximate reviewed. The rotation variables of the finite procedure of neglecting the mass of the shell, rotation method are chosen to be the incremental rotations with respect to the Xl which leads to a simple single degree of freedom analysis. For problems of impact by and X2 axes of a moving coordinate system rigidly tied to the shell. Both the rotation smaller masses, the higher response frequencies of the cylinder become important. increments between two successive increments The impact duration, peak force, and peak and the rotation corrections between two deflection relative to the quasi-static response. successive iterations are used as the (Edited author abstract) 17 Refs. incremental rotations. The previous covergent stress is employed to update the geometric Christoforou, A.P. (Univ of Utah, Salt Lake City, stiffness matrix and its performance is UT, USA); Swanson, S.R. ASME Aerosp Div Publ AD compared with that of the standard geometric v 13 Recent Advances in the Macro- and Micro• stiffness matrix update method. (Edited Mechanics of Composite Materials Structures, author abstract) 20 Refs. Presented at the Winter Annual Meeting of the American Society of Mechanical Engineers, Hsiao, Kuo-Mo (Nat! Chiao Tung Univ, Hsinchu, Chicago, IL, USA, Nov 27-Dec 21988. Publ by Taiwan); Chen, Yeh-Ren. Comput Struct v 31 n 3 American Soc of Mechanical Engineers (ASME), 1989 P 427 -438. New York, NY, USA, 1988 P 77-84.

036978 On the Analysis of Shallow Shells ANISOTROPY with Complex Contours. In this paper, we offer a variational method and some solutions 036980 Membrane Theory for Anisotropic for the problem of determining the stress• Laminated Shells of Revolution. The strain state of thin-walled structural elements present paper discusses the derivation and

364 Excerpts from The Enoineerino Index Annual J 989 application of the membrane theory equations spherical shells with simply supported governing the small deformation of laminated, boundaries. Numerical examples show that anisotropic, elastic shells of revolution. The the approach developed in the paper is equations are derived by use of the Hellinger• effective. (Author abstract) 9 Refs. Reissner variational principle in conjunction Ye, Jianqiao (Hefei Poly technical Univ, Hefei, Jpn). with the asymptotic expansion technique. Appl Math Modelling v 12 n 5 Oct 1988 p 467 - 470. They are then used to analyze specific shells under loadings of practical interest. (Author 036984 Optimal Design of a Cylindrical abstract) 3 Refs. Shell Under Overall Bending with Axial Logan, D.L. (Rose-Hulman lnst of Technology, Force. The problem of optimal design of a Terre Haute, IN, USA); Widera, G.E.O. J Pressure cylindrical shell loaded by bending moment Vessel Technol Trans ASME viii n 2 May 1989 p Mo and axial force N is presented. As a 130-135. criterion of optimality we assume the minimum value of the cross-sectional area for BENDING given values of external loadings. In the general case the shape of the central line of 036981 Plane Bending of a Long Cylindrical the profile and thickness of the wall of a shell Shell During Simple Thermomechanical are used as design variables. The constraints Deformation. This paper examines dynamic are connected with strength and with local processes in a long cylindrical shell-tube in the stability of the wall of a shell. The concept of case of simple thermomechanical deformation a 'shell of uniform stability' is applied and two under the influence of mechanical and different types of profiles of uniform stability thermal loads. Since the shell is long it is are looked for, namely the uniform stability regarded as a beam with corrected stiffness in profile with variable thickness and a constant bending, tension, and torsion. Governing thickness profile of uniform stability. (Author relations for small strains and finite abstract) 9 Refs. displacements are obtained on the basis of Kruzelecki, Jacek (Technical Univ, Cracow, Pol). thermodynamic relations from the nonlinear Bull Pol Acad Sci Tech Sci v 36 n 3-4 1988 P theory of elasticity. Nonlinear equations of 141-150. motion for the plane bending of such a shell-tube are obtained. 10 Refs. 036985 Theory and Numerics of Thin Kayuk, Ya. F. (Acad of Sciences of the Ukrainian Elastic Shells with Finite Rotations. A SSR, Kiev, USSR); KiI'chinskaya, G.A. Sov Appl bending theory for thin shells undergoing Mech v 24 n 2 Aug 1988 P 157-162. finite rotations is presented, and its associated finite element model is described. The 036982 Monomial Test: Testing the Flexural kinematic assumption is based on a Reissner• Behavior of the Degenerated Shell Mindlin theory. The work-conjugate stress Element. Shear locking of the degenerated resultants and stress couples are integrals of shell element is a result of the development of the Biot stress tensor. This tensor is invariant spurious shear strain by the element, when with respect to rigid body motions and subjected to high order Kirchhoff therefore appropriate for the formulation of displacement fields. The shear locking constitutive equations. The rotations are phenomenon is analyzed in this paper using described by using Eulerian angles. The finite an analytical test. The effects of the element descretization of arbitrary shells is integration scheme, order of the element, performed using isoparametric elements. The order of the modeled Kirchhoff field and the advantage of the proposed shell formulation element distortion are analyzed explicitly and and its numerical model is shown by quantitatively for the four-node, eight-node application to different non-linear plate and and nine-node degenerated shell elements. shell problems. Finite rotations can be (Author abstract) 23 Refs. calculated within one load increment. Thus Briassoulis, Demetres (Univ of Illinois, the step size of the load increment is only Urbana-Champaign, IL, USA). Comput Struct v 29 n limited by the local convergence behaviour of 6 1988 P 949-958. Newton's method or the appearance of stability phenomena. (Edited author abstract) 036983 New Approach for the Bending 27 Refs. Problem of Shallow Shell by the Boundary Gruttmann, F. (Univ Hannover, Hanover, West Element Method. A very simple method is Ger); Stein, E.; Wriggers, P. Ing Arch v 59 n 1 1989 suggested in this paper to analyze shallow P 54-67.

365 Excerpts from The Ennineerinn Index Annual 1989

BLASTING they are prone to buckling, and to such an extent that this is often the dominant 036986 Using Geometry to Improve consideration in their design. Early attempts Survivability. The research effort has to determine buckling pressures were concentrated on developing the Hyperbolic unsatisfactory. Although initial geometric Paraboloid (HYP AR) structural system for distortions are now recognised as the cause of buried shelters. Individual HYPAR panels• this, little comprehensive work has been hyperbolic paraboloidal curved surfaces-are conducted on doubly-curved shells, joined together in varying geometries to form particularly hemispheres, subjected to external protective shelters. The HYP AR structure has pressure and having asymmetric initial shapes. several advantages: reduced wall thickness; This paper presents the results of such a reduced materials and field labor costs; and study, in two parts. In Part I, the background reduced field erection time. The HYP AR research on doubly-curved shells is briefly panel uses its geometry and construction reviewed. The kinematic, equilibrium and materials to efficiently dissipate the energy constitutive equations used in the work are released by the detonation of conventional stated. The adopted numerical procedure weapons. The HYPAR panel is a composite which can generate static or dynamic solutions consisting of an outer layer of fiberglass• is described along with the results of reinforced asphalt, a middle layer of steel• convergence studies. (Edited author abstract) reinforced portland cement concrete, and an 44 Refs. inner layer of polyester fabric. The reinforced Shao, W.J. (Ministry of Communications, Shanghai, asphalt and concrete layers are structural ones China); Frieze, P.A. Thin-Walled Struet v 8 n 2 1989 which help dissipate blast energy through p99-118. deformation and cracking, while the polyester fabric provides a spall protection. 4 Refs. 036989 Simple Buckling Problems Within Burkett, William R. Mil Eng v 80 n 523 Aug 1988 the Shell Theory of Rubber-like P 450-452. Materials. In an earlier paper, the authors have formulated a fairly general theory of BUCKLING finite strains deformation of shells of an incompressible hyperelastic material. The 036987 Influence of Initial Imperfections basic equations of this theory were derived, on the Buckling of Orthotropic Truncated from 3-D finite elasticity under the single Spherical and Conical Shells. The influence assumption: material fibers initially normal to of small geometric imperfections in the shape the shell reference surface remain straight in of the middle surface on the non• the process of an isochronic deformation. axisymmetric buckling and post-critical Consequently the resulting 2-D model of the behavior of thin elastic shallow orthotropic shell incorporates effects due to transverse truncated spherical shells under uniform shear and transverse normal deformations as external pressure truncated conical shells well as higher order effects accommodated in under axial compression is studied by the dependency of the 2-D strain energy Lyapunov-Schmidt method. Cases of buckling function on the gradient of strain measures. are investigated when the least bifurcation In this note they present some further results load of non-axisymmetric buckling of a for the buckling of initially straight rods corresponding ideal shell is a double under axial end forces. They illustrate eigenvalue of the linearized problem and limitations of particular variants of the general either two unstable eigenmodes or one stable shell theory. 5 Refs. and one unstable eigenmode interact. It is Makowski, J. (Ruhr-Univ, Bochum, West Ger); obtained that small imperfections lower the Stumpf, H. Z Angew Math Meeh v 68 n 6 1988 P value of the upper critical load of an ideal 251-252. shell. Examples are presented of special non-axisymmetric shell buckling cases. 14 Refs. 036990 Zwei Varianten der Bermus, I.M. (Rostov Univ, USSR); Srubshchik, Schalenbeulrechnung im Elastoplastischen L.S. Sov Appl Meeh v 24 n 2 Aug 1988 P 149 -156. Bereich. [Two Different Methods'for Shell Buckling Calculation in the Elastic-Plastic 036988 Static and Dynamic Numerical Region]. The material behavior in the Analysis Studies of Hemispheres and elastic-plastic region depends on the fact Spherical Caps. Part I. Background and whether the concerned point is loaded or Theory. Shell-like structures are prevalent in unloaded. For buckling calculations one nature. However, because of their slenderness transfers generally the criterion for loading or

366 Excerpts from The Enoineerino Index Annual 1989

unloading from the prebuckling mode of the 036993 Beulversuche an Duennwandigen ideal shell. But there are no ideal shells. Every Fluessigkeitsgefuellten Schalen. [Buckling real shell has initial imperfections, and real Tests on Thin-Walled Fluid-Filled events start with the growing of one buckle. Shells.]. This paper deals with the problem of Hence it corresponds better to the reality to the buckling of thin walled cylindrical tanks transfer the criterion for loading or unloading under the action of a fluid filling and an axial from the buckling mode. A calculation load. In addition, the partial removal of the procedure of that kind is presented; its bottom membrane of such tanks is studied. The applications demonstrated by numerical experimental results obtained can be used for examples. (Edited author abstract) In German. the testing of mathematical models. 3 Refs. In Esslinger, Maria (DFVLR, Braunschweig, West Ger); German. Poblotzki, Gert. Forschungsber Dtsch Forsch Rammerstorfer, Franz Georg (Technische Univ Versuchsanst Luft Raumfahrt DFVLR n FB 88-26 Wien, Vienna, Austria); Billinger, Wolfgang; Fischer, 1988pl-49. Franz Dieter. DIAl Desterr Ing Archit l v 133 n 8 Aug 1988 P 430-43l. 036991 On Buckling of Ellipsoidal Cups Under Internal Pressure. A method for the 036994 Numerical Analysis of Diamond calculation of the critical load for a semi• Buckles. Both linear and nonlinear analyses ellipsoidal shell with a stiffening rib at the edge are performed on the buckling of a cylindrical is presented. The external and internal shell under axial compression. Among the buckling energy of the shell is described. The post buckling shapes of the cylindrical shell, a Rayleigh quotient is used as the static buckling number of diamond modes are found to be criterion, assuming the deflection function to possible. The analysis is compared to those depend on four shape parameters. Some conducted by A. Maewall and W. Nachbar, numerical examples are presented showing the M.A. Crisfield, and Y. Yoshida et al. influence of the rib stiffness and the shell Agreement is established in conceiving the dimensions on the critical pressure value. deformed shape with circumferential number (Author abstract) 6 Refs. of 14 as the stable postbuckling mode of the cylindrical shell. The transition from the Magnucki, K. (Technical Univ of Poznan, Poznan, axisymmetric mode to a diamond mode of Pol); Wegner, T.; Szye, W. Ing Arch v 58 n 5 1988 P collapse is shown to be an instantaneous 339-342. process triggered in the proximity of the critical state by a small perturbation of the 036992 Schalenbeulen: Von der DASt• load increment. (Edited author abstract) 17 Richtlinie 013 zur DIN 18800, Tell 4. [Shell Refs. Buckling: From DASt Guideline 013 to DIN Liu, Wing Kam (Northwestern Univ, Evanston, IL, 18800. Part 4]. Following a review of the USA); Lam, Dennis. Finite Elem Anal Des v 4 n 4 buckling safety proof for shells according to Feb 1989 p 291-302. DASt guideline 013 which must be kept in two stages, the method of representation in DIN 036995 Theoretical and Experimental Study 18800, Part 4 is explained in detail. It is shown of a Curved Strip Compressed by a Flat that the large rlt dependency of the reduction Plate. The quasi-static loading of a curved factor ex which exists for the axially compressed strip compressed by a flat, rigid plate is cylinder can be suppressed for the building considered, with particular reference to large material steel. In this way, it is possible to deformations and the ensuing buckling conduct the buckling safety proof in a single behavior. Experiments were performed on stage for all shells examined analogous to the curved strips of constant width but of different buckling of columns. Only two basic buckling thickness. The strips were initially deformed curves, for K) 'normal' and K2 for 'very' to a fixed radius of curvature and stress imperfection-sensitive shells, are sufficient. relieved before pinning the ends. The span With the aid of detailed investigations, it is was held constant at about 305 mm. The shown that the K2 curve may possibly be raised deformation characteristics have been slightly. As compared with dimensioning analyzed using an incremental finite element methods according to DASt guideline 013 used technique. Particular attention has been paid in the past, economic benefits would be to modeling the situation when a node possible using this method. (Author abstract) contacts the plate and the condition for 14 Refs. In German. separation of the strip from the plate. The Bornscheuer, Friedrich Wilhelm. Bautechnik v 65 n predicted loads and deformation modes 10 Oct 1988 p 325-33l. agreed well with experimental results from

367 Excerpts from The Engineering Index Annual 1989

tests on steel and aluminum specimens. uniform external pressure is analysed using (Edited author abstract) 9 Refs. the spline finite strip method. A Total Iseki, H. (McMaster Univ, Hamilton, Ont, Can); Lagrangian formulation on the displacement Sowerby, R.; Bhattacharyya, D.; Gatt, P. J Appl Meeh dependent pressure load in the orthogonal Trans ASME v 56 n 1 Mar 1989 p 96-104. curvilinear reference frame is derived. An improvement for the arc-length iteration 036996 Buckling of Edge Damaged, method is presented. The postbuckling Cylindrical Composite Shells. The stability equilibrium path and the contour map of of thin composite layered anisotropic equal radial deflection computed an~ in good cylindrical shells under axial compression is agreement with the experimental and considered for the case of nonuniform analytical results reported in Esslinger, M. and boundary conditions. Such conditions are Geier, B., Postbuckling Behaviour of employed to model the situation where there Structures, Springer-Verlag, Wien, New York, is edge damage to the shell. The influence of 1975. (Author abstract) 14 Refs. weakening or a crack at an edge on the Cheung, Y.K. (Univ of Hong Kong, Hong Kong); critical buckling load of a variety of single and Zhu, D.S. Thin-Walled Struet v 7 n 3-4 1989 P multilayered shells is investigated. Results 239-256. indicate that isotropic shells exhibit a rather sudden steep reduction in the critical buckling 036999 Non-probabilistic Models of load for relatively small edge damage. Uncertainty in the Nonlinear Buckling of However, some anisotropic composite shells Shells with General Imperfections: may not be so sensitive and, in contrast, only Theoretical Estimates of the Knockdown a gradual reduction may be brought about by Factor. A nonprobabilistic, set-theoretical the edge damage. The degree of sensitivity to treatment of the buckling of shells with edge damage appears to be dependent, in uncertain initial geometrical imperfections is some complex fashion, on the various presented. The minimum buckling load is geometric and physical shell parameters. determined as a function of the parameters (Author abstract) 8 Refs. which describe the (general infinite) range of Sabag, M. (Technion - Israel Inst of Technology, possible initial imperfection profiles of the Haifa, Isr); Stavsky, Y.; Greenberg, J.B. J Appl Meeh shell. The central finding of this paper is a Trans ASME v 56 n 1 Mar 1989 p 121-126. theoretical estimate of the knockdown factor as a function of the characteristics of the 036997 Bifurcation Buckling of Circular uncertainty in the initial imperfections. Two Cylindrical Shells Under Uniform External classes of set-theoretical models are employed. Pressure. This paper presents asymptotic The first class represents the range of solutions for the eigenvalue problems of variation of the most significant N Fourier buckling under uniform external pressure of a coefficients by an ellipsoidal set in N• circular cylindrical shell having an arbitrary dimensional Euclidean space. The minimum combination of the boundary conditions for buckling load is then explicitly evaluated in the simply supported, clamped, and free ends. terms of the shape of the ellipsoid. (Edited A simple formula for the buckling pressure is author abstract) 29 Refs. derived, which is shown to be accurate Ben-Haim, Yakov (Technion - Israel Inst of enough for engineering purposes by Technology, Haifa, Isr); Elishakoff, Isaac. J Appl comparison with available results. The Meeh Trans ASME v 56 n 2 Jun 1989 p 403 -41 o. eigenvalues calculated for all possible combinations of the boundary conditions show 037000 Post-buckling Behavior and that the buckling pressures are affected Imperfection Sensitivity of Spherical Shells significantly by the presence of a free end as Based on Nonlinear Elastic Stability well as axial constraint at a supported end. Theory. Using the nonlinear elastic stability (Author abstract) 17 Refs. theory and its applications to shells, we have Koga, Tatsuzo (Univ of Tsukuba, Tsukuba, Jpn); investigated the post-buckling behavior and Morimatsu, Shigeyuki. AIAA J v 27 n 2 Feb 1989 p imperfection sensitivity of spherical shells with 242-248. amplitude modulation. For this purpose, we assume that the buckling modes have the 036998 Postbuckling Analysis of Circular form of Legendre polynomials with an Cylindrical Shells Under External exponential function as a modulating factor. Pressure. The postbuckling behavior of We use a numerical analysis technique with circular cylindrical shells of finite length under high precision. The amplitudes of the post-

368 Excerpts from The Enoineerino Index Annual 1989 buckling modes and the critical loading design procedure is suggested. (Edited author factors of the spherical shell with various abstract) 15 Refs. In German. imperfection modes are presented. (Edited Knoedel, Peter (Univ Karlsruhe, Karlsruhe, West author abstract) 10 Refs. Ger); Maierhoefer, Dieter. Stahlbau v 58 n 3 Mar Fan, Q.S. (Tsinghan Univ, Beijing, China). 1989 p 81-86. Thin-Walled Struct v 8 n I 1989 P 1-18. 037004 Experimental Investigation on the 037001 Postbuckling Analysis of Shells by Dynamic Buckling of a Cylindrical Shell Spline Finite Strip Method. The postbuckling Due to Seismic Excitation. (lst Report: analysis of shells is studied by the spline finite Plastic Buckling Due to Bending Load). The strip method. The selection of higher order fundamental characteristics of plastic dynamic terms in the incremental variational principle buckling of a thin cylindrical shell due to is discussed. An improvement on the arc• seismic excitation, where bending load was length iteration method is presented. The predominant, were clarified experimentally. examples all demonstrated the versatility and The relationship between seismic response accuracy of the present method. The displacement acceleration, strain of cylindrical computed results for a circular cylindrical shell model and input acceleration was shell under axial compression correlate very investigated. The dynamic buckling load was well with the experiment results. (Author compared with that for static buckling, and abstract) 15 Refs. the differences between them were discussed Zhu, D.S. (Univ of Hong Kong, Hong Kong); as well as the threshold for postbuckling. Cheung, Y.K. Comput Struct v 31 n 3 1989 P (Author abstract) 6 Refs. In Japanese. 357-364. Fujita, Katsuhisa; Ito, Tomohiro; Wada, Hiroshi. Nippon Kikai Gakkai Ronbunshu C Hen v 55 n 515 037002 Transverse Shear Effects in Stability Jul 1989 P 1634-1637. Problems of Laminated Shallow Shells. This paper presents the analysis of the accuracy of 037005 New Solution for Vessel Liner the classical shell theory in the prediction of Buckling Analysis. The thermally buckling loads of laminated shallow shells of constrained and perfectly confined cylindrical revolution loaded by external pressure or shell finds its critical buckling load in infinity. axially compressed. The shells studied are Disturbances such as shape or support circular cylinders, barrels, inverse barrels and imperfections are required to yield finite spherical sections. In each case the boundary critical buckling loads. Based on a conservative conditions are simple supports. (Author imperfection model, the new solution allows abstract) 7 Refs. the quantification of the influence of Muc, Aleksander (Univ of Liverpool, Liverpool, imperfections on buckling stress. As a large Engl). Compos Struct v 12 n 3 1989 P 171-180. deflection solution, it follows the load displacement path under increasing prestress 037003 Zur Stabilitaet von ZyIindern Vnter up to neutral equilibrium. Thus, the Axiallast und Randmomenten. [Stability of occurrence of subcritical limit load conditions Cylindrical Shells V nder Axial Loads and due to non-linear bending can be determined. Edge Moments]. Existing methods of (Edited author abstract) 12 Refs. determining the critical axial loads of Tschiersch, R.T. (Thyssen Henrichshuette AG, cylindrical shells take into account only the Hattingen, West Ger); Huessler, W. ASME Pressure membrane stress state. However, parts of the Vessels Piping Div Publ PVP v 139 Design and shell structures are loaded by additional edge Analysis of Piping, Pressure Vessels and moments. These result from external forces, Components, 1988, Presented at the 1988 ASME from the edge conditions themselves or from Pressure Vessels and Piping Conference, Pittsburgh, the deviation of the membrane forces due to PA, USA,Jun 19-23 1988. Publ by American Soc a break in the generatrix. This paper reports of Mechanical Engineers (ASME), New York, NY, on a study, which investigated the influence of USA, 1988 P 133-138. edge moments on the nonlinear bifurcation loads of axially compressed cylinders. Edge 037006 Static Buckling of the Shells of moments are shown to reduce the bifurcation Revolution Due to the Asymmetric load irrespective of the length of the cylinder. Loading. Finite element buckling analysis The results obtained were approximated by program of the shells of revolution under an easy to handle formulas. After some remarks asymmetric loading was developed. In this on the imperfection sensitivity, a practical program, the buckling mode for asymmetric

369 Excerpts from The Eneineerine Index Annual 1989

loading is presented as a summation of free COMPOSITE vibration modes. The program was verified by comparing with the test and the theoretical 037009 Finite Deformations of Thin results. (Author abstract) 7 Refs. Anisotropic and Composite Shells and Chiba, T. (Ishikawajima-Harima Heavy Industries Defining Relations. Defining relations for Co, Yokohama, Jpn); Sugino, H.; Mieda, T.; composite shells formed by superposition of Yoshida, M.; Ohya, H.; Kobayashi, N. ASME layers with specified structure of the Pressure Vessels Piping Div Publ PVP v 150 reinforcement were derived using Green's Application of Modal Analysis to Extreme Loads, strain formula and the Cauchy stress tensor as Presented at the 1988 ASME Pressure Vessels and a starting point. An asymptotic analysis was Piping Conference, Pittsburgh, P A, USA, Jun carried out for revealing the kind of functions 19 - 23 1988. Publ by American Soc of Mechanical contained in the defining relations, with Engineers (ASME), New York, NY, USA, 1988 P plastic and creep deformations taken into 1-7. account. A system of experiments was suggested for finding these functions on the assumption that with finite deformations the 037007 Nonlinear Investigations of material is nonlinearly elastic. The cause of a Composite Shells by Finite Element deviation of the obtained results from given Method. For investigations of structures computational conditions was suggested as a consisting of layered fiber composite shells a noticeable manifestation of inelastic properties. special shell finite element has been developed Evaluations for glass reinforced plastics are and applied to some illustrative problems. presented. 12 Refs. The element's features are: geometrically nonlinear formulation; arbitrary set-up of the Teregulov, I.G. (Kazan Inst of Civil Engineering, composite (i.e. symmetric or non-symmetric USSR). Meek Compos Mater v 23 n 4 Jan 1988 p stacking sequences with different layer 453-458. materials); material non-Iinearities in terms of stiffness degradation due to layer cracking; 037010 Stress-strain State of a Composite thermal loading. Due to the FE-formation Shell with Circular Slit. A shell of revolution used, buckling analyses can be conducted by with an infinitely thin slit cut on the solving accompanying eigenvalue problems. circumference was subjected under (Author abstract) 19 Refs. mathematical simulation to a distributed load. A system of coordinates was introduced to Dominger, K. (Vienna Technical Univ, Vienna, describe the state of stress and strain of the Austria); Rammerstorfer, F.G. ASME Pet Div Publ shell. The elasticity relations were derived and PD v 24 Composite Material Technology 1989, the state of stress and strain of each shell was Twelfth Annual Energy-Sources Technology determined and reduced to the solution of a Conference and Exhibition, Houston, TX, USA, system of equations. The boundary-value Jan 22-25 1989. Publ by American Soc of problem of the slit was solved with the network Mechanical Engineers (ASME), New York, NY, method. A calculation algorithm system was USA, 1988 P 117-125. recommended which was based on Godunov's orthogonal matching method. It was found 037008 Buckling Design of Vierendeel from analyzing the curves that a Recticular Shells. Double layer reticular shell circumferential slit with axisymmetric load structures carry very little transverse shear, induces an inhomogeneous state of stress and thus, it may be appropriate to substitute the strain. 3 Refs. inter-layer diagonal members with 'space' Gerasimenko, P.V. (All-Union Extramural members perpendicular to the middle surface. Polytechnic Inst, Moscow, USSR); Preobrazhenskii, In this paper the shear stiffness of double I.N. Meek Compos Mater v 23 n 4 Jan 1988 p layer grids without diagonals is presented and 459-462. used to calculate the design buckling load for domes built with this geometry. (Author 037011 Allowing for Binder Stiffness and abstract) 8 Refs. Reinforcement Extensibility in Designing a Castano, Francisco (Unistrut Space Frame Systems, Shell of Revolution Made of a Composite Canton, MI, USA). Proe Sess Relat Steel StTUet StTUet Material. A method for determining the Congr Proceedings of the Sessions Related to Steel configuration and equilibrium state of a shell Structures at Structures Congress '89, San under the effects of internal pressure with Francisco, CA, USA, May 1-5 1989. Publ by allowance for the extensibility of the fibers and ASCE, New York, NY, USA, 1989 P 195-204. the elasticity of the threads was devised. The

370 Excerpts from The Enaineerina Index Annual 1989 boundary value problem for linearized coordinate axes of the shell. To expand the equations was solved by the method of initial possibility of the model for evaluating the parameters with the use of Godunov's stress-strain state at the microscopic level, the procedure for orthogonalization. Two cases order and number of resolvent equations are given: a shell with a movable head made by were independent of the number of layers as spiral winding wherein the initial form of the well as the ratio of the physico-geometric shell is designed as being equilibrium for a properties. In this paper, the model is recticular shell with a geodesic winding, and a generalized to the case of laminated shallow geodesic shell wound on a mandrel of the same shells made of anisotropic layers. The model profile for which the strains were calculated considers transverse shear and compression, under internal pressure and a compressive tangential and normal forces of inertia, and force applied to the head. The method makes geometric nonlinearity. Kinematic hypotheses it possible to determine the geometry of the are introduced to reduce the three• shell and its stress state. 6 Refs. dimensional problem to two dimensions. Two Biderman, V.L. (N.E. Bauman Moscow Higher examples illustrating the ability of the model Technical lnst, USSR); Mart'yanova, G.V.; Sorokin, to reflect the three-dimensional nature of the F.D. Meek Compos Mater v 23 n 5 Mar 1988 p stress-strain state of multilaminate plates and 579-585. shells are examined. 12 Refs. Prisazhnyuk, V.K. (Kiev Highway lnst, USSR); 037012 Optimization of Structures of Piskunov, V.G. Meek Compos Mater v 23 n 6 May Reinforced Cylindrical Shells Made of 1988 p 719-726. Composites. A method is given for selecting the parameters for the design optimization of 037014 Analysis of Thermoelastic Stresses reinforced cylindrical shells which satisfies the in Laminated Shells of Double Curvature. A system of restrictions and minimizes the target curvilinear coordinate system was used to function. The active physical restrictions construct a model describing the thermoelastic included general and local stability, the stresses in laminated shells of double strength of the material of the cloth of the curvature. It was assumed that the stresses shell, and the reinforcing set. The design and depended linearly on strains and temperature. technological restrictions imposed on the Near the edges of the outer layer the shell geometrical parameters of the shell were also element was regarded as two finite elements; taken into account. Two possible forms of the one element modeled the packet of inner loss of stability of the reinforced shells were layers and the second modeled the outer shell evaluated. Strength calculations of the cloth layer. The solution of the thermoelastic were based on a macromodel according to problem satisfied the condition of the which the load-carrying capacity of the entire minimum of potential energy of the shell. packet was exhausted when the limiting stress Shear stress distributions were determined. state was reached in at least one layer. An The method was applied to a stiff cylindrical algorithm was constructed for optimum design shell with a thin outer layer heated uniformly on the basis of heuristic combinatorial analysis. from within. The stresses determined on the It was shown that longitudinal-transverse edge of the outer layer were compared with reinforcement in respect of mass is 1.5-2.0 results of holographic measurements of strains times more effective than the unidirectional of a steel shell with a sheet made of carbon• longitudinal reinforcement. 4 Refs. fiber plastic stuck to it and were found to Tomashevskii, V.T. (Marshall A.A. Grechko Naval agreed qualitatively with the experimental Military Acad, Leningrad, USSR); Anufriev, A.P.; data. 4 Refs. Shalygin, V.N.; Yakovlev, V.S.; Kalimulin, R.l. Meek Bakulin, V.N. (S. Ordzhonikidze Moscow lnst, Compos Mater v 23 n 5 Mar 1988 p 603-607. USSR); Kaledin, V.O.; Rassokha, A.A. Meek Compos Mater v 23 n 6 May 1988 p 732-737. 037013 Model of Composite Shallow Shells and Plates for Solving Problems of Statics, 037015 Axisymmetric Divergence of Dynamics, and Contact Interaction. In an Ring-stiffened Composite Cylindrical Shells earlier paper, the authors constructed a Subject to Axial Compression. Static theory for the evaluation of the stress-strain aeroelastic instability of structures, which is state of composite structures for the case of also called divergence, represents an important laminated composite shallow shells and plates theoretical and practical problem. Divergence of orthotropic materials in which the principal of composite structures has been intensively directions of orthotropy coincided with the studied due to increasing utilization of

371 Excerpts from The Enaineerina Index Annual 1989 composite materials in the aerospace industry. three-layer plastic structures fabricated from In this paper, axisymmetric divergence of an ideally plastic material that obeys the Hill simply supported, internally ring-reinforced plasticity condition. We also compare designs composite shells is considered. The shell is obtained by the constant-dissipation method subject to an air flow, directed parallel to the and equal-strength designs; we demonstrate shell axis, and to static axial loading. The that equal-strength designs display a greater analytical conditions of divergence are volume of the supporting layers. For the obtained both for discrete ring stiffeners and sandwich shells considered here, equal• based on the smeared stiffeners technique. 4 strength designs are understood to mean Refs. those for which, at each meridian point, the Birman, Victor (Univ of New Orleans, New plasticity condition is realized as an equality in Orleans, LA, USA).] Appl Meek Trans ASME v 55 one of the supporting layers, and as a n 4 Dec 1988 p 984-985. nonstrict inequality in the other. (Edited author abstract) 16 Refs. 037016 Design of Composite Cylindrical Nemirovskii, Yu.V.; Shul'gin, A.V. Meek Solids v 23 Vessels for Fluid Loading. A theoretical n 51988 P 104-112. approach is presented to examine the problem of the fluid loading of a simply supported 037019 Finite-element Method in Problems Glass Reinforced Plastic (GRP) composite cylindrical pipe. The shell layup is composed of Nonline Deformation of Reinforced of specially orthotropic layers, the Shells of Arbitrary Shape. A method of calculation of reinforced shells of arbitrary arrangement of which may be nonsymmetrical shape is proposed. It applies the finite element through the wall thickness. The theory is method to problems of nonlinear deformation developed using Sanders' thin shell theory, of these shells and it is based on specification neglecting the effect of transverse shear. An example of the use of the method is given, of primary geometrical information regarding where the behavior of a horizontal pipe is the object. Such information can be provided examined when it is partially or totally filled by the radius vectors of the nodes of the with fluid. Three layups are examined, one of elements and the positions of the unit normal an isotropic construction using chopped vectors to the surface at these nodes. strand mat (CSM) and two of a laminated Differences in the geometry of the shells construction. (Author abstract) 5 Refs. under consideration are unimportant from the standpoint of algorithmization of the Banks, W.M. (Univ of Strathclyde, Glasgow, Scod); calculations, since the same node-by-node Tooth, A.S.; Wilson, P.M.] Pressure Vessel Teeknol information is required for calculations. A Trans ASME v III n 2 May 1989 p 102-108. universal approach can &pan an extensive class of calculation problems for reinforced shells 037017 Shear Deformable Theory of of arbitrary shape, operating in the large• Laminated Composite Shallow Shell-type displacement region. As an example the Panels and Their Response Analysis: II. problem of compression of a cylindrical panel Static Response. In the second part of this of rectangular shape is considered. The paper, by using the static counterparts of the method used allows the problem to be solved governing equations derived in Part I, the for arbitrary elastic displacements. static response of shallow composite shell-type panels subjected to a sinusoidal transverse Kuznetsov, V.V.; Soinikov, Yu.V. Meek Solids v 23 load is investigated. The numerical n 31988 P 129-135. applications, encompassing a large number of boundary conditions and various lamination 037020 Hygrothermal Effects on the schemes, allow one to obtain some conclusions Stability of a Cylindrical Composite Shell which are formulated in the paper. (Edited Panel. In this paper the finite element author abstract) 1 Ref. method is applied to study the problem of Khdeir, A.A. (Virginia Polytechnic lost & State moisture and temperature effects on the Univ, Blacksburg, VA, USA); Librescu, L.; stability of a general orthotropic cylindrical Frederick, D. Acta Meek v 77 n 1-2 Apr 1989 p composite shell panel subjected to axial or 1-12. in-plane shear loading. The element employed is a 9-node isoparametric shell element. Since 037018 Sandwich Shells of Absolute the hygrothermal effects on the elastic Minimum Volume. We consider a number of properties of the matrices and the fibers are new solutions of optimal design problems for very different, the degrading of the matrices

372 Excerpts from The Enaineerina Index Annual 1989

and the fibers are very different, the Mechanical Engineers (ASME), New York, NY, degrading of elastic moduli, the transverse USA, 1988 P 71-76. shear effect and the induced initial stress are all considered in the present study. Numerical 037022 Divergence Instability of Reinforced investigation shows that if the temperature Composite Cylindrical Shells. Divergence increase from 300 0 K to 422°K and the instability of a simply supported orthotropic moisture concentration is saturated, the composite shell reinforced in both axial and buckling load with both the degrading of circumferential directions is considered. The elastic moduli and transverse shear shell is subject to an axial static load and to an deformation considered is approximately 12% action of an outside supersonic gas flow in the lower than Snead/Papazoto's result where direction parallel to the shell axis. Two only the degrading of elastic moduli is variants of the solution considered in the considered. (Edited author abstract) 10 Refs. paper include discrete widely spaced stiffeners Lee, S.Y. (Nat! Cheng-Kung Univ, Tainan, and closely spaced stiffeners; the latter case Taiwan); Yen, W.J. ASME Aerosp Div Publ AD v 13 can be treated using a smeared stiffeners Recent Advances in the Macro- and Micro• technique. It is proven that divergence Mechanics of Composite Materials Structures, instability of shells treated by smeared Presented at the Winter Annual Meeting of the stiffeners technique can occur only if they are American Society of Mechanical Engineers, subject to axial compressive loads exceeding Chicago, IL, USA, Nov 27 - Dec 2 1988. Publ by the static buckling value. (Author abstract) 9 American Soc of Mechanical Engineers (AS ME), Refs. New York, NY, USA, 1988 P 21-31. Birman, V. (Univ of New Orleans, New Orleans, LA, USA). ASME Aerosp Div Publ AD v 13 Recent 037021 Delamination Effects on Composite Advances in the Macro- and Micro-Mechanics of Shells. An analytical investigation was Composite Materials Structures. Presented at the performed to study the effect of delamination Winter Annual Meeting of the American Society of on the response of cylindrical composite shells Mechanical Engineers, Chicago, IL, USA, Nov subjected to external loadings. It was of 27 - Dec 2 1988. Publ by American Soc of particular interest to determine the buckling Mechanical Engineers (ASME), New York, NY, load and the post-buckling behavior of USA, 1988 P 169-175. externally pressurized cylindrical composite shells containing delamination. An analytical 037023 Failure Prediction for Composite model was developed which consists of a Shells: Shear Deformable Finite Element structural analysis for calculating the global Formulation. Piecewise smooth stress-based deformations of the structures and a fracture failure criteria are implemented in a shear analysis for determining the delamination deformable finite element formulation. Both growth in the structures. A nonlinear finite plate and shell elements are utilized to element code based on the updated Lagrange represent thin to moderately thick laminated formulation was developed for the model. structures. Accurate stresses are obtained both Based on the results of calculations, it was in the plane of each ply as well as in the found that delamination can significantly through-the-thickness direction. Such stress effect the buckling load and response of information is essential in differentiating cylindrical composite shells subjected to between fiber, matrix and delamination externally pressurized loadings, depending failures. (Author abstract) 14 Refs. upon the initial length and location of the Engblom, JJ. (Texas A&M Univ, College Station, delamination, ply orientation and laminate TX, USA). ASME Pet Div Publ PD v 24 Composite curvature. The calculated strain energy Material Technology 1989, Twelfth Annual release rate at the crack tips indicates that Energy-Sources Technology Conference and delamination growth occurs at the wake of Exhibition, Houston, TX, USA, Jan 22 - 25 1989. buckling due to Mode II shear fracture. Publ by American Soc of Mechanical Engineers (Author abstract) 24 Refs. (ASME), New York, NY, USA, 1988 P 37-41. Chang, F.-K. (Stanford Univ, Stanford, CA, USA); Kutlu, Z. ASME Aerosp Div Publ AD v 13 Recent 037024 Computer-Aided Manufacturing of Advances in the Macro- and Micro-Mechanics of Filament-Wound Composite Shells. An Composite Materials Structures, Presented at the interactive CAM system developed for Winter Annual Meeting of the American Society of automated manufacturing of filament-wound Mechanical Engineers, Chicago, IL, USA, Nov axisymmetric shells is reported. 27 - Dec 2 1988. Publ by American Soc of Microprocessors are designed to drive motors

373 Excerpts from The Enoineerino Index Annual 1989 for multi-axes control of mandrel rotation, dihedral angles of n-frequency spherical and carriage and cross feeder translations, and eye ellipsoidal octahedral and icosahedral geodesic rotation. A personal computer system is used domes with or without truncation, for plotting as host and has software to initiate the orthographic and axonometric projections, microprocessors, to supervise the motions of and for tabulating the chord lengths and the rotating mandrel and of the robot-like dihedral angles for sawing the structural assembly of carriage, cross feeder, and eye. elements for construction. (Author abstract) 4 Operator interactive capability of the software Refs. make it possible to manually interrupt and Teter, W.D. (Univ of Delaware, Newark, DE, perform on-the-spot adjustment and reset. USA); Nicholls, R.L. Bull Int Assoc Shell Spat Struct The variety of filament-wound shells made by v 29-2 Aug 1988 P 47-53. this automated system is reported. (Edited author abstract) 12 Refs. 037027 Das System VWMESH zur Pao, Y.C. (Univ of Nebraska, Lincoln, NB, USA); Idealisierung von Tragstrukturen im Karamooz, S.; Spencer, B.E.; Keester, PJ. Comput CAE-Konzept. [VWMESH System for an Eng Proc Int Comput Eng Con! Exhib v 1 (of 2), Ideal Design of Supporting Structures in the Proceedings of the 1989 ASME International CAE Concept. Presentation of an Interactive Computers in Engineering Conference and Module for the Eiasto-Mechanical Ideal Exposition, Anheim, CA, USA, Jul 30-Aug 3 Design of Thin-walled Supporting 1989. Publ by American Soc of Mechanical Structures, Available for Instance in the Engineers (ASME), New York, NY, USA, 1989 P CAD Medium in Carbody Design, Aircraft 553-557. Construction, Mechanical Engineering or in the Shipbuilding Sector]. The development COMPUTER AIDED ANALYSIS of weight and cost optimized supporting structures requires an early safe statement on 037025 Strength Analysis Algorithm of the performance criteria of the component Discrete Stiffened Conic Shells. Computer which must be made available to the designer aided analysis algorithm is developed for the in the design phase by way of suitable stressed-strain state of circular conic shells of forecasting media. To this end the most irregular structure stiffened by stringers and important test results obtained by the frames under the effect of arbitrary loads application of modern simulation methods applied to the frames. The problem solution must be brought to the attention and desk of is obtained in the Fourier series using the the designer and must be made available for method of the matrix pass by means of the interpretation without passing the construction computer BESM-6-programmed algorithm. stage before. For the physical relationships Contrary to known algorithms of the method which can be forecast by means of the FEM of finite elements the suggested algorithm analysis idealizing networks are needed for does not need considerable expenditures of the original structure. (Edited author abstract) machine time and time for preparation of the 7 Refs. In German. initial data necessary for the calculation. A Sorgatz, Ulrich (RWTH, Aachen, West Ger); stressed state in the casting of the shell Deuter, Helmut. VDI Z v 131 n 3 Mar 1989 p 26-32. supported as a cantilever under the effect of tangential concentrated load, the effect of the 037028 Modeling of Plate and Shell shell taper angle and frame elasticity on this Structures with P-Version of the FEM. Finite state are investigated. The beam theory to element models for the analysis of plates and calculation of broad fuselage of planes under shells, based on the concept of hp-extension the effect of local forces is shown to be are presented. A methodology for the control nonapplicable. (Author abstract) 4 Refs. In and analysis of the error of the finite element Russian. solution is developed. Numerical results Kabanov, V.V.; Levitskaya, T.E. Probl Prochn n 7 obtained using the proposed methodology are Jul 1988 P 97 -100. given. (Author abstract) 16 Refs. Sahrmann, Glenn J. (Sverdrup Technology Inc, COMPUTER AIDED DESIGN Middleburg Heights, OH, USA). Comput Util Stroct Eng Computer Utilization in Structural 037026 Geodesign: A Computer Program Engineering, Proceedings of the sessions at for Geodesic Dome Geometries. A computer Structures Congress '89, San Francisco, CA, USA, algorithm is described for obtaining the May 1-51989. Publ by ASCE, New York, NY, coordinates of vertices, chord factors, and USA, 1989 p 277-285.

374 Excerpts from The Engineering Index Annual 1989

CONCRETE of their curving shapes and the apparent structural derivation of their forms. Every 037029 Effect of Support Movement on fabric structure includes compression elements, Hyperbolic Paraboloid Shells. For many just as most shells include both tension and hyperbolic paraboloid shells, the horizontal bending elements. Furthermore, both forms, reaction is provided by horizontal ties between through the introduction of stiffening the supports. It is shown that the horizontal elements, have enormous range for subjective movement of the supports associated with the manipulations of form to achieve desired elongation of these ties will alter sufficiently sculptural effects. Both fabric structures and the stresses in the shell membrane and the concrete shells rely on an interplay of tension axial forces and moments in the supporting and compression, and much of their aesthetic edge members that these movements must be success is a function of the skill with which this considered in the analysis. The effect of the interplay is handled by the designer. outward support movement for gable-type HP Huntington, Craig G. (Huntington Design Associates shells supported on four corners is to reduce Inc, Oakland, CA, USA). Proc Sess Relat Steel Struct the arching effect across the diagonal supports, Struct Congr Proceedings of the Sessions Related to resulting in behavior that resembles more Steel Structures at Structures Congress '89, San closely that predicted by membrane theory. Francisco, CA, USA, May 1-5 1989. Publ by ASCE, When such shells are placed to form continuous New York, NY, USA, 1989 P 706-715. structures, the effect of the outward support movement causes the portion of shell in the CONTROL vicinity of the first rows of interior supports to behave as inverted umbrella HP shells. 037032 Optimal Control of a Pre-stressed, (Author abstract) 8 Refs. Orthotropic Thin Cylindrical Shell Subjected Simmonds, Sidney H. (Univ of Alberta, Edmonton, to a Constant Pressure at Its Interior Alberta, Can). J Struct Eng v 115 n 1 Jan 1989 p Wall. The open loop optimal control of a 19-31. pre-stressed, orthotropic thin cylindrical shell subjected to a constant pressure at its interior 037030 Collapse Load Analysis of wall relative to a given index of performance Prestressed Concrete Surface Structures with is investigated. The optimal control function Unbonded Tendons by the Finite Element is obtained by using a calculus of variations Method. The basis of the theoretical approach on the basis of a thin-shell theory. investigation is a formulation of the principle The response and the hoop stress of virtual work which is suitable for (circumferential stress) of the controlled shell incremental-iterative analysis of PC surface are presented in graphical form and structures by the finite element method (FEM). compared with those of an uncontrolled shell. It contains the expression for the virtual work Moreover, it is observed that the time of forces exerted by the tendons on the required for the effectiveness of the control remaining part of the surface structure, treated increases as the orthotropy coefficient as a free body. Geometric nonlinearity is increases. An interesting aspect of the considered on the basis of W.T. Koiter's shell investigation is the singularity of the mass theory of small displacements and moderately matrix. (Author abstract) 6 Refs. large rotations. Physical nonlinearity is taken Sadigh-Esfandiari, R. (California State Univ, Long into account by means of appropriate Beach, CA, USA); Sloss, J.M.; Bruch, J.C. Jr. J constitutive equations for intact and cracked Sound Vib v 125 n 1 Aug 221988 P 123-130. concrete, respectively, reinforcing steel and prestressing steel. The numerical investigation CORROSION consists of collapse load analysis of a PC slab with unbonded tendons. It demonstrates the 037033 Corrosion Wear of a Thick-Walled usefulness of the theoretical concept. (Edited Cylindrical Shell of a Nonlinearly Elastic author abstract) 17 Refs. Material. During service the elements of Hofstetter, Guenter (Technical Univ of Vienna, many structures are subject to the combined Vienna, Austria); Mang, Herbert A. Finite Elem Anal action of loads, temperatures, and corrosive Des v 5 n 2Jul1989 p 141-165. working media. In this work the case in which the corrosive medium does not influence the 037031 Manipulation of Shell and Fabric mechanical properties of the material but does Structure Form. Fabric structures and cause corrosion failure of the surface layers concrete shells are readily compared because was considered. The depth of corrosion wear

375 Excerpts from The Engineering Index Annual 1989

was used as the parameter characterizing the orthotropic plastic theory by Hill are process of corrosion failure of the surface. employed in the creep range. The creep Algorithms were constructed and used to strains are related to the stresses by McVetty's develop a program in FORTRAN-4 language equation with a thermal effect multiplier by with the use of which a series of problems was Arrhenius. The basic differential equations solved. The method makes it possible to quite derived are numerically solved by a finite effectively evaluate the behavior of shells of difference method. As a numerical example, nonlinearly elastic materials in a corrosive the creep of a two-layered, anisotropic medium with the relationship of the properties cylindrical shell composed of mild steel and of the material and the corrosion rate to stainless steel subjected to uniform internal temperature. 4 Refs. pressure is analyzed. (Edited author abstract) Ovchinnikov, I.G. (Saratov Polytechnic lnst, USSR); 14 Refs. In Japanese. Garbuz, E. V. Sov Mater Sci v 23 n 4 Jan 1988 p Takezono, Shigeo; Migita, Kohji. Nippon Kikai 405-408. Gakkai Ronbunshu A Hen v 54 n 507 Nov 1988 p 2019-2027. 037034 Optimization of the Life and Cost of Cylindrical Shells Subject to Mechanical and DEFECTS Chemical Failure. The purpose of this work is to create mathematical models of 037036 Plates and Shells with Crack-like optimization of cylindrical shells for general Flaws. The formulation of new hierarchial cases in which the corrosion rate is a function finite elements for the analysis of laminated of stresses. A thin-walled cylindrical shell of plates and shells in the presence of flaws are specified radius and length and pivotsupported discussed. The performance of the elements is on the ends and compressed with an axial elevated with the help of a number of load was taken as the model structure. Two example problems and the results available in optimization problems were formulated. The the published literature. (Author abstract) 19 first, in which the corrosion rate was assumed Refs. as a linear function of the stress intensity, was written in the form of linear mathematical Basu, P.K. (Vanderbilt Univ, Nashville, TN, USA); programming. The second, in which the Ahmed, N.U.; Woo, K.S. Comput Vtil Struct Eng limitation in time was introduced, was Computer Utilization in Structural Engineering, formulated in the form of nonlinear Proceedings of the sessions at Structures Congress programming and accounted for both the '89, San Francisco, CA, USA, May 1-5 1989. Publ initial cost and expenditures made on the by ASCE, New York, NY, USA, 1989 P 286-295. structure at various times. Certain results of calculation using the two models are DEFLECTION considered. 5 Refs. Zelentsov, D.G. (Ferrous Metallurgy Mechanization 037037 Deflection and Snapping of Ring• Scientific & Production Union, Dnepropetrovsk, Loaded Spherical Caps. The axisymmetric USSR); Pochtman, Yu. M. Sov Mater Sci v 23 n 4 behavior of both shallow, and deep, ring• Jan 1988 p 400-412. loaded spherical caps, which are simply supported but otherwise unconstrained at CREEP their edges, is investigated using a large-strain shell theory based on a variational principle. 037035 Creep of Anisotropic Multi-Layered A numerical technique is used to extract the Moderately Thick Shells of Revolution. This solution. Particular attention is paid to highly paper describes an analytical formulation and nonlinear phenomena such as snapthrough, a numerical solution for creep problems of single and multiple snapback, and load-free anisotropic multilayered moderately thick everted states. (Author abstract) 9 Refs. shells of revolution with application to a Brodland, G. Wayne (Univ of Waterloo, Waterloo, cylindrical shell. The analytical formulation is Ont, Can); Cohen, H. J Appl Mech Trans ASME v developed by extending the Reissner-Naghdi 56 n 1 Mar 1989 p 127-132. theory for elastic shells with consideration given to the effect of shear deformation. For 037038 Elastic-Plastic Large Deflection the constitutive relation, Hooke's law for Analysis of Axisymmetric Shells. A new orthotropic materials is used in the elastic finite element formulation for elastic-plastic deformation, and equations based on the large deflection analysis of shells of revolution orthotropic creep theory derived from the is presented. The new formulation contains

376 Excerpts from The Ennineerinn Index Annual 1989

most of the best features of nonlinear finite orthotropic layers of variable thickness. The element analyses currently available in the shells were deformed by shock loads. This literature, together with some new numerical method is based on a Timoshenko-type schemes to improve the capability, accuracy geometric equation of nonlinear shell theory and speed of the computation. It is thoroughly and physical relations from the theory of verified using a variety of problems. The effective moduli. The boundary value problem doubly curved thin shell finite element used was solved by finite difference discretization has been widely applied to linear elastic stress of the Lagrange-D'Alembert variational analysis and linear stability analysis by the equation and by integrating over time. present authors and their co-workers. In place Equations of motion were obtained. of the widely-used relations of Donnell, Computations were performed on a BESM-6 Novozhilov or Sanders, more comprehensive computer. Experimental and numerical results nonlinear thin shell strain-displacement were compared. For the experiment the relations are used, which account for dynamic deformation of a viscoelastic shell of nonlinear strains caused by in-plane poly methyl methacrylate was used. The shells displacements. Unlike most previous nonlinear were formed by multiple-zone spiral winding axisymmetric shell formulations, in-plane of glass-plastic strip. It was found that by shearing is included throughout the treatment. varying the number of zones and layers in the For plastic analysis, a multi-layered approach winding, the stress level in the region of the is adopted employing the Prandtl-Reuss pole opening could be reduced. 15 Refs. normal flow rule with isotropic hardening or Abrosirnov, N.A. (Gorkii State Univ, Gorky, USSR). perfect plasticity. (Edited author abstract) Meeh Compos Mater v 23 n 4 Jan 1988 p 447 - 453. Teng, J.G. (Univ of Sydney, Sydney, Aust); Rotter, J.M. Comput Struet v 31 n 2 1989 P 211-233. 037041 Nonlinear Theory of the Central Bending of Three-Layer Shells with Defects 037039 Assumed Strain Finite Element in the Form of Sections of Bonding Model for Large Deflection Composite Failure. Thin three-layer shells with a Shells. A nine node finite element model has light-weight filler and having sections of been developed for analysis of geometrically bonding failure on one of the surfaces of non-linear laminated composite shells. The contact between the filler and an external formulation is based on the degenerate solid layer were theoretically examined. For the shell concept and utilizes a set of assumed case of central bending of such shells, a strain fields as well as assumed displacement. complex of nonlinear relations was Two different local orthogonal co-ordinate constructed which were used to formulate systems were used to maintain in variance of nonlinear problems concerning contact the element stiffness matrix. The formulation interaction of the external layers with the assumes strain and the determinant of the filler, with allowance for unilateral contact on Jacobian matrix to be linear in the thickness the sections of bonding failure. The direction. This allows analytical integration in Kirchhoff-Love hypotheses traditionally used the thickness direction regardless of ply in the theory of three-layer shells were layups. The formulation also allows the adopted to describe the mechanics of reference plane to be different from the shell deformation of the external layers. 11 Refs. midsurface. The results of numerical tests Pairnushin, V.N. (Kazan Aviation Inst, USSR). Sov demonstrate the validity and the effectiveness Appl Meeh v 23 n 11 May 1988 p 1038 -1 043. of the present approach. (Author abstract) 17 Refs. 037042 Approaches to Numerical Solution Yeorn, C.H. (Univ of Maryland, College Park, MD, of Linear and Nonlinear Boundary-value USA); Lee, S. W. Int J Numer Methods Eng v 28 n 8 Problems of the Theory of Layered Aug 1989 P 1749-1768. Anisotropic Shells. Certain approaches to the numerical solution of boundary-value DEFORMATION problems are presented, describing the stress-strain state of layered shells with 037040 Numerical Study of the isotropic and anisotropic layers of variable Axisymmetric Deformation of Composite thickness in the linear and geometrically Shells of Revolution Under Shock Loads. A nonlinear formulations on the basis of classical method was proposed of numerically solving and improved models for nonuniform force problems of transient deformation of and temperature interactions. The proposed composite shells composed of rigidly joined approaches to the numerical solution of the

377 Excerpts from The Engineering Index Annual 1989 static shell problems are realized by programs well-known shear locking that appears in some in FORTRAN and tested on many examples. finite element representations, were not Solutions of some problems based on the observed. However, in connection with discussed methods are demonstrated. 10 Refs. kinematically slightly supported boundaries, Grigorenko, Va. M. (Acad of Sciences of the such as corresponding to membrane theory, Ukranian SSR, Kiev, USSR). Sov Appl Meeh v 23 n oscillating solutions may occur. 21 Refs. 10 Apr 1988 p 923-927. Wimmer, H. (Univ of Innsbruck, Innsbruck, Austria). Aeta Meeh v 73 n 1-4 Aug 1988 P 163 -175. 037043 Deformation of a Spherical Shell Under Internal Loading by a Shock 037046 Betti's Theorem for Rotationally Generated by an Underwater Electrical Symmetric Infinitesimal Deformations Discharge. This article is devoted to a Superimposed on the Finite Deformation of theoretical and experimental study of the a Thin Shell of Revolution. It is intuitively nonsteady hydroelastic deformation of a thin clear that the tangent stiffness matrix for a spherical shell subjected to an underwater finitely deformed shell, treated as a two• electrical discharge at its center. The range of dimensional continuum, should be symmetric. application of model representation of the The governing differential equations for latter in the form of a point source and a continuing rotationally symmetric quasi-static source of finite dimensions with an ideally bending and extensional deformation of thin flexible boundary is determined. The test shell shells of revolution with no shear deformation was composed of two stamped hemispheres are employed to derive Betti's theorem from which were subsequently welded about their which symmetry of the tangent stiffness perimeters. 8 Refs. matrix follows, provided the pressure load is Saprykin, Yu. V. (Acad of Sciences of the Ukrainian conservative. (Author abstract) 9 Refs. SSR, Kiev, USSR); Tsurkin, V.N.; Shvets, I.S.; DaDeppo, D.A. (Univ of Arizona, Tuscon, AZ, Sholom, V.K. Sov Appl Meeh Oct 1988 p 392-396. USA); Keppel, W.J. Ind Math v 38 pt 1 1988 P 71-82. 037044 Stability of a Viscoelastic Shell of Double Curvature. In this paper, we consider 037047 FDM in Arbitrary Curvilinear the stability of a viscoelastic ellipsoidal shell. Co-ordinates-Formulation, Numerical We examine the behavior of the shell in Approach & Applications. The basic concept relation to the load, curvatures, and of automatization of operations in curvilinear eccentricity of the support ellipse. We co-ordinate systems are briefly presented and establish the conditions for 'snapping' of the applied to the analysis of large deformations of shell to occur, and for asymmetrical membrane shells by the FDM. Several equilibrium forms to appear and develop. 1 examples provide the basis for a comparison of Ref. this approach with other descriptions of Vorovich, 1.1.; Drobysheva, T.P. Meeh Solids v 22 n deformation. 23 Refs. 61987 P 174-178. Tworzydlo, Wlodzimierz, W. (Technical Univ of Krakow, Cracow, Pol). Intl Numer Methods Eng v 28 037045 Application of the Two-Dimensional n 2 Feb 1989 p 261-277. Hermitian Finite-Difference Method to Linear Shear Deformation Theory of Plates 037048 Consistent Linearization in Elasto• and Arbitrarily Curved Shells. In this paper Plastic Shell Analysis. The present paper is the linear shear deformation theory of thin directed towards elasto-plastic large shells formulated by Basar/Kratzig has been deformation analysis of thin shells based on the used to demonstrate a special kind of the concept of degenerated solids. The main Hermitian finite-difference method. The aspect of the paper is the derivation of an governing differential equation system efficient computational strategy placing established in an appropriate matrix form emphasis on consistent elasto-plastic tangent contains only first derivatives of the unknown moduli and stress integration with the radial tensor components. After transformation into return method under the restriction of 'zero an algebraic form by applying two• normal stress condition' in thickness direction. dimensional operators and solving the global The advantageous performance of the system, no further differentiation of the standard Newton iteration using a consistent unknown field functions is necessary. The tangent stiffness matrix is compared to the procedure shows fast convergence and, in classical scheme with an iteration matrix based general, numerical instabilities like the on the infinitesimal elasto-plastic constitutive

378 Excerpts from The Engineering Index Annual 1989

tensor. Several numerical examples also function method is used accurately to treat the demonstrate the effectiveness of the standard contact condition involving a finite amount of Newton iteration with respect to modified and sliding. Axisymmetric large deformations of quasi-Newton methods like BFGS and others. contacting spherical shells are analyzed, and it (Author abstract) 21 Refs. is shown that elastic unloading resulting from Ramm, E. (Univ of Stuttgart, Stuttgart, West Ger); the sliding definitely affects the crushing of Matzemiller, A. Eng Comput (Swansea Wales) v 5 n 4 one shell by another. The possibility of Dec 1988 p 289- 299. nonaxisymmetric bifurcation of deformation is examined on the basis of the J2-deformation 037049 Whole-Field Optical Examination of theory. (Author abstract) 10 Refs. Cylindrical Shell Deformation. An optical Kitagawa, Hiroshi (Osaka Univ, Suita, Jpn); Hiura, technique for the measurement of radial Seiji.]SME Int] Ser 1 v 32 n 2 Apr 1989 p 199-207. deformation in circular cylindrical shells is discussed. The technique is a modification and 037052 Determination of Shell improvement of an earlier method, using a Constructions Deformations with conical mirror of simple geometry to view a Application of Linear Transformation grating reflected from the inner surface of the Theory. In this paper concepts for shell. The new system allows more precise determining shell structure deformations are alignment of the components of the optical presented for the case of the surface of a system with the shell. Fringes obtained by tria pial ellipsoid. Observations by the spatial superposition as in the Ligtenberg moire incision method in a rectangular xyz method, or deviations of lines from a regular coordinate system are assumed. The method pattern in a photographic image provide a of determining the deformation components measure of the slope changes on the surface of in the points under examination in the the shell. Theoretical relations are presented t = T - To time interval is based on the for three grid orientations, at least two of principle of a minimum sum of the squares of which have to be used in conjunction to the (vx' vy ' v,) corrections. (Edited author determine the two components of slope. abstract) 8 Refs. In Russian. Illustrations for the use and accuracy of the Baran, P.1. (Kiev Engineering-Constructional lnst, technique are presented for two cases. (Edited Kiev, USSR); Przewlocki, Stefan. Zesz Nauk Politeeh author abstract) 8 Refs. Lodz Budownietwo n 39 1988 P 151-159. Krishnakumar, S. (Univ of Tasmania, Hobart, Aust); 037053 Experimental Study of Deformation Foster, C.G. ExpMeeh v 29 n 1 Mar 1989 p 16-22. of Thin Conical Shells During Penetration into Soil. The penetration of various solids 037050 New Method of Multisegment into deformable media has been previously Integration for the Nonlinear Analysis of considered. At the same time, insufficient Shells of Revolution. A new method of attention has been paid to deformation of thin multi segment integration has been developed shells in the process of penetration into soil. for solving boundary value problems of a This paper describes an experimental study of system of nonlinear ordinary differential deformation of thin-walled shells upon equations as encountered in the large indentation into soil; it determines the effect deflection analysis of the axisymmetric of the angle of taper, the shape of the tip, deformations of the shells of revolution. The and the manner of attachment of the method developed here involves much less concentrated mass to the shell structure on computational work than the multisegment the deformation process. The authors integration developed by Kainins and Lestingi. employed an experimental setup consisting of The new method has been applied to a number a pneumatic gun with a control panel for of problems to ascertain its soundness and regulating the delivery of compressed gas, a accuracy. (Edited author abstract) 28 Refs. target, and measurement and recording Uddin, Md. Wahhaj (Bangladesh Univ of equipment with an automatic control unit. Engineering & Technology, Dhaka, Bangladesh). Int The gun was capable of accelerating shells to J Pressure Vessels Piping v 38 n 1 1989 P 39-55. specified velocities. 5 Refs. Bakulin, V.N.; Ovcharov, P.N.; Potopakhin, V.A. 037051 Elastic-plastic Unstable Deformation Meeh Solids v 23 n 41988 P 183-186. of Shells in Contact (Case of a Spherical Shell). This paper deals with the numerical 037054 Deformation of Slender Shells with analysis of large elastic-plastic deformation of Openings. Cutouts of various shapes are shells in contact with each other. The penalty often made in shell structures for design

379 Excerpts from The Enaineerina Index Annual 1989

purposes or fabrication convenience. This 037057 Modelling of the Progressive paper describes a numeric method for solving Extensible Plastic Collapse of Thin-Walled a wide range of problems of the stressed• Shells. A theoretical model describing the strained state of shells with cutouts. Results of progressive extensible plastic collapse of some specific studies are reported. 21 Refs. thin-wall conical and cylindrical shells is Dmitriev, V.G.; Preobrazhenskii, I.N. Meek Solids v presented. The proposed theory enables the 23 n 1 1988 P 169-175. load-deflection curves during axial compression following the deformation history 037055 Dynamic Deformation of of the shell to be evaluated. The comparison Orthotropic Cylinders. The theory of thick of theoretical curves with experimental ones orthotropic shells is used here to analyze a shows a fair degree of accuracy. (Author cylinder subjected to dynamic loads. The abstract) 14 Refs. formulation includes shear deformation and Mamalis, A.G. (Natl Technical Univ of Athens, rotatory inertia effects similar to the Athens, Greece); Manolakos, D.E.; Viegelahn, G.L.; first-order, shear deformation, laminated plate johnson, W. Int] Meek Sei v 30 n 3-41988 Some theory. Dynamic line loads (along the Papers Presented at the International Symposium longitudinal direction) and patch loads are on Structural Failure, Second International considered. The time-dependent part of the Symposium on Structural Crashworthiness, load is a step pulse or a half sine wave. Cambridge, MA, USA,jun 6-81988 P 249-261. (Author abstract) 11 Refs. Cederbaum, G. (Virginia Polytechnic Inst & State Univ, Blacksburg, VA, USA); Heller, R.A. ASME DESIGN Pressure Vessels Piping Div Publ PVP v 146 Advances in Macro-Mechanics of Composite Material Vessels 037058 Design of Barrel Shells by the and Components, Presented at the 1988 ASME Strength Method. For shells and folded plates, Pressure Vessels and Piping Conference, Pittsburgh, the ACI Code (318-83), Section 19, permits PA, USA,jun 19-23 1988. Publ by American Soc the reinforcing to be selected by strength of Mechanical Engineers (ASME), New York, NY, design. The method of applying this to barrel USA, 1988 P 43-48. shells is not specified. Possible procedures and the results for an interior barrel of a multiple series of barrel shells is described and 037056 Large Elastic Deformation of Shear compared to other methods of selecting Deformable Shells of Revolution: Numerical reinforcing. (Author abstract) and Experimental Results. Through an Ketchum, Milo S. Stroet Eng Praet v 4 n 3-4 integrating matrix approach, a numerical 1987-1988 P 165-177. solution is obtained to the equations governing large elastic deformation of a clamped circular 037059 Formwork for Spiral Ramps at cylinder due to internal pressure. The shell Dolphins' Stadium. The problems presented equations include the effects of large strains, by forming spirals included: wider forms thickness changes, and transverse shear needed for the ramps' slabjoist system at deformation. The numerical solution is outer edge; forms needed to provide for compared to results from asymptotic analysis ramp's slope; after the first revolution, and experiments on rubber cylinders. A formwork had to be supported on the specialized Rivlin-Saunders strain energy structure below, and had to be designed to be density function is assumed for the rubber, removed readily from one section to another. with material constants determined from These problems were solved by assembling a tensile tests and deformed cylinder profiles at number of modules, each consisting of a beam a high inflation pressure. (Author abstract) 15 table section and its shoring. The shoring Refs. incorporated adjustable scaffold frames that Kempski, M.H. (Rochester Inst of Technology, could be lowered 6 to 8 inches to facilitate Rochester, NY, USA); Taber, L.A.; Su, Fong·Chin. stripping of concrete and repositioning of the Am Soe Meek Eng Pap Preprint-American Society module at another level. The article discusses: of Mechanical Engineers, Presented at the Winter forming the first 180 ° of ramp, the second Annual Meeting, Chicago, IL, USA, Nov 27-Dec 2 180 ° of ramp and the ramp beyond the first 1988. Publ by American Soc of Mechanical 360°. Engineers (ASME), New York, NY, USA, 1988 Kathe, Chris (Ceco Corp, jacksonville, FL, USA). WA/APM486. Coner Constr v 33 n 11 Nov 1988 4p.

380 Excerpts from The Enoineerino Index Annual 1989

037060 Pure Building. This paper outlines 037063 Nonuniqueness of Equilibrium the need for building integration in the States for Axisymmetric Elastic Shells in design of fabric structures by examining the Tension. The problem of non uniqueness of different necessary components and how they static axisymmetric solutions for a non• fit together. It provides examples of this linearity elastic cylindrical shell in which the integrated process that suggests its use in ends are pulled apart with a constant traction conventional construction. (Author abstract) while retaining the radii of its ends fixed is Goldsmith, Nicholas S. (FTL Associates, New York, studied. In the elastic case, we prove the NY, USA). Proe Sess Relat Steel Struet Struet Congr existence of buckled states and the possibility Proceedings of the Sessions Related to Steel of necking. In the hyperelastic case a global Structures at Structures Congress '89, San existence and nonuniqueness theorem is Francisco, CA, USA, May 1-5 1989. Publ by proved, via the energy criterion. (Author ASCE, New York, NY, USA, 1989 P 726-735. abstract) 19 Refs. Pastrone, Franco (Univ di Torino, Turin, Italy); Tonon, Maria Luisa. J Elast v 21 n 1 1989 P 43-59. ELASTICITY 037064 Nonlinear Analysis of Elastomeric 037061 Application of Generalized Ray Keyboard Domes. The large deflection of an Methods in Hydroelasticity Problems of elastomeric dome is studied using the finite Thin Shells of Noncanonical Shape. A element method. The material properties of substantial simplification in the solution of the elastomer are described by a hyperelastic hydroelasticity problems, for primarily shells model in order to capture the strain energy of noncanonical shape, can be utilization of stored in the dome during deformation. The generalized ray methods based on replacement nonlinear responses are determined by the of the wave equation by its equivalent modified Riks procedure. The calculated first-order vector differential equation, a load-deflection curve agrees well with generalized transport equation, and by the experimental results. In addition, a pressurized analysis of the wave fronts that occur during thick-walled spherical hyperelastic shell is shell interaction with the fluid. A further analyzed and the stress results obtained by the development of the method proposed earlier finite element method are in excellent to the case of nonstationary radiation agreement with the closed-form solutions. problems and to stationary problems is The results provide a better understanding of examined in this paper. The approach is the mechanical behavior of elastomeric apparently applicable for shells of arbitrary keyboard domes and demonstrate the shape, however its realization is shown in usefulness of the finite element method in axisymmetric and plane problems. 24 Refs. designing such structures. (Author abstract) 15 Refs. Podil'chuk, Yu. N. (Acad of Sciences of the Ukrainian SSR, Kiev, USSR); Rubtsov, Yu. K. Sov Lau, John H. (Hewlett-Packard Lab, Palo Alto, CA, Appl Meeh v 23 n 10 Apr 1988 p 981-988. USA); Jeans, Albert H. Am Soc Meeh Eng Pap Preprint-American Society of Mechanical Engineers, Presented at the Winter Annual Meeting, 037062 On Drilling Degrees of Chicago, IL, USA, Nov 27 - Dec 2 1988. Publ by Freedom. Variational principles employing American Soc of Mechanical Engineers (ASME), independent rotation fields are investigated. In New York, NY, USA, 1988 WA/EEP8 9. the two-dimensional case these lead to membrane elements with 'drilling degrees of ELASTOPLASTICITY freedom', of practical use in shell analysis. We argue that convenient interpolatory patterns 037065 Elastic-Plastic Analysis of a Radially require modifications of the classical Loaded Spherical Shell. An elastic-plastic variational framework. Several formulations analysis of a spherical loaded radially through are proposed and shown to be convergent for a rigid inclusion is performed. The sphere is displacement/rotation interpolations of all modeled as a shallow shell of infinite extent. orders. (Author abstract) 29 Refs. The Tresca yield condition is used to derive Hughes, Thomas J.R. (Inst for Computer Methods the elastic-plastic moment-curvature in Applied Mechanics & Engineering, Stanford, CA, relationship in a simple form. This is used to USA); Brezzi, F. Comput Methods Appl Meeh Eng v develop a computationally efficient solution 72 n 1 Jan 1989 p 105-12l. method. (Author abstract) 22 Refs.

381 Excerpts from The Engineering Index Annual 1989

Brooks, G.N. (Univ of Tennessee, Knoxville, TN, Radovinskii, A.L. Meeh Solids v 23 n 5 1988 P USA); Leung, C.-P. J Pressure Vessel Technol Trans 117-122. ASME v III n 1 Feb 1989 p 39-46. ENERGY DISSIPATION 037066 Elastojvisco-plastic Dynamic Response of Thin Shells of Revolution by 037068 Energy Dissipation in Braced Means of Overlay Model. The numerical Cylindrical Shells. This paper presents an analysis of the elasto/visco-plastic dynamic experimental and numerical investigation of response of axis ymmetricaI thin shells the energy dissipation characteristics of mild subjected to arbitrary loads is carried out by steel cylindrical shells subjected to large the elasto/visco-plastic overlay model which is deformations under line loadings acting able to express the Bauschinger effect and the parallel and perpendicular to the shells' strain rate dependence. Namely, Perzyna's longitudinal axes. The effects of diametrical equation is used for the constitutive relation bracing, cylindrical length and external of each layer of the overlay model, and as a loading orientation on the deformation whole, the Bauschinger effect and the patterns and energy dissipation capacities are influence of viscosity in plastic range of the described. The results are applied to the material are taken into account. The equations design of a new impact attenuation system of motion and the relations between the used in highway safety applications. (Author strains and displacements are derived by abstract) 9 Refs. extending the Sanders linear theory in elastic Carney III, J.F. (Vanderbilt Univ, Nashville, TN, shells. The numerical method selected for this USA); Pothen, S. Int J Meeh Sci v. 30 n 3 -4 1988 problem is a method using finite difference in Some Papers Presented at the International both space and time. (Edited author abstract) Symposium on Structural Failure, Second 16 Refs. In Japanese. International Symposium on Structural Tao, Katsumi; Takezono, Shigeo; Ohtsubo, Kazumi; Crashworthiness, Cambridge, MA, USA, Jun 6-8 Mochidone, Hiroyuki; Matsuoka, Hironobu. Nippon 1988 P 203-216 Kikai Gakkai Ronbunshu A Hen v 55 n 513 May 1989 p 1145-1152. FAILURE

ELECTROMAGNETIC FIELD EFFECTS 037069 Influence of Geometry on Limit States of Elastic-Plastic Toroidal Shells 037067 Elastic Conducting Shells in Under Pressure with Bending. A study of Alternating Electromagnetic the limit states of elastic-plastic toroidal shells Fields. Problems of excitation of elastic under combined bending and pressure is vibrations of shells by variable electromagnetic presented. Generally, two different modes of fields are considered. For problems of this failure have been observed, however, the type, we give the equations in vector form, the possibility of their existence depends on the corresponding initial and boundary conditions, value of pipe factor. It is shown that the and the limits of applicability of the equations, appearance of the determined limit state is and we provide a description of the general also strongly connected with the elastic technique for solving them. For the carrying capacity of the torus and in this way electrodynamic part of the problem, we give with the position of hoop stresses peak. The an expression for the total-power functional, numerical results explain, in detail, the and we formulate the orthogonality conditions discussed problem. (Edited author abstract) 11 for the eigensolutions of the corresponding Refs. equations; for problems involving shells in Muc, Aleksander (Technical Univ of Cracow, specified harmonic fields, we write out the Cracow, Pol). Thin-Walled Struet v 7 n 3-4 1989 P expansion formula for the magnetic potential 197-212. of the eddy currents in eigensolutions. As an example, we consider the problem of relative FRACTURE rotation of a thin-walled elastic sphere and a constant oblique magnetic field, considered in 037070 Local Stresses and Strains in Axially the rigid-shell approximation in some earlier Cracked Cylindrical Shells. A perturbation papers; we also obtain formulas for solution is obtained for the local stress-strain determining the magnetic pressure on the fields in an axially cracked cylindrical shell. sphere when a constant magnetic field is The tenth-order differential equations are used applied. (Edited author abstract) 6 Refs. that take into account the transverse shear

382 Excerpts from The Engineering Index Annual 1989 deformation. The perturbation of a curvature problem of maintaining monolithic character parameter, A., is employed. The stress intensity throughout production. Optimal hardening factors for finite size cylindrical shells subjected regimes were assessed for cylinders made of to bending and internal pressure are evaluated. fiberglass based on the VM-I fiber and binder Sufficient accuracy can be obtained without EDT-I0 or binder EKR. To establish the using fine mesh sizes in regions near the crack causes of the differences in the test results the tip. Also analyzed are the influence of cylinder variations in the physicomechanical properties diameter and shearing stiffness on bulging. of the solid polymers EDTI0 and EKR as (Edited author abstract) 7 Refs. functions of temperature were investigated. Liu, C.T. (Acad Sinica, Beijing, China); Wu, X.J. The optimization problem was solved Theor Appl Fraet Meeh v 11 n 1 Apr 1989 p 51 - 58. numerically. 10 Refs. Turusov, R. A. (Acad of Sciences of the USSR, 037071 Finite Element Analysis of a Moscow, USSR); Korotkov, V.N.; Rogozinskii, A.K.; Circumferentially Cracked Cylindrical Shell Kuperman, A.M.; Sulyaeva, Z.P.; Garanin, V.V.; Loaded in Torsion. Finite element methods Rozenberg, B.A. Meeh Compos Mater v 23 n 6 May are used to evaluate all possible fracture modes 1988 p 773-777. at the tip of a circumferential crack in an isotropic cylindrical shell subjected to torsion. MANUFACTURE The finite element results are compared with shallow-shell theory data for cylinders with 037073 On the Determination of the different geometries. The results indicate that Redrawing Ratio in the Redrawing of there is good agreement between the Cylindrical Shells with a Numerical membrane stress intensity factors calculated Simulation (2nd Report, on the from finite element displacements at the crack Determination of the Redrawing Ratio by tip and the factors found using shallow-shell the Reduction of the Maximum Deep theory for small crack lengths. For longer Drawing Force). A determination method for cracks, disagreement between these two the redrawing ratios has been proposed by approaches is very pronounced. In particular, analyzing the redrawing process of cylindrical the bending stress intensity factors from the shells from flat circular blanks using the finite element analysis are significantly greater elementary theory of plasticity. These than the corresponding values determined redrawing ratios were calculated using the from the shallow-shell theory. It is observed criterion based on the reduction of the that the out-of-plane, antisymmetric maximum deep drawing forces. These deformation near the crack produces mixed theoretical results on the variations of the mode fracture with crack opening and tearing redrawing ratios with the profile radius, the displacements. (Author abstract) 14 Refs. blank thickness, the frictional force, the Kumosa, M. (Univ of Cambridge, Cambridge, Engl); blankholder load and the strain-hardening Hull, D. Eng Fraet Meeh v 32 n 1 1989 P 123 -136. exponent are presented using a developed computer program aimed at rationalizing, HEAT TREATMENT planning and simulating the redrawing process. It is shown that the maximum deep 037072 Technological Monolithic Character drawing forces decreased at about 10-40% of Shells Formed from Polymeric comparing the predicted drawing force with Composition Materials. Solution of the the usual drawing force. This is based on the problem of maintaining a monolithic character experience of many years standing and skilled throughout production requires the labor. (Author abstract) 13 Refs. In Japanese. development of such a heat-treatment regime Iseki, Hideo; Murota, Tadao; Katoh, Kazunori. that would make it possible to obtain Nippon Kikai Gakkai Ronbunshu C Hen v 54 n 505 monolithic thick-wall wound articles formed Sep 1989 p 2249-2256. from reinforced plastics. The heat-treatment process includes two stages: hardening of the 037074 Reduction of the Metal Volume in initially liquid polymer-binder in the Pressed Conical Shells. A reduction in the composition of the structure and cooling of the metal volume in pressed axisymmetric shells of already hard polymeric composite. In this narrowing form (high-pressure containers, paper, an attempt was made to demonstrate transition elements, fairings etc.) can be the need for conducting detailed investigations achieved by improving the uniformity of of the mechanical phenomena in the complex thickness of the components being produced. hardening process for the final solution of the An improvement in the uniformity of

383 Excerpts from The Engineering Index Annual 1989

thickness of pressed axisymmetric shells of variation of redrawing ratio with profile narrowing form is attained by combining radius, blank thickness, frictional force, compression and drawing operations while blankholder load and strain-hardening producing such shells. A technology of exponent are presented using a developed multi-stage pressing, in which the concluding computer program aimed at rationalizing, drawing operations have been replaced by planning and simulating the redrawing compression of the bottom region of the process. It is shown that the maximum non• blank, has been developed for manufacture of attainment value decreased to about 20-70% axisymmetric shells with a large relative compared to those values of other height. 2 Refs. optimization criteria. (Author abstract) 16 Maslov, V.D.; Popov, I.P.; Gostev, A.1. Sov Eng Res Refs. In Japanese. v 8 n 1 1988 P 59-61. Iseki, Hideo; Sowerby, Robert. Nippon Kikai Gakkai Ronbunshu C Hen v 54 n 508 Dec 1988 p 3115-3121. 037075 On the Determination of the Redrawing Ratio in the Redrawing of MATHEMA TICAL MODELS Cylindrical Shells with a Numerical Simulation (3rd Report, on the 037077 Elastic-Plastic Ring-Loaded Determination of the Redrawing Ratio by Cylindrical Shells. The elastic plastic solution the Reduction of the Maximum Deep for an infinitely long cylindrical shell with an Drawing Energy). A determination method axisymmetric ring load is presented. Except for redrawing ratios has been proposed by for the material nonlinearity, the standard analyzing the redrawing process of cylindrical assumptions of small deflection shell theory shells from flat circular blanks using an were made. Because the principal directions elementary theory of plasticity. These are known for the axisymmetric problem, the redrawing ratios were calculated using a Tresca yield condition was used. This made it criterion based on the reduction of the possible to obtain closed-form expressions for maximum deep drawing energy. Variation of the elastic-plastic, moment-curvature relations, redrawing ratio with profile radius, blank greatly simplifying the computational task. thickness, frictional force, blankholder load The actual stress distribution through the and strain-hardening exponent were obtained thickness was used, making these relations using a developed computer program aimed exact. Yielding was contained near the load. at rationalizing, planning and simulating the Thus, for the analysis the cylinder was divided redrawing process. It is shown that the along its axis into elastic-plastic and purely maximum deep drawing energy decreased elastic regions. Solutions were obtained for about 10-40%, comparing the predicted each region which were then matched at their drawing energy by the usual determination intersection to give the complete solution. All method for the redrawing ratios. (Author results are given in dimensionless form so that abstract) 14 Refs. In Japanese. they may be applied to any shell. (Author Iseki, Hideo; Sowerby, Robert; Katoh, Kazunori. abstract) 12 Refs. Nippon Kikai Gakkai Ronbunshu C Hen v 54 n 508 Brooks, Gregory N. (Univ of Tennessee, Knoxville, Dec 1988 p 3106-3114. TN, USA).] Appl Meeh Trans ASME v 55 n 4 Dec 1988 p 761-766. 037076 On the Determination of the Redrawing Ratio in the Redrawing of 037078 Mechanics and Finite Elements of Cylindrical Shells with a Numerical Shells. This article begins with a brief review Simulation (4th report, on the Determination of the foundations: The classical theory of of the Redrawing Ratio by the Minimax Love is described with attention to the Optimization of Compromise underlying hypothesis and consequent Programming). A determination method for limitations. A more general theory is described the redrawing ratios has been proposed by which removes the constraints of Love; the analyzing the redrawing process of cylindrical inclusion of transverse strains admits simpler shells from flat circular blanks using the finite elements, accommodates the thick shell elementary theory of plasticity, and by via layers and even a transition to the three• applying multi-objective optimization theory. dimensional approximation. The concept of These redrawing ratios were calculated using the finite element is reviewed in the context of the minimax optimization of a compromise the discrete approximation of shells. Specific solution of multi-objective optimization attention is given to those problems which are theory. These theoretical results on the peculiar to shells: The predominant roles of

384 Excerpts from The En8ineerin8 Index Annual 1989

flexural and extensional deformations, the Hampton, V A, USA); Lester, H.C.; Abler, S.B. J lesser role of transverse shear, can lead to Vib Acoust Stress Reliab Des v III n 3 Jul 1989 P excessive stiffness ('locking'). Origins and 337-342. procedures are described to circumvent these problems. (Edited author abstract) 147 Refs. Wempner, Gerald (Georgia Inst of Technology, NONDESTRUCTIVE EXAMINATION Atlanta, GA, USA). Appl Meek Rev v 42 n 5 May 1989 p 129-142. 037081 Non Contacting Testing and NDT for Composite Shells. There is, today, a NOISE ABATEMENT strong need for reliable large-field ways of inspecting for the initial quality of composite 037079 Statistical Theory of Internal structures and for monitoring, over long Soundproofing in Cylindrical Shells. In a times, the continued integrity of such number of cases of practical interest, an structures. This paper introduces two new interesting question is about the capability of methods which, when used in combination, thin-walled shells of localizing wave energy has strong promise of meeting this need. The close to the radiator encased in this shell, i.e., first, called Spectral Density Analysis is a is separated by it from the environment. This purely optical method for full field phenomenon represents the concept of measurement of surface displacements. The internal soundproofing (isolation). The paper second is a fiber-optic laser based method to concludes that as the case of soundproofing of generate and detect ultrasonic waves for a shell from the external field (enclosure), the interrogating the interior of structures. It is following physical phenomena are important: called Thermal Acousto Photonic NDE. 1. Increase of soundproofing effectiveness is (Author abstract) 5 Refs. nonmonotonous with respect to the frequency. Burger, C.P. (Texas A&M Univ, College Station, 2. Dips (notches) in the spectral characteristic TX, USA). ASME Pressure Vessels Piping Div Publ of soundproofing are due to resonant PVP v 146 Advances in Macro-Mechanics of phenomena in the shell and in air volume Composite Material Vessels and Components, within the shell. 3. The experimental analysis Presented at the 1988 ASME Pressure Vessels and of the internal soundproofing of shells (using Piping Conference, Pittsburgh, PA, USA, Jun standard measuring techniques) does not 19-23 1988. Publ by American Soc of Mechanical reveal these dips (notches) in soundproofing Engineers (ASME), New York, NY, USA, 1988 P due to averaging in the octave frequency 167-171. bands. 4 Refs. Guzhas, D.R. Vib Eng v 3 n 1 1989 P 21- 26. PLASTICITY

037080 Evaluation of Active Noise Control 037082 Numerical-Analytical Solution of in a Cylindrical Shell. This paper examines the Thermoplasticity Problem for Locally the physical mechanisms governing the use of Heated Shallow Shells. We construct a active noise control in an extended volume of numerical-analytic solution of the a cylindrical shell. Measured data were thermoplasticity problem for locally heated compared with computed results from a shallow shells. The solution is obtained by previously derived analytical model based on using the method of integral equations and infinite shell theory. For both the analytical the self-correcting method of successive model and experiment, the radiation of loadings. As an example, we investigate the external monopoles is coupled to the internal thermally stressed state in plates heated by acoustic field through the radial displacement normal-circular heat sources. In the case of of the thin, elastic, cylindrical shell. An active unilateral heating of a plate by normal-circular noise control system was implemented inside heat sources, we estimate the accuracy of our the cylinder using a fixed array of discrete solution. We consider the problem of monopole sources, all of which lie in the plane optimization of the heating parameters of a of the exterior noise sources. Good agreement plate with the aim of bringing the residual between measurement and prediction was compressive stresses into a specified region of obtained for both internal pressure response favorable values (from the standpoint of and overall noise reduction. (Edited author strength). (Author abstract) 10 Refs. abstract) 6 Refs. Maksimovich, V.N.; Khomlyak, L.V. Meek Solids v Silcox, R.J. (NASA Langley Research Cent, 23 n 51988 P 123-129.

385 Excerpts from The Engineering Index Annual 1989

PLASTICS APPLICATIONS PRESSURE EFFECTS

037083 Use of Semimomentless Theory to 037085 Improved Asymptotic Early-Time Design Multiply Closed Cylindrical Shells of Response Formulae for Submerged Elastic a Reinforced Plastic. Multiply closed, Shells Impinged Upon by an Incident convex, thin-walled cylindrical shells of Pressure Pulse. The early-time solutions for arbitrary cross section are widely used in this class of problems have often been different types of power plants. obtained by the use of integral transform Semimomentless theory was used in this paper techniques and the method of steepest to account for the effect of any distributed or descents to asymptotically evaluate the inverse concentrated loads if they were discontinuous transform integrals. These steepest descent along the shell and was illustrated using a solutions overestimated the elastic restoring composite shell as an example. A onceclosed force of the shell for the early time period in cylindrical shell of rectangular cross section which the shell response is of practical was examined. The shell was secured in interest. The accuracy of the early-time cantilever fashion and loaded by a transverse solution is improved by a correction of this force distributed uniformly over the length. elastic restoring force term. 13 Refs. After minimizing the potential energy Huang, H. (US Naval Surface Warfare Cent, Silver functional, a system of resolvent equations was Spring, MD, USA). Am Soe Meeh Eng Pap Preprint obtained, and the calculations were performed - American Society of Mechanical Engineers, for an orthotropic material with given Houston, TX, USA, Jan 22-251989. Publ by stiffness characteristics. The structure of the American Soc of Mechanical Engineers (ASME), material was assumed to be constant for each New York, NY, USA, 1989 OCNll 5p. panel used in the shell. 3 Refs. Dudchenko, A.A. (S. Ordzhonikidze Moscow SOUND INSULATION Aviation Inst, Moscow, USSR). Meeh Compos Mater v 23 n 4 Jan 1988 p 437 -443. 037086 Soundproof Characteristics of Sandwich Cylindrical Shells with a Honeycomb Core Partially Exposed in Free Field. An analysis is presented for the sound• 037084 Experimental Study of Coefficients proof characteristics of sandwich cylindrical of Variation of Strength Characteristics of shells with honeycomb core excited by axially Glass-Fiber-Reinforced Plastic Shells under propagating internal plane acoustic waves. The Internal Shock Loading. Variation shell is exposed in a free field by the length of coefficient estimates were obtained of the I, however is otherwise covered with infinitely limit load and limit strain on cylindrical long rigid cylindrical walls. To simplify the glass-fiber-reinforced plastic shells under shell equations, it is assumed that the core impulsive loading. The test objects were free material resists only transverse shear forces cylindrical glass-fiber-reinforced plastic shells and that the facing resist only bending into which steel 20 reinforcing shells were moments. The sound transmission loss of the inserted. The glassplastic shells were made by shell wall, TL, is derived and calculated the method of 'wet' winding of the fabric and numerically for various values of the physical impregnated with binder EDT-IO. Loading parameters involved. (Author abstract) 20 was accomplished by exploding a spherical Refs. In Japanese. charge in the center of the shell. Estimates of Chonan, Seiji. Nippon Kikai Gakkai Ronbunshu CHen the mathematical expectation and the v 54 n 508 Dec 1988 p 2883-2889. standard deviation were calculated by the method of functional probabilities and STABILITY statistical modeling. It was found that under extreme shock loads, glass-plastic shells have 037087 Determination of Critical Parameters higher strength than under static loading, of Momentary External Pressure for a according to the limit strain criterion. 10 Refs. Spherical Shell with Initial De8ection. A Vorontsova, O.S.; Syrunin, M.A.; Fedorenko, A.G.; solution is presented for the problem of the Khomutinin, Yu.V.; Tsypkin, V.I.; Bilyk, N.A.; dynamic loss of stability of a spherical shell Ivanov, A.G. Meeh Compos Mater v 23 n 4 Jan 1988 subjected to momentary external pressure. The p 443-447. shell, reinforced in two directions, is regarded

386 Excerpts from The Enoineerino Index Annual 1989

as being structurally orthotropic. The critical considered. The linear stability problem and value of compressive forces in the radial the deformation of the shell under large sections of the shell are determined within the deflections with the construction of the 'load• framework of a linear formulation of the deflection' graphs is investigated. 2 Refs. problem, with the use of analytical criteria of Samol'yanov, 1.1. (L'vov Polytechnic Inst, USSR). dynamic instability, for linear and parabolic Sov Appl Meeh Oct 1988 p 353-357. laws of change in the compressive forces over time. 3 Refs. 037091 Stability of a Multilayer Cylindrical Amiro, I. Va. (Acad of Sciences of the Ukrainian Shell in Interlayer Pressure. The problem of SSR, Kiev, USSR). Sov Appl Meeh v 23 n 10 Apr 1988 the stability of a cylindrical shell or circular p 903-907. ring with one-side connection with the surrounding elastic or absolutely rigid space 037088 Stability of Shells of Revolution of has been studied in a number of investigations. Fiber Composites with Initial Cracks in the In solving this problem for thin shells it is Microstructure. A method of calculating the possible to neglect the variation of the shell stability and initial postcritical behavior of geometry as a result of subcritical behavior, shells of revolution of composite materials with and also changes in the area of contact with variable mechanical characteristics dependent the surrounding space during the loss of on microstructural damages at the interface stability. Consequently, the solution can be between the components is presented. The obtained in linear formulation, as carried out stability of glass-plastic cylindrical and conical in the present paper. 4 Refs. shells with different degrees of damage to the Pal'chevskii, A.S. Sov Appl Meeh Oct 1988 p material is examined. The method makes it 358-362. possible to study the stability of shells of composite materials in which the components 037092 Analysis of Parametric Oscillations separate from one another during mechanical of Shells of Revolution with Variable or other types ofloading. 9 Refs. Parameters. This paper examines the Vanin, G.A. (Acad of Sciences of the Ukrainian SSR, parametric oscillations of thin shells of Kiev, USSR); Semenyuk, N.P. Sov Appl Meeh v 23 n revolution of arbitrary contour closed in the 10 Apr 1988 p 908-914. annular direction. The shells were assembled from a certain number of orthotropic and 037089 In8uence of Conditions of End isotropic layers of variable thickness. The Fixing on the Stability of Longitudinal material of each layer is assumed to be elastic Compressed Multilayer Conical Shells. The and governed by Hooke's generalized law. problem of the stability of multilayer The problem is solved on the basis of the orthotropic conical shells-and also cylindrical linear theory of shells and assuming that the shells, as a particular case - is considered, and hypothesis of nondeformable normals for the the influence of the boundary conditions on entire packet of the shell as a whole is the critical values of the longitudinal satisfied. 9 Refs. compressive force is analyzed. A family of Vasilenko, A.T. (Acad of Sciences of the Ukrainian curves of the critical load as a function of the SSR, Kiev, USSR); Cherin'ko, P.N. Sov Appl Meeh current value of L/Rme for shells with different Oct 1988 p 363-367. conditions at the ends is shown. Analysis of the results offers the possibility of dividing the 037093 Initial Post-Critical Behavior and consideration of the boundary conditions into Flaw Sensitivity of Composite Cylindrical two groups with four versions in each. 9 Refs. Shells with Difference Reinforcement Shul'ga, N.A. (Acad of Sciences of the Ukrainian Schemes. Results of the stability of reinforced SSR, Kiev, USSR); Primak, A.P. Sov Appl Meeh Oct shells are used to study the character of their 1988 p 348 - 352. post-critical behavior and sensitivity to the initial geometrical defects. The formulated 037090 Stability of a Sloping Panel of problem is solved through the theory of initial Negative Gaussian Curvature. The problem post-critical behavior and Koiter's special of the stability of a thin elastic shell of the theory. A circular cylindrical shell of the hyperbolic paraboloid type, rectangular in the length L, radius R, and thickness t consisting plane, when the contour lines coincide with the of N layers with different fiber orientations is direction of the principal curvatures is examined. 6 Refs.

387 Excerpts from The Enoineerino Index Annual 1989

Semenyuk, N.P. (Acad of Sciences of the Ukrainian boards, orthogonally attached to each other SSR, Kiev, USSR); Zhukova, N .B. Sov Appl Meeh by nails. As far as the investigated hypar-shells Oct 1988 p 385-392. are concerned, reaching of the ultimate load (in this paper the term 'ultimate load' is used 037094 Loss of Stability for a Spherical in a restrictive sense) is found to be the Shell. On the basis of three-dimensional relevant mode of loss of stability. This agrees linearized stability theory, we obtain the with experimental results reported in the characteristic equation for determining the literature. (Author abstract) 23 Refs. In critical inner radius of a spherical support, German. whose outer surface is acted upon by a load Rattasepp, T. (Technische Univ Tallinn, Tallinn, equal to the contact pressure on the boundary USSR); Mang, H.A. Bauingenieur v 64 n 6 Jun of the support and the rock mass. The 1989 p 255-266. magnitude of the contact pressure is determined in solving the problem of the STEEL precritical stress-strain state of the support and the elastic-plastic mass, which has an interface 037097 Optimized Wall Thickness of Shells between zones of elastic and plastic of Revolution. The aim of this paper was to deformation. (Edited author abstract) 7 Refs. develop a concept for the design of shells of Meshkov, S.I.; Shashkin, A.I. Meeh Solids v 23 n 5 revolution with different Gaussian curvature 1988 P 113-116 using a simplified finite element buckling analysis. A cooling tower shell was used as an 037095 Numerische Stabilitaetsanalyse example for calculations. 7 Refs. Linear und Nichtlinear, Deformierbarer, Wittek, Udo (Univ Kaiserslautern, Kaiserslautern, Parametererregter Schalentragwerke. West Ger). Proe Sess Relat Steel Struet Stroet Congr [Numerical Stability Analysis of Linearly Proceedings of the Sessions Related to Steel and Nonlinearly Deformable Shell Structures at Structures Congress '89, San Structures Under Parametric Francisco, CA, USA, May 1-5 1989. Publ by Excitation]. The present contribution derives ASCE, New York, NY, USA, 1989 P 686-695. a numerical concept for the stability analysis of linearly and nonlinearly responding shell STRAIN structures under parametric excitation. Starting from a displacement discretization of 037098 Deformation Bounds for Cyclically the incremental principle of virtual Loaded Shell Structures Operating under displacements and using Ljapunow's stability Creep Conditions. Constitutive relations, definitions, handy stability bounds are based on the Bailey-Orowan's creep theory, presented, especially also for nonlinear are used to develop a maximum work fundamental motions. Two of many computed condition which includes the influence of an examples demonstrate their applicability; the internal state. A bounding theorem on correctness of the results is checked by displacement is obtained for structures properties of line-search evaluated subjected to cyclic loading. An application of neighbouring motions. (Author abstract) 15 the bound is illustrated. (Author abstract) 6 Refs. Refs. Eller, Conrad (Ruhr-Univ Bochurn, Bochurn, West Cocks, Alan C.F. (Univ of Leicester, Leicester, Ger); Kraetzig, W. B. lng Areh v 59 n 5 1989 P Engl); Leckie, F.A. J Appl Meeh Trans ASME v 55 n 345-356. 3 Sep 1988 p 509-516.

037096 Zur Stabilitaet Flacher 037099 Refined Small Strain and Moderate Eckgestuetzter Hyparschalen aus Holz mit Rotation Theory of Elastic Anisotropic Geradlinigen Randtraegern. [On the Stability Shells. A general refined shell theory that of Shallow, Wooden Hypar-shells with accounts for the transverse deformation, small Straight, Point-Supported Edge Beams]. This strains, and moderate rotations is presented. paper is concerned with finite element The theory can be reduced to various existing stability analysis of shallow, thin hypar-shells shell theories including: the classical (i.e., made of timber, with straight, COrner• linear Kirchhoff-Love) shell theory, the supported edge beams. A feature of the Donnell-Mushtari-Vlasov shell theory, the analysis model is the direct consideration of Leonard-Koiter-Sanders moderate rotations the structural anisotropy of the shell shell theory, the von Karman type shear• membrane consisting of two layers of wooden deformation shell theory and the moderate-

388 Excerpts from The Enoineerino Index Annual 1989

rotation shear-deformation plate theory IL, USA, Nov 27 - Dec 2 1988. Publ by American developed by Reddy. The present theory is Soc of Mechanical Engineers (ASME), New York, developed from an assumed displacement NY, USA, 1988 WA/APM37 7. field, nonlinear strain-displacement equations that contain small strain and moderate STRESSES rotation terms, and the principle of virtual displacements. (Edited author abstract) 47 Refs. 037102 Analysis of an Axisymmetric Schmidt, R. (Univ of Wuppertal, Wuppertal, West Thermoelastic Plastic Stress-Strain State of a Ger); Reddy, IN. ] Appl Meeh Trans ASME v 55 n Laminar Shell Under Repeated Loading. 3 Sep 1988 p 611 - 61 7. Simple repeated loading processes were considered on laminar shells of revolution by 037100 Assumed Strain Stabilization loads of both the same and the reverse sign as Procedure for the 9-Node Lagrange Shell for the initial loading. The investigation was Element. An assumed strain (strain done within the framework of the Kirchhoff• interpolation) method is used to construct a Love hypothesis. It was assumed that the stabilization matrix for the 9-node shell creep strain is negligibly small as compared to element. The stabilization procedure can be the instantaneous elastic-plastic strains. A thin justified based on the Hellinger-Reissner shell of revolution with meridian section of variational method. It involves a projection arbitrary shape and consisting of variable• vector which is orthogonal to both linear and thickness layers was considered. The shell was quadratic fields in the local co-ordinate system subjected, from an initially unstressed and of each quadrature point. All terms in the unstrained state, to axisymmetric loads and development involve 2 X 2 quadrature in the nonuniform heating that varied in time in 9-node element. Example problems show such a way that plastic strain domains good accuracy and an almost optimal rate of occurred in which unloading then took place. convergence. (Author abstract) 40 Refs. The results of the analysis showed that the Belytschko, Ted (Northwestern Univ, Evanston, IL, active loading process occurred in the first two USA); Wong, Bak Leong; Stolarski, Henryk. IntJ steps in the shell in the form of a plastic strain Numer Methods Eng v 28 n 2 Feb 1989 p 385-414. zone at the shell inner surface. 6 Refs. Babeshko, M.E. (Acad of Sciences of the Ukrainian 037101 Refined Small Strain and Moderate SSR, Kiev, USSR); Prokhorenko, l.V.; Rotation Theory of Elastic Anisotropic Sokolovskaya. V.l. Sov Appl Meeh v 23 n 11 May Shells. A general refined shell theory that 1988 p 1054-1058. accounts for the transverse deformation, small strains, and moderate rotations is presented. 037103 Combined Theoretical and The theory can be reduced to existing shell Experimental Method of Determining theories including the classical (i.e., linear Residual Stresses in Wound Composite Kirchhoff-Love) shell theory, Donnell• Shells. A combined theoretical and Mushtari-Vlasov shell theory, Leonard-Koiter• experimental method of determining residual Sanders moderate rotations shell theory, von stresses, and the strains of wound composite Karman type shear-deformation shell theory shells induced by these stresses, is suggested. and moderate rotation shear deformation The method makes use of shells of revolution plate theory developed by J.N. Reddy. The that are formed by a system of layers of present theory is developed from an assumed unidirectional composite material placed at displacement field, nonlinear strain given angles to the generatrix. Each of the displacement equations that contain small elementary unidirectional layers is allotted strain and moderate rotation terms, and the rigidities in tension and compression as well as principle of virtual displacements. The in shear. The elastic constants of such a layer, governing equations exhibit strong coupling including the modulus and Poisson's ratio, are between the membrane and bending determined experimentally in tests of deformation which should alter the bending, circularly wound tubular specimens. For stability, and post-buckling behavior of certain determining residual stresses it is assumed that shell structures as predicted using available the deformations of the layer are composed of theories. (Edited author abstract) 47 Refs. elastic, thermal, and curing components and Schmidt, R. (Univ of Wuppertal, Wuppertal, West deformations induced by prestressing of the Ger); Reddy, IN. Am Soe Meeh Eng Pap Preprint• reinforcing elements. The method was American Society of Mechanical Engineers, experimentally verified in tests of cylindrical Presented at the Winter Annual Meeting, Chicago, shells made of glass reinforced plastic

389 Excerpts from The En8ineerin8 Index Annual 1989

comprised of glass fiber VMPS and epoxy J Appl Meeh Trans ASME v 55 n 3 Sep 1988 p resin ED-20 binder. The results confirm the 629-634. possibility of using the combined theoretical and experimental method for determining 037106 Stress-Strain Fields at Crack Tip in technological stresses and deformations of Axially Cracked Cylindrical Shells and the wound composite shells. 5 Refs. Calculation of Stress Intensity Factors. A Morozov, E.V. (K.E. Tsiolkovskii Moscow lnst of perturbation solution for stress-strain fields Aviation Technology, USSR). Meeh Compos Mater v (including modes I, II, III) at crack tip in 23 n 6 May 1988 p 802-807. axially cracked cylindrical shells is given. The analysis, using 10th-order differential equations which take the transverse shear 037104 Axisymmetric Elastoplastic Stress deformations into account, involves State of Branched Shell Systems with perturbation in a curvature parameter y2, Nonisothermal Loading Processes. The (y2 = [12(Inv2) J'a2/Rh). Stress intensity axisymmetric elastoplastic stress state of a factors for finite size cylindrical shells under branched shell with a complex form of the bending and internal pressure loading are meridian and poles is investigated, in evaluated. A good accuracy can be obtained conditions of quasistatic thermal and force without using fine meshes in a region near loading which varies over time. A shell of the crack tip. Besides, the influence of the revolution with a branched meridian is finite size and the shearing stiffness on considered in conditions of axisymmetric bulging factors, which are commonly used in connective heat transfer with the surrounding engineering, are analyzed. (Author abstract) 6 medium, under the action of a variable load. Refs. The problem is solved within the framework Liu, Chuntu (Acad Sinica, China); Wu, Xijia. Aeta of the Kirchhoff-Love hypothesis in a Meeh Sin v 3 n 3 1987 P 223-230. geometrically linear, quasistatic formulation; creep deformation is neglected in comparison with the instantaneous elastoplastic 037107 Surface Crack in Shells Under deformation. The equations of state employed Mixed-Mode Loading Condition. The are the relations of the theory of simple problem of a shallow shell containing a surface loading processes, taking account of their crack and subjected to general loading previous history which are linearized by the conditions is considered. It is shown that, as method of variable elasticity parameters. 8 in the three-dimensional elasticity formulation, Refs. the mode I state can be separated whereas modes II and III remain coupled. A line Galishin, A.Z. (Acad of Sciences of the Ukrainian spring model is developed to formulate the SSR, Kiev, USSR). Sov Appl Meeh Sep 1988 p part-through crack problem under mixed• 234-38. mode conditions. A shallow shell of arbitrary curvature having a part-through crack located 037105 Large Elastic Deformation of Shear on the outer or the inner surface of the shell Deformable Shells of Revolution: Numerical is then considered. Reissner's transverse shear and Experimental Results. Through an theory is used to formulate the problem by integrating matrix approach, a numerical assuming that the shell is subjected to all five solution is obtained to the equations governing moment and stress resultants. The uncoupled large elastic deformation of a clamped circular antisymmetric problem is solved for cylinder due to internal pressure. The shell cylindrical and toroidal shells having a surface equations include the effects of large strains, crack in various orientations and the primary thickness changes, and transverse shear and the secondary stress intensity factors are deformation. The numerical solution is given. (Edited author abstract) 20 Refs. compared to results from an asymptotic Joseph, P.F. (Lehigh Univ, Bethlehem, PA, USA); analysis and from experiments on rubber Erdogan, F. J Appl Meeh Trans ASME v 55 n 4 Dec cylinders. A specialized Rivlin-Saunders 1988 p 795-804. strain-energy density function is assumed for the rubber, with material constants 037108 Investigation of the Spherical determined from tensile tests and deformed Membrane Cap Under Partial Load. It is cylinder profiles at a high inflation pressure. shown how the internal forces due to an (Author abstract) 15 Refs. axially non-symmetric load of a spherical cap Kempski, M.H. (Rochester lnst of Technology, can be determined within the framework of Rochester, NY, USA); Taber, L.A.; Su, Fong-Chin. the membrane theory. We present the

390 Excerpts from The Engineering Index Annual 1989 method of internal forces for the terms of the 037112 Bifurcation of Axisymmetric Fourier expansion. In a numerical example Equilibrium of Thin Shells of Revolution these forces are computed for a spherical cap with Regular Shaped Imperfections. An

0 with the half central angle cPo = 38 • As can asymptotic formula is derived to characterize be seen, for n = 2,3,4 closed formulae can be the effect of a regular axisymmetric shape obtained, while for n ~ 5 the calculation has imperfection upon the classical critical load of to be carried out numerically. (Edited author a perfect convex shell belonging to a certain abstract) 4 Refs. class. 4 Refs. Olitzscher, Frank. Acta Tech (Budapest) v 100 n 3-4 Teterin, I.Yu. (Leningrad Univ, Leningrad, USSR). 1987 P 225 - 238. Leningrad Univ Mech Bull n 2 1988 P 62-64. 037113 Assessment of Assumed Strain 037109 Shallow Shells with Local Deviations Methods in Finite Rotation Shell Analysis. A in Shape. A simple solution is presented for critical assessment of the 4-node assumed strain the stress analysis of shallow shells with element as proposed by E.N. Dvorkin and K.J. imperfections in the geometry. The model is Bathe is made. The element performed based on the bending equations of the shell, excellently in all investigated shell problems and the imperfection is considered by an which sometimes caused difficulties for other equivalent load method. A Ritz solution for a assumed strain techniques. For efficient given shape of local imperfection is obtained in computation in the non-linear range, explicit form, and the expressions are applied linearization of the virtual work equation is to the case of an elliptical paraboloidal shell. done to yield the consistent tangent stiffness. (Author abstract) 14 Refs. The shell formulation is done for stress and Godoy, L.A. (Univ Nacional de Cordoba, Cordoba, strain tensors based on local element Argent); Quinones, D.; Wagner, R. Bull Int Assoc coordinates. To demonstrate the effectiveness Shell Spat Struct v 29 - 2 Aug 1988 P 55 - 62. and rapid convergence of the non-linear formulation, three examples are tested for 037110 Stress Distribution by the large displacements. (Edited author abstract) Misalignment of Spherical and its Allowable 19 Refs. Limit. The expressions for stress distribution Stander, Nielen (Univ Stuttgart, Stuttgart, West in the region of misalignment of spherical Ger); Matzenmiller, Anton; Ramm, Ekkehard. Eng shells have been derived on the basis of the Comput (Swansea Wales) v 6 n I May 1989 p 58 - 66. theory of plates and shells. The analytical expressions are verified with the results 037114 Investigation of Partially obtained by FEM and photoelastic experiment. Pressurized Thick Cylindrical Shells. In The effect of several parameters on stress applications of thick cylinders, such as gun concentration has been analyzed with the barrels and hydraulic jacks, the internal expressions derived. The regressions of the pressure is not only variable, but the pressure analytical results of 76 misalignment have been front at each moment moves along the length made and the expressions for engineering of the cylinder leading to the division of these calculations are given. The nomograph for the cylinders into two segments with allowable limits of geometric irregularities is discontinuous loading. In this work, the FEM presented. (Edited author abstract) has been applied to investigate the state of stress existing at the discontinuity zone of Kui, Jishan (Nanjing Inst of Chemical Technology, thickness or pressure (transition zone). Results Nanjing, China); Wang, Jiuqing. HuagongJixie v 15 n indicate the existence of a considerable 61988p341-347,353. bending moment due to the variation of longitudinal stress across the thickness at the 037111 Solution of the Axisymmetric transition zone. These results could help the Problem for a Shallow Conical Shell by the designers to optimize the thicknesses of the Small Parameter Method. By the method of cylinders in such applications as mentioned small parameters, an approximate solution is above. (Edited author abstract) II Refs. constructed for the problem of a rotating Mahmood, Najdat A. (Military Engineering Coli); shallow conical shell. The error of the method Jweeg, Muhsin J.; Rajab, Mumtaz Y. Modell Simul is estimated by comparing it with the results Control B v 25 n 3 1989 P 47-64. obtained by a numeric computer simulation. (Author abstract) 2 Refs. 037115 Thick General Shells Under General Sakharov, V.Yu. (Leningrad Univ, Leningrad, Loading. Three equilibrium equations in USSR). Leningrad Univ Mech Bull n 2 1988 P 60 - 61. terms of three displacements are derived in

391 Excerpts from The Ennineerinn Index Annual 1989

scalar mathematics form, by linear, small-strain steady operating conditions is presented. The elasticity principles, for the case of general heat conduction equation incorporating heat thick-walled shells under general loading. generation due to solidification was solved by These reduce to well-known forms for the finite element method to obtain the spatially particular cases of flat-plates and thick circular steady temperature distribution when cylindrical shells. (Author abstract) considering material flow. Elastic-plastic Donnell, Lloyd H. ] Appl Meeh Trans ASME v 56 n stresses in the solidified shell were also 2Jun 1989 p 391-394. evaluated. A parameter study was carried out in order to obtain the optimal operating 037116 Shear Deformable Finite Element condition such as shell thickness, site of crater for the Analysis of General Shells of end, and stress distribution as functions of the Revolution. A 64-dof isoparametric casting speed and cooling condition. (Author quadrilateral finite element is presented for abstract) 6 Refs. In Japanese. the analysis of generally laminated shells of Tatsumi, Naohisa; Wang, Zhi-Gang; Inoue, Tatsuo. revolution. The effects of shear deformation Nippon Kikai Gakkai Ronbunshu A Hen v 55 n 514 and rotary inertia are accounted for by using Jun 1989 p 1389-1393. shear deformation theory that employs the parabolic shear strain variation across the 037119 Elastic Stress Analysis of Two thickness. The classical thin shell theory is the Oblique Intersecting Cylindrical Shells special case of shear deformation theory used Subjected to Internal Pressure. In this paper, in the present study. Thus, the thin shell the elastic stress distribution in two oblique element also can be obtained from the present intersecting cylindrical shells subjected to thick shell element by simply having the internal pressure is discussed. We first displacement parameters (UI and VI) associated investigated the elastic stresses and with the shear rotations as zeros. The displacements to the intersected shell numerical results presented illustrate the (cylindrical vessel) with an arbitrary curved performance of the element and the effects of hole under internal pressure. In making this shear deformation. (Author abstract) 33 Refs. analysis, a curvilinear coordinate system (e, ~) Bhimaraddi, A. (Univ of Canterbury, Christchurch, is used and one of which e= eo is made to NZ); Carr, A.J.; Moss, P.J. Comput Struet v 31 n 3 coincide with the hole contour r. The 1989 P 299-308. governing equation is the equation of shallow shell in this coordinate system. When the hole 037117 Stressed State of Inhomogeneous contour is an ellipse, the obtained solution is a Elastic Shells of Revolution. An extension is complex function expressed in Mathieu discussed regarding an averaging technique function. Then, we discussed the stresses and for the case of quasi-periodic structures with displacements expressed in the edge effect curvilinear anisotropy, as applied to problems form on the basis of Flugge's equations for the of elasticity written in the displacements. In intersecting shell (nozzle). At last, a boundary this paper, the authors employ the technique condition along the intersection curve is to reduce the static problem of derived. Numerical computation was inhomogeneous elasticity in the stresses, conducted, and the results are compared with utilizing hypotheses of shell theory (i.e., the experiments. (Author abstract) 10 Refs. problem of equilibrium of an inhomogeneous Chien, Huei-Lin (Nanjing lnst of Chemical anisotropic shell of quasi-periodic structure to Technology, Nanjing, China); Wu, Shao-Jun. ASME a recursive sequence of problems for a Pressure Vessels Piping Div Publ PVP v 139 Design homogeneous anisotropic shell. The authors and Analysis of Piping, Pressure Vessels and offers a solution for the problem of Components, 1988, Presented at the 1988 ASME equilibrium of a shell formed by a winding or Pressure Vessels and Piping Conference, Pittsburgh, coil that is acted upon by internal pressure. 8 PA, USA,Jun 19-23 1988. Publ by American Soc Refs. of Mechanical Engineers (ASME), New York, NY, Levin, V.D.; Pobedrya, B.E. Meeh Solids v 23 n 4 USA, 1988 P 119-124. 1988 P 140-145. 037120 Cutouts in Laminated Plates and 037118 Simulation of Temperature and Shells. A finite element method for evaluating Elastic-Plastic Stresses in Solid Shell During stresses around cutouts in thin to moderately Continuous Casting Process. An analytical thick laminated composite plate and shell method to simulate the temperature and the structures is presented. Ahmad's eight noded stress fields in a continuous casting slab under isoparametric quadrilateral shell element

392 Excerpts from The Eneineerine Index Annual 1989

(Ahmad et aI., 1970) is extended to laminated clamped hemispherical shells subjected to composite structures by incorporating the suddenly applied loads, including idealized thickness concept. The element includes an step pressure, a rectangular pressure impulse arbitrary number of bonded layers, each of of finite duration and realistic blast pressure which may have a different thickness, over the total or partial area. The orientation of principal material directions mathematical model is formulated in terms of and elastic properties. The transverse shear the mid-surface displacements and cross• deformation is taken into account in section rotation with effects of transverse developing the stiffness matrix. (Author shear strain and rotary inertia taken into abstract) 9 Refs. account. The Rayleigh-Ritz method is Widera, G.E.O. (Univ of Illinois at Chicago, employed to solve the hemispherical shell Chicago, IL, USA); Moumene, M. ASME Pressure vibration problem by assumed modes in Vessels Piping Div Publ PVP v 146 Advances in Legendre polynomials, and the normal mode Macro-Mechanics of Composite Material Vessels and superposition is used in the analysis of its Components, Presented at the 1988 ASME Pressure dynamic response. Numerical results for the Vessels and Piping Conference, Pittsburgh, PA, natural frequencies, mode shapes, structural USA,Jun 19-23 1988. Publ by American Soc of deformation and dynamic stresses are obtained Mechanical Engineers (ASME), New York, NY, with the fiber orientation parallel or USA, 1988 P 155-158. perpendicular to the meridian direction as a design guide. (Edited author abstract) 20 Refs. 037121 Thermal Stresses in Thick Spherical Chao, C.C. (Nat! Tsing Hua Univ, Hsinchu, Shell with Internal Heat Generation. The Taiwan); Tung, T.P. Int J Impact Eng v 8 n 3 1989 elastic thermal stresses in thick spherical shells P 191-207. with internally uniform heat generation have been studied analytically. The dimensionless 037123 Elasto/Visco-Plastic Dynamic stress functions have been developed. The Response ofAxisymmetrical Shells Under computer generated graphs for the stress Mechanical and/or Thermal Loading. An functions for various outside to inside radii analytical method for the e1asto/visco-plastic ratios are presented to facilitate computation dynamic problems of axis ymmetrica I thin of the stresses at any radial location of the shells subjected to mechanical and/or thermal shell. The stress functions for the thermal loads is developed. The equations of motion stresses for solid sphere with internal heat and the relations between the strains and generation have also been developed. The displacements are derived by extending radial location for the maximum values of the Sanders' elastic shell theory. For the dimensionless stress functions have been constitutive relations, the Perzyna elasto/ determined and shown on the graphs. The visco-plastic equations including the graphs for the stress functions are general temperature effect are employed. The enough to compute the radial and hoop fundamental equations derived are stresses which are produced by the numerically solved by the finite difference temperature gradient encountered in the method. As numerical examples, the simply shells. Additional aspects of the subject are supported cylindrical shells made of mild steel discussed. (Edited author abstract) 8 Refs. are treated and the following two cases are Bhaduri, S. (Univ of Texas at EI Paso, EI Paso, TX, analyzed; a nonuniform temperature cylinder USA); Kapoor, P.S. ASME Pet Div Publ PD v 21 subjected to impulsive pressure, and an Technical Economics, Synfuels, and Coal Energy- internal pressure cylinder subjected to 1989, Presented at the Twelfth Annual Energy• impulsive thermal load. In both cases the Sources Technology Conference and Exhibition, variations of displacements and internal forces Houston, TX, USA, Jan 22 - 25 1989. Publ by with time are discussed. (Author abstract) 13 American Soc of Mechanical Engineers (AS ME), Refs. In Japanese. New York, NY, USA, 1988 P 65-70. Tao, Katsumi; Takezono, Shigeo; Taguchi, Toshihiro; Hotada, Kazuo. Nippon Kikai Gakkai STRUCTURAL ANALYSIS Ronbunshu A Hen v 54 n 503 Ju1 1988 p 1457 -1464.

037122 Step Pressure and Blast Responses 037124 Investigation of the Spherical of Clamped Orthotropic Hemispherical Membrane Cap under Partial Load. This Shells. This paper is concerned with studies paper shows how the internal forces due to an on the axisymmetric free vibration and axially non-symmetric load of a spherical can dynamic response of polar orthotropic cap be determined in the frame of the

393 Excerpts from The Enoineerino Index Annual 1989

membrane theory. It presents the method of excitation sweeps showed a dynamic instability. internal forces for the terms of the Fourier The frequency range over which the response expansion. In a numerical example these is unstable decreases with increasing forces are computed for a spherical cap with a pretension. The dynamic to static strain ratio particular half central angle. Calculation decreased from 20% to 2.3% as pretension results are discussed. (Edited author abstract) increased from the lowest to the highest 5 Refs. value. (Author abstract) 20 Refs. Olitzscher, Frank. Acta Tech (Budapest) v 100 n 2-3 Gasparini, D.A. (Case Western Reserve Univ, 1987 P 225-238. Cleveland, OH, USA); Perdikaris, P.C.; Kanj, N.] Struct Eng v 115 n 2 Feb 1989 p 363 - 381. 037125 Formulation and Accuracy of a Circular Cylindrical Shell Theory Due to a 037127 Infinite, Elastic, Cylindrical Shell Higher-Order Approximation. In this paper, with a Finite Number of Ring the most general higher-Qrder equations of Constraints. The axisymmetric excitation of three-dimensional static and dynamic theories an infinite, elastic, cylindrical shell with a for a circular cylindrical shell are derived by finite number of ring constraints is discussed. expanding the displacements into an infinite Exact solutions are presented for the cases of power series with respect to the radial one and two constraints. These are then coordinate of the shell. The present examined in an asymptotic limit that formulation can be taken into account actually corresponds to light fluid-loading and small any higher-order terms for both cases of static curvature. (Author abstract) 9 Refs. and dynamic problems. Several theories which Lawrie, J.B. (Univ of Bristol, Bristol, Engl).] Sound were proposed previously, can be deduced by Vib v 130 n 2 Apr 22 1989 P 189-206. the employment of the lower-order terms in our theory. Three typical theories such as 037128 Membrane Shell as an Under• 3-order theory, Levinson-type theory and constrained Structural System. Statical• Levinson-Voyladjis-Baluch-type theory are also kinematic analysis is employed to provide a newly derived from the present formulation. new perspective on the structural behavior of Numerical results of natural frequencies for membrane shells and the related limitations of simply-supported cylindrical shells are the linear membrane theory. The obtained compared to the exact solution as well as results include a resolution of an apparent many theories. (Author abstract) 8 Refs. In paradox in the statics of membranes, a Japanese. description and explanation of the peculiar Hirano, Kisaburou; Hirashima, Kenichi. Nippon behavior of toroidal membranes with an Kikai Gakkai Ronbunshu A Hen v 54 n 506 Oct 1988 arbitrary cross-section, and a stronger version p 1915-1919. of a central theorem in the membrane theory. (Author abstract) 7 Refs. 037126 Dynamic and Static Behavior of Kuznetsov, E.N. (Univ of Illinois at Cable Dome Model. The static and dynamic Urbana-Champaign, IL, USA).] Appl Meek Trans behavior of a cable dome was studied by ASME v 56 n 2 June 1989 p 387 - 390. testing a 1/50 scale model. Three different pretension levels were considered. The static 037129 Modal Analysis of a Shell's Acoustic response of the model under a symmetric and Radiation in Light and Heavy Fluids. A an antisymmetric loading was investigated. modal analysis study of acoustic radiation by a The cable dome's behavior changes from a finite cylindrical shell immersed in light of compressive to a tensile membrane with heavy fluid is presented. Attention is focused increasing applied central load. The cable on the explanation of radiation phenomena in model exhibits a hardening response, both fluids. The concepts of radiation, especially in the antisymmetric mode. The structural and evenly damped modes are nonlinearity becomes more pronounced with explained. These lead to clarification of the decreasing pretension. The stiffness in the shells' vibro-acoustic behaviour in heavy fluid antisymmetric mode is dominated by the and to confirmation of the well known case of geometric stiffness from pretensioning. In the light fluid. Relationships between these new vertical acceleration (symmetric) test at the concepts and the more classical one of radiating intermediate pretension the first dominant and non-radiating modes are presented. It is mode was antisymmetric. A sail exciter was shown that this previous classification of modes also used to apply a single asymmetric is insufficient to clarify the heavy fluid-shell controlled force. Up and down harmonic coupling, especially in the critical frequency

394 Excerpts from The Enoineerino Index Annual 1989

range. In this range the behaviour of a shell in also built and tested in laboratory to validate water is very different from that of one in air, the results. (Author abstract) 24 Refs. and is entirely controlled by modes which are Tzou, H.S. (Univ of Kentucky, Lexington, KY, overdamped by radiation. In particular, it is USA); Gadre, M.] Sound Vib] Sound Vib v 132 v shown that structural damping is ineffective in 132 n 3 n 3 Aug 8 Aug 819891989 P 433-450. reducing radiated power in the critical frequency range when the fluid is water. 037132 Analysis of Laminated Shells. (Author abstract) 22 Refs. Laminated shell structures are increasingly Laulagnet, B. (INSA, Villeurbanne, Fr); Guyader, being used in chemical, marine and aerospace J.L.] Sound Vib v 131 n 3 Jun 22 1989 P 397 - 415. applications. A significant amount of research has been conducted in the past on studying 037130 Analysis of Elasto/Visco-Plastic the structural response of these structures. A Dynamic Response of General Thin Shells by review of various investigations on the analysis Means of Overlay Model. The numerical of these shells is given here. Specifically, this analysis of the elasto/visco-plastic dynamic review deals with the development of various response of the general thin shells to arbitrary theories for modelling the thick laminated loads is carried out by the use of the elasto/ shells including shear effects; analytical visco-plastic overlay model which is able to studies, development of various finite elements express the Bauschinger effect and the strain to model these shells including applications to rate dependence. Namely Perzyna's equation is tire modelling; buckling and post buckling used for the constitutive relation of each layer analysis of perfect and imperfect laminated of the overlay model and as a whole the shells; vibration and dynamic response analysis Bauschinger effect and the influence of of various laminated shells. (Author abstract) viscosity in the plastic range of the material are 148 Refs. taken into account. The equations of motion Kapania, R.K. (Virginia Polytechnic Inst & State derived from the Sanders nonlinear theory for Univ, Blacksburg, VA, USA). ASME Aerosp Div Publ thin shells by adding the inertia terms are used, AD v 13 Recent Advances in the Macro- and and the relations between strains and Micro-Mechanics of Composite Materials Structures, displacements where rotations of the shell are Presented at the Winter Annual Meeting of the considered for the membrane strains are American Society of Mechanical Engineers, employed. (Edited author abstract) 18 Refs. In Chicago, IL, USA, Nov 27 - Dec 2 1988. Publ by Japanese. American Soc of Mechanical Engineers (ASME), Tao, Katsumi; Takezono, Shigeo. Nippon Kikai New York, NY, USA, 1988 P 177-187. Gakkai Ronbunshu A Hen v 55 n 514 Jun 1989 p 1453-1460. 037133 Analysis of Glulam Lattice Dome. Glued-laminated timber (glulam) domes have 037131 Theoretical Analysis of a Multi• become competitive in the engineering of Layered Thin Shell Coupled with large-span roof structures. Three-way glulam Piezoelectric Shell Actuators for Distributed grid domes, such as the Triax and Varax Vibration Controls. Structural dynamics and domes, are particularly well-suited for glulam controls of distributed mechanical systems have construction because the members lie on great drawn much attention in recent years. In this circles and, thus, have the same radius of paper, a multilayered thin shell coupled with an curvature. The curved members are active distributed vibration actuator• interconnected by patented steel hubs. The polymeric piezoelectric polyvinylidene fluoride restraints offered by these connectors are the (PVDF)-is proposed and evaluated. Dynamic major differences in the designs of the Triax equations for the generalized multi-layered and Varax domes. The domes rest on tension thin shell coupled with the polymeric rings made of steel or reinforced concrete. piezoelectrets are derived based on Love's Because of their economy and acoustic theory and Hamilton's principle. Each layer of quality, Triax and Varax domes are widely the shell can be a polymeric piezoelectric used for multipurpose facilities involving control layer subjected to feedback voltages sports, recreational, and social activities. The resulting in a local control force to suppress the purpose of this paper is to report on a project vibration of the shell. To demonstrate the that was initiated to formulate a finite derived equations, a cantilever beam coupled element method of analysis that can predict with the polymeric piezoelectric actuator is the complete structural response of glulam derived by directly simplifying the modified space frames and lattice domes up to collapse. Love's equations. An experimental model was 25 Refs.

395 Excerpts from The Enoineerino Index Annual 1989

Holzer, S.M. (Virginia Polytechnic Inst & State Mechanical Engineers (ASME), New York, NY, Univ, Blacksburg, VA, USA); Huang, C.Y.; USA, 1989 P 743-751. Davalos, J.F.; Loferski, J.R. Struet Des, Anal Test Structural Design, Analysis and Testing, STRUCTURAL DESIGN Proceedings of the sessions at Structures Congress '89, San Francisco, CA, USA, May 1-5 1989. Publ 037136 Carrying Capacity and Optimal by ASCE, New York, NY, USA, 1989 P 914-921. Design of Reinforced Cylindrical Shells. Models were constructed for calculating the carrying capacity and 037134 Why Bifurcation: A Study of a optimizing the design of cylindrical shells Recticulated Dome. Numerical results for a reinforced by regular frames and supported hexagonal lattice dome subjected to uniform by discrete 'saddle' supports of various gravity loading are presented. We demonstrate configurations or resting on a continuously that a perfect nonlinear bifurcation analysis plastic base. The closed shell was considered plays a crucial role in the identification of the to be made from an ideal rigidly plastic critical imperfection. In the process we also material with constant thickness with a given advertise the capabilities of some recently yield point and to be filled with fluid. It was developed techniques for computational assumed that exhaustion of the shell carrying bifurcation problems with symmetry. (Author capacity occurs with rupture. Calculations of abstract) 6 Refs. the upper boundaries of the limit loads were Healey, Timothy L. (Cornell Univ, Ithaca, NY, performed in a broad range of thicknesses. USA). Struet Des, Anal Test Structural Design, Parameters for the analysis of the shell Analysis and Testing, Proceedings of the sessions at carrying capacity reinforced by regular Structures Congress '89, San Francisco, CA, USA, annular ribs were established. Analysis of the May 1-5 1989. Publ by ASCE, New York, NY, optimal designs shows that the models first USA, 1989 P 942 - 948. tend to assure a given carrying capacity because of an increase in thickness and only 037135 Application of Mathematical then are the frames introduced. 4 Refs. Programming to the Limit Analysis of Shell Dekhtyar, A.S. (Kiev Art Inst, Kiev, USSR). Sov Structures. Limit analysis of a shell structure Appl Meeh v 23 n 11 May 1988 p 1049-1054. has been expressed, in the present paper, as a nonlinear programming problem, where the 037137 Wplyw Geometrycznych I principle of virtual displacement in Fizycznych Parametrow Trojwarstwowej combination with rigid perfect-plastic Powloki Wnlcowoj Nn Jej Statecznosc Przy assumption and von Mises yield criterion are Obclazenlach Zlozonych. [Influence of used. The structure is separated into several Physical and Geometrical Parameters of rigid and plastic regions for the purpose of Sandwich Cylindrical Shell Under Composed saving computer storage, since the Load for its Stability]. The paper presents displacement functions should be generated numerical analysis results of stability loss for only in plastic regions. By use of the Lagrange an elastic, open, cylindrical sandwich shell multiplier method, the primary problem can with light-weight core and with thin faces of be expressed as a non-linear programming equal thickness. The shell is loaded by problem without restrictions. By using the composed load, i.e. compression longitudinal gradient of the object function, a set of forces, lateral surface pressure and shear edge suitable displacement velocities can be found forces. The influence of shell curvature, shell by iteraction to minimize the object function length, the thickness of each layer, and the and obtain an upper bound solution of the core elasticity modulus on the values of upper ultimate load of the structure. A cylindrical and lower critical load is investigated. (Edited shell and a tubular T-joint are computed and author abstract) 4 Refs. In Polish. the results are satisfactory in comparison with Sekulski, Zygmunt; Szyc, Waclaw. Arch Budowy Masz classical solutions or experimental results. v34n31987p321-336. (Author abstract) 7 Refs. Chen, T.Y. (Shanghai Jiao Tong Univ, Shanghai, TESTING China); Chen, W.M.; Wang, Y.Q. Proe Int Offshore Meeh Arct Eng Symp v II (of VI), Proceedings of the 037138 Deformation and Fracture of Eighth International Conference on Offshore Two-Layer Metal-Plastic Shells Under Mechanics and Arctic Engineering-1989, Hague, Internal Shock Loading. The goal of this Neth, Mar 19-23 1989. Publ by American Soc of paper was to study the feasibility of making

396 Excerpts from The En8ineerin8 Index Annual 1989

fuller use of the strength reserves of a mentioned composites vary significantly as a glass-plastic in a thin-walled shell under function of the component content by internal shock loading. We studied the volume, the bonding scheme and a number of deformation and fracture of cylindrical two• other technological factors. Taking account of layer metal-plastic shells (a shell of steel 20 the real properties of composites, including was inserted without a gap inside the glass• the anisotropy and nonlinearity of the strain plastic shell) under an internal explosion. diagram attention must be paid in formulating Fracture was established from the break• the problems, compiling the governing through of explosion products, ruptures of equations, refining the computational schemes, the strain gages, and external inspection. We and performing the strength analyses of determined the maximum hoop strains in the structural elements (rods, plates, shells) or the first phases of tension and compression for typical structures of complex geometric shape. the most heavily loaded central section of the 9 Refs. shells. The deformation process took the form Guz', A.N. (Acad of Sciences of the Ukrainian SSR, of rapidly decaying vibrations. We also Kiev, USSR); Chernyshenko, I.S.; Georgievskii, evaluated the effect of the steel on the decay V.P.; Maksimyuk, V.A. Sov Appl Meeh Oct 1988 p of vibrations in the shell in a simplified 337-342. formulation for the case of decaying sinusoidal free vibrations of a system with Coulomb 037141 Refinement of Shear Theory of friction. Characteristic chronograms and Laminar Orthotropic Sloping Shells. This oscillograms of the strains of the glass-plastic paper proposes refinement of the shear and steel shells are shown with a cross section theory. A second-approximation model is of the metal-plastic shells. Test results are proposed, allowing this effect to be described analyzed. 6 Refs. on the basis of an approach invariant with Tsypkin, V.I.; Rusak, V.N.; Ivanov, A.G.; respect to the number of layers in the system Fedorenko, A.G.; Vorontsova, O.S. Meeh Compos and allowing the distortion of the normal in Mater v 23 n 5 Mar 1988 p 586-590. the course of shell deformation to be taken into account. The discontinuities in the THEORY smoothness of the functions between the outer layers are observed both for tangential 037139 Numerical Solution Method for and for normal stress, which allows the Dynamical Problems of Shell Theory. The lamination process of the structure to be forced vibrations of shells of revolution modeled. 12 Refs. subjected to a load changes in an arbitrary Rasskazov, A.O. (Kiev Highway Inst, USSR); manner with time was examined. The Burygina, A.O. Sov Appl Meeh Oct 1988 p 343-347. majority of the existing algorithms for numerical analysis of thin elastic shell 037142 Higher Order Theories for Thick vibrations are based on the method of Cylindrical Shells. A variational derivation is expansion of eigenmodes and on asymptotic used to obtain 10th and 12th order shell method. This paper describes a method that is theories along with the associated boundary not associated with the constraints of the conditions. A computer program produces the above-mentioned algorithms. Analysis of the coefficients in the reductions of the sets of results shows that the vibration mode of a equilibrium equations to equivalent single shell subjected to a unit rectangular pulse 10th and 12th order equations. Exact differs noticeably from the lowest eigenmodes. solutions for closed shells which decay in the 6 Refs. axial direction are obtained and compared Naraikin, O.S. (M.E. Bauman Higher Technical with exact three dimensional solutions in order to assess the accuracy of the shell Inst, USSR). Sov Appl Meeh v 24 n 2 Aug 1988 P theory as an approximation to the elasticity 126-132. theory. (Author abstract) 9 Refs. 037140 Stress State of Thin-Walled Faraji, Susan (Univ of Lowell, Lowell, MA, USA); Elements of Structures Fabricated from Archer, R.R. Aeta Meeh v 74 n 1-4 Oct 1988 p 9-24. Nonlinearly Elastic Orthotropic Composite Materials. Experimental results indicate that 037143 Self-Equilibrated Singular Solutions the material of certain composites (glass-plastic of a Complete Spherical Shell: Classical on a fabric base, organic plastics, etc.) Theory Approach. The elastic response of a possesses nonlinear properties; the elastic complete spherical shell under the influence of characteristics and strain diagram of the concentrated loads (normal point loads,

397 Excerpts from The Enaineerina Index Annual 1989

concentrated tangential loads, and proposed numerical treatment of the concentrated surface moments) which apply in membrane and bending fields, based on a a self-equilibrating fashion is obtained. The mixed HeIlinger-Reissner formulation, mathematical analysis incorporates the classical provides excellent results for the 4-node uncoupled system of equations for the bilinear isoparametric element. (Edited author transverse displacement Wand a stress abstract) 46 Refs. function F. The solution formulae for all Simo, J.C. (Stanford Univ, Stanford, CA, USA); three types of singular loading are in closed Fox, D.O.; Rifai, M.S. Comput Methods Appl Meeh form and they are expressed in terms of Eng v 73 n 1 Apr 1989 p 53-92. complex Legendre and other elementary functions. The two latter portions of the 037146 Maguerre-Mindlin Shallow Shell analysis are associated with a multivalued Elements. Two isoparametric Lagrangian stress function F which leads to a single-valued shallow shell elements are presented: a 4-node stress and displacement formulae. (Edited element Quad4 and a 9-node element Quad9. author abstract) 19 Refs. These elements are based on Mindlin/ Simos, Nikolaos (City Univ of New York, New Reissner plate elements. These elements are York, NY, USA); Sadegh, Ali M.] Appl Meeh Trans sophisticated by adding conventional ASME v 56 n 1 Mar 1989 p 105-112. membrane stiffness and membrane-bending coupling terms based on Maguerre's 037144 On a Stress Resultant Geometrically approximate shallow shell theory. This results Exact Shell Model. Part I: Formulation and in double curved shell elements which Optimal Parametrization. The main thrust originally possess severe membrane locking of this work is to demonstrate that classical behavior. This defect is overcome in the same shell theory, phrased as one-director Cosserat way as the shear locking problem is solved. surface, leads itself to an efficient numerical (Edited author abstract) 10 Refs. implementation which is free from Kraus, Gerhard (Ingenieurbuero fuer mathematical complexities and suitable for Strukuranalyse, Berlin, West Ger). Eng Comput large scale computation. Examples are given (Swansea Wales) v 6 n 1 Mar 1989 p 44-48. which contain simulations involving extremely large displacements and rotations obtained 037147 Work-Conjugate Boundary with the formulation described. It is shown Conditions in the Nonlinear Theory of Thin that this approach is able to reproduce the Shells. Work-conjugate boundary conditions exact solutions of standard benchmark linear for a class of nonlinear theories of thin shells problems often used to assess the performance formulated in terms of displacements of the of numerical formulations based on the reference surface are discussed. Applying degenerated solid approach. 48 Refs. theorems of the theory of differential forms it Simo, J.C. (Stanford Univ, Stanford, CA, USA); is shown that many of the sets of static Fox, D.D. Comput Methods Appl Meek Eng v 72 n 3 boundary conditions which have been proposed Mar 1989 p 267-304. in the literature do not possess work-conjugate geometric counterparts. The general form of 037145 On a Stress Resultant Geometrically four geometric boundary conditions and their Exact Shell Model. Part II: The Linear work-conjugate static boundary conditions is Theory; Computational Aspects. Computa• constructed and three particular cases are tional aspects of a linear stress resultant analyzed. The boundary conditions given here (classical) shell theory, obtained by systematic are valid for unrestricted displacements, linearization of the geometrically exact rotations, strains and/or changes of curvatures nonlinear theory are examined in detail. In of the reference surface. (Author abstract) 30 particular, finite element interpolations for the Refs. reference director field and the linearized Makowski,J. (Ruhr Univ, Bochum, West Ger); rotation field are constructed such that the Pietraszkiewicz, W.] Appl Meeh Trans ASME v 56 n underlying geometric structure of the 2June 1989 p 395-402 continuum theory is preserved exactly by the discrete approximation. A discrete canonical, 037148 Formulation and Accuracy of the singularity-free mapping between the five and Circular Cylindrical Shell Theory Due to the six degree of freedom formulation is Higher Order Approximation. The most constructed by exploiting the geometric general higher order equations of the three• connection between the orthogonal group dimensional static and dynamic theories for a (SO(3)) and the unit sphere (S2). The circular cylindrical shell are derived by

398 Excerpts from The Ennineerinn Index Annual 1989

expanding the displacements into an infinite Temperature-time history and heat flow rates power series with respect to the radial have been obtained. The problem considered coordinate of the shell. The present theory has got its application in the transient thermal takes into account any higher order terms for analysis of an adiabatic engine. Any other both the static and dynamic problems. Several similar problem in metallurgical, aeronautical, theories, which have been proposed, can be furnace design, boiler design applications may deduced by using the lower order terms of our be solved by the formula obtained. (Author theory. Three typical theories are the third• abstract) 8 Refs. order theory, the Levinson theory and the Prasad, Ravindra (Banaras Hindu Univ, Varanasi, Levinson-Voyiadjis-Baluch theory, which are India); Samria, N.K. Appl Sci Res (The Hague) v 46 n redefined according to the present theory. 2Jun 1989 p 141-157 Numerical results of natural frequencies for the simply supported cylindrical shell, as well as THERMOELASTICITY many other theories, are compared with the exact solutions. (Author abstract) 8 Refs. 037151 Thermoelasticity of a Regularly Hirano, Kisaburou (Oita Natl Coil of Technology, Nonhomogeneous Thin Curved Layer with Oita, Jpn); Hirashima, Kenichi.JSME IntJ Ser 1 v 32 Rapidly Varying Thickness. A regular n 3Jul1989 p 337-340. nonhomogeneous (composite), anisotropic, thin curved layer with rapidly oscillating THERMAL EFFECTS material parameters and thickness is considered for the case when mean thickness 037149 Parabolic Shells Subjected to Solar and period scale have small magnitudes of the Radiation. Questions of the theory and same order. A three-dimensional analysis of parabolic shells under solar side and thermoelasticity problem for this layer is central illumination were considered. A reduced to a homogenized shell model by thermal balance equation was constructed means of an asymptotic homogenization incorporating the heat fluxes and coefficients method for periodic structures. This general of thermal conduction and radiation transfer model is applied to the derivation of along with expressions for the optical thermoelastic and thermal constitutive coefficients of metals. Equations were derived equations for network periodic shells. The for determining the temperature fields. Using relations obtained lay the foundation for a these fields, the stress-strain states for a new continuous model of thermoelasticity and parabolic shell closed at the apex and for the heat conductivity for network period shells domain of connection of the shell to a stiffener and plates. (Edited author abstract) 15 Refs. ring were examined. 6 Refs. Parton, Vladimir Z. (Moscow Inst of Chemical Gudramovich, V.S. (Acad of Sciences of the Engineering, Moscow, USSR); Kalamkarov, Ukrainian SSR, Dnepropetrovsk, USSR); Diskovskii, Aleksandr L. J Therm Stresses v 11 n 4 1989 l.A.; Sel'skii, Yu, S. Sov Appl Meeh v 23 n 11 May P 405-420. 1988 p 1043-1049. 037152 Stochastic Thermoelasticity of 037150 Transient Temperature Distribution Laminated Shells. The paper proposes a in an Internally and Externally Insulated theory and develops a numeric method for Cylindrical Shell. This paper presents the computing the stochastic characteristics of analytical solution for unsteady state stress fields in the layers of a multilayer shell temperature distribution in a cylindrical shell needed for estimating its reliability and having thin layer of thermal insulation coating longevity. The statistical characteristics of the at the inner and outer surfaces. The formula external temperature field are assumed to be has been derived assuming different initial known. Centered fields of temperatures and temperatures of shell and insulation coating displacements are considered, assuming that while the contact between them has also been the expectations of the fields have already assumed to be imperfect. The internal and been evaluated. The assumptions adopted in external surfaces of the shell and coatings are the construction of the theory are divided exposed to the convective boundary into three kinds. Thermophysical hypotheses: conditions of third kind. The generalized thermophysical parameters of the materials of formula obtained has been used to obtain the the layers are temperature independent. warming-up-period of the cylindrical wall of a Mechanical hypotheses: the rigid layers of a Diesel engine coated internally and externally multilayer shell conform to the Kirchhoff• by ceramic insulation material. A plot of Love hypothesis. Stochastic hypotheses: the

399 Excerpts from The Ennineerinn Index Annual 1989

statistical characteristics of displacement fields are calculated numerically, and the effects of and stress fields are analyzed in the the spinning of the shell on the free vibration framework of a correlation theory. The are studied. (Author abstract) 7 Refs. In external temperature field is a stationary Japanese. time-random, space-homogeneous field. Yamada, Cen; Kobayaski, Yukinori; Sawae, (Edited author abstract) 14 Refs. Tatsuhiro; Irie, Toshihiro. Nippon Kikai Gakkai Butko, A.M.; Novichkov, Yu.N. Mech Solids v 23 n Ronbunshu C Hen v 54 n 505 Sep 1988 p 2009-2015. 21988 p 133-143. 037155 Evaluation of the Modal Density of VIBRATIONS Paraboloidal and Similar Shells. Modal densities of various structures have been found 037153 Nonlinear Analysis of Doubly both theoretically in terms of expressions Curved Symmetrically Laminated Shallow involving integrals, and also experimentally. Shells with Rectangular Planform. A They are of interest to designers of, for multi-mode solution to the dynamic example, satellite aerials and spacecraft Marguerre-type nonlinear equations is structures. The theoretical method is presented for the nonlinear free vibration of hampered by the difficulty of evaluating the doubly curved, symmetrically laminated, integrals. For certain shells such as a thin imperfect shallow shells of rectangular plate, spherical cap or circular cylinder, the plan-form on a Winkler-Pasternak elastic integrals can be evaluated analytically. In this foundation. The shell edges are assumed to paper a numerical method is presented for be transversely supported and the variation of the computation of modal densities of other rotational stiffness is identical along opposite shell geometries, in particular the paraboloidal edges. Generalized double Fourier series with shell. Both the isotropic and honeycomb types time-dependent coefficients and the method are considered. Enough details of the of harmonic balance are used in the solution. numerical method are given to allow the The boundary condition for the varying reader to adapt it to other shapes for which rotational stiffness is fulfilled by replacement analytic integration is not possible. (Author of bending moments along the four edges by abstract) 3 Refs. an equivalent lateral pressure. Based on a Elliott, C.H. (Portsmouth Polytechnic, Portsmouth, single-mode approximation numerical results Engl). ] Sound Vib v 126 n 3 Nov 8 1988 P 477 -483. for the amplitude-frequency response of doubly curved isotropic, orthotropic, cross-ply 037156 Non-Linear Vibration Analysis of and angle-ply shallow shells with square Fluid-Filled Cylindrical Shells. A theoretical plan form are presented for various boundary analysis is presented for determining the conditions, material properties, curvature elastic non-linear vibrations of a prestressed ratios, initial imperfections, edge tensions, and thin-walled cylindrical shell filled with an ideal moduli of the elastic foundation. (Edited fluid. For the vibrations of the shell itself, the author abstract) 25 Refs. dynamic version of the Sanders non-linear Chia, C.Y. (Univ of Calgary, Calgary, Alberta, Can). equations for the case of moderately small Ing Arch v 58 n 4 1988 P 252 - 264. rotations is employed. Modal expansions are used for the displacements of the shell middle 037154 Free Vibration of a Spinning surface that are required to satisfy the Spherical Shell. An analysis is presented for 'classical simply supported' boundary the free vibration of a spinning spherical shell. conditions and the circumferential periodicity For this purpose, the governing equations and condition. The fluid is taken as non-viscous the boundary conditions of the shell are and incompressible, and the coupling between derived by applying Hamilton's principle to the deformable shell and this medium is taken the strain and kinetic energies of the shell. into account. The velocity potential is The variables in the equations can be written expanded in terms of harmonic functions as summation of the quasi-static components which satisfy the Laplace equation term by which are independent of time and the term. The Galerkin method is used to reduce dynamic ones. The linear equations on the the problem to a system of coupled algebraic vibration about the deformed state are solved non-linear equations for the modal amplitudes. by using the transfer matrix method. The Solutions are presented to show the effects of method is applied to a spinning clamped-free fluid and shell parameters on the non-linear spherical shell. The quasi-static and dynamic vibrations of the shell. (Author abstract) 27 displacement and the frequency parameters Refs.

400 Excerpts from The Engineering Index Annual 1989

Goncalves, P.B. (Pontificia Univ Catolica, Rio de for thick shells of revolution having Janerio, Braz); Batista, R.C. J Sound Vib v 127 n 1 meridionally varying curvature. Based on the Nov 221988 P 133-143. improved thick shell theory, the Lagrangian of the shells of revolution are obtained, and 037157 Hydroelastic Vibrations of Liquid• the equations of motion and the boundary Filled Finite Length, Rotating Cylindrical conditions are derived from the stationary Shells. A theoretical investigation is presented condition of the Lagrangian. The method is for the hydroelastic vibration of finite length, demonstrated for thick shells of revolution rotating cylindrical shells partially filled with having elliptical, cycloidal, parabolical, incompressible and nonviscous liquid. Gravity catenary and hyperbolical meridional and surface tension is neglected, while the curvature. The results by the present method initial tension due to the rotation is are compared with those by the thin shell considered. On the basis of the Fluegge-type theory and the effects of the rotary inertia equations, the shell with both edges clamped is and the shear deformation upon the natural analyzed by the variation of parameters. It is frequencies are clarified. (Author abstract) 11 found that the magnitude of the initial Refs. tension due to the centrifugal force depends Suzuki, Katsuyoshi; Yachita, Takumi; Kosawada, on the rotating speed and the quantity and Tadashi. Nippon Kikai Gakkai Ronbunshu C Hen v 54 density of liquid. The frequency increases n 508 Dec 1988 p 2822 - 2829. with the initial tension, while it decreases with the inertia of liquid. (Author abstract) 7 Refs. In Japanese. 037160 Asymmetric Vibrations of Shells of Revolution Having Meridionally Varying Tani, Junji; Zhang, Hebing. Nippon Kikai Gakkai Curvature and Thickness. An exact method Ronbunshu C Hen v 54 n 507 Nov 1988 P using power series expansions is presented for 2633-2639. solving asymmetric free vibration problems for shells of revolution having meridionally 037158 Theoretical and Experimental Study varying curvature and thickness. The of Vibrations of Thick Circular Cylindrical governing equations of motion and the Shells and Rings. The free vibrations of boundary conditions are derived from the thick circular cylindrical shells and rings are stationary conditions of the Lagrangian of the discussed in this paper. The well-known shells of revolution. The method is energy method, which is based on the demonstrated for shells of revolution having three-dimensional theory of elasticity, is used elliptical cycloidal, parabolical, catenary and in the derivation of the frequency equation of hyperbolical meridional curvature. The the shell. The frequency equation yields natural frequencies are numerically calculated resonant frequencies for all the for these shells having second degree circumferential modes of vibration, including thickness variation. (Author abstract) 8 Refs. the breathing and beam-type modes. In Japanese. Experimental investigations were carried out on several models in order to assess the Suzuki, Katsuyoshi; Miura, Kazuyuki; Kosawada, validity of the analysis. This paper first Tadashi. Nippon Kikai Gakkai Ronbunshu C Hen v 54 describes briefly the method of analysis. In n 508 Dec 1988 p 2830-2836. the end, the calculated frequencies are compared with the experimental values. A 037161 Free Vibration Analysis of Singly very close agreement between the theoretical Curved Shell by Spline Finite Strip and experimental values of the resonant Method. The spline finite strip method has frequencies for all the models was obtained been applied to the free vibration analysis of a and this validates the method of analysis. singly curved shell panel. The convergence of (Author abstract) 14 Refs. the method is reviewed. Additional numerical Singal, R.K. (Communications Research Cent, examples on shells of different geometrical Ottawa, Ont, Can); William, K. J Vib Acoust Stress shapes are employed to demonstrate the Reliab Des v 110 n 4 Oct 1988 p 533-537. accuracy and versatility of the method. Design charts showing the variations of the four 037159 Asymmetric Vibrations of Thick lowest modes with the geometry of such panels Shells of Revolution Having Meridionally are presented. (Edited author abstract) 20 Refs. Varying Curvature. An exact method using Cheung, Y.K. (Univ of Hong Kong, Hong Kong); power series expansions is presented for Li, W.Y.; Tham, L.G. J Sound Vib v 128 n 3 Feb 8 solving asymmetric free vibration problems 1989 P 411-422.

401 Excerpts from The Engineering Index Annual 1989

037162 Effect of Boundary Conditions on finitely deformed static state and the the Free Vibrations of Circular Cylindrical superposed secondary dynamical state which Shells. A simple formula for the natural are obtained, respectively, by the theory of frequency is derived as an asymptotic solution finite elasticity and the theory of small for the eigenvalue problems of the breathing deformations superposed on large, elastic type of free vibrations of a circular cylindrical deformations are solved analytically and in shell. It is applicable under any possible closed form to yield the frequency expression. combinations of the boundary conditions for Some numerical results are provided to study the simply supported, the clamped, and the the effect of several parameters. (Author free ends. A characteristic value involved in abstract) 12 Refs. the formula depends on the combination of Evirgen, H. (Cazi Univ, Ankara, Turk); Ertepinar, three representative boundary conditions A.J Sound Vib v 130 n 2 Apr 221989 P 177-187. SR(w = u = 0), SF(w = N = 0), and FR(N = S = 0), indicating that the free vibration 037165 Vibration Analysis of Thick characteristics depend on whether an end is Rotating Cylindrical Shells Based on the free or supported and whether the supported Two-dimensional Elasticity Theory. Vibra• end is allowed or not to move freely in the tion analysis of infinite thick rotating axial direction. The accuracy of the formula is cylindrical shells is described on the basis of examined by a comparison with numerical the two-dimensional elasticity theory. Starting solutions and experimental results. (Author from the state of plane strain, the basic abstract) 9 Refs. equation in the steady rotating state, which is Koga, Tatsuzo (Univ of Tsukuba, Tsukuba, Jpn). used to obtain the initial stresses, is derived AIAAJ v 26 n 11 Nov 1988 P 1387-1394. from Hamilton's principle, and the frequency equation, including the effect of the initial 037163 Inextensional Free Vibrations of stresses due to the rotation, is formulated by Circular Cylindrical Shells. Asymptotic Ritz's method. The numerical results for the solutions are obtained for the eigenvalue frequencies in the non-rotating and rotating problems of the inextensional free vibrations state are compared with those based on of circular cylindrical shells, considering all 45 Timoshenko type shell theory and the possible combinations of the boundary available range in the latter theory is conditions, characterizing the simply examined about the thickness and rotating supported, the clamped, and the free ends. In speed of a shell. (Author abstract) 7 Refs. In addition to the well-known L. Rayleigh and Japanese. A.E.H. Love types of inextensional vibrations Saito, Takashi; Endo, Mitsuru; Fujimoto, Kohji. for shells with the free ends, a type Nippon Kikai Gakkai Ronbunshu C Hen v 55 n 511 represented by a linear combination of those Mar 1989 p 525-53l. classical ones is found in cases where one end is free and the other is supported in such a manner that it can move freely in the axial 037166 Free Vibration Analysis of Coupled direction. The existence of the three types of External Fluid-Elastic Cylindrical Shell• inextensional mode is proved by an Internal Fluid Systems. The free vibrations experiment, and the mode shapes are of an infinitely long cylindrical shell under visualized by holographic interferometry. axisymmetrical hydrodynamic pressures due to (Author abstract) 7 Refs. external and internal fluids are studied Koga, Tatsuzo (Univ of Tsukuba, Tsukuba, Jpn); theoretically. The basic equations of motion Saito, Arihumi. AIAA J v 26 n 12 Dec 1988 p for axisymmetric vibrations of such a shell are 1499-1505. given, based on the bending theory. These equations are solved analytically by means of 037164 Small Radial Vibrations of Layered, Fourier cosine transformation, and the general H yperelastic, Spherical Shells of Arbitrary frequency equation for the coupled systems is Wall Thickness Subjected to Finite, Initial obtained by consideration of the dynamic Radial Deformations. Small, radial vibrations interaction between the shell surface and fluids. of layered spherical shells of arbitrary wall Furthermore, seven cases are derived from the thickness and subjected to initial external general coupled frequency equation. The and/or internal pressure causing finite radial general frequency equation is calculated for deformations are investigated. The material of some kinds of mass density of the internal each layer is assumed to be of neo-Hookean fluid. (Edited author abstract) 6 Refs. type. The governing equations of both the Endo, Ryuji (Inst of Vocational Training, Aihara,

402 Excerpts from The Enaineerina Index Annual J 989

Jpn); Tosaka, Nobuyoshi. jSME Int j SeT 1 v 32 n 2 of circular cylindrical shells, which are used in Apr 1989p217-221. centrifugal separators to enrich uranium, and rotating at higher speeds, it is considered that 037167 Dynamic Stability of Fluid-Coupled circular cylindrical shells are connected with Coaxial Cylindrical Shells under Vertical bellows. Vibration analysis of circular Excitation. Theoretical analyses are presented cylindrical shells connected with bellows is for the dynamic stability of a free-clamped carried out by the substructure synthesis coaxial cylindrical shell partially filled in the method for various numbers and dispositions annular gap with incompressible, in viscid of bellows, and the optimum ones are liquid and subjected to vertical excitation. The examined. Moreover, the transfer matrix dynamic version of the Donnell equations and method, by which the critical speeds are simply the velocity potential theory are used for the obtained, is described and the results are motions of the shell and the liquid, respectively. examined by the substructure synthesis The problem is solved by using the modified method. (Author abstract) 5 Refs. In Japanese. Galerkin method so as to satisfy the boundary Saito, Takashi; Endo, Mitsuru; Yachigo, Katsuyuki. conditions, and the governing equation is Nippon Kikai Gakkai Ronbunshu C Hen v 55 512 Apr reduced to a type of coupled Mathieu's 1989 p 887 -893. equation. The instability boundaries where parametric resonance occurs are determined 037170 Vibrations of a Cylindrical Shell by using Hsu's method. It is found that a Acted Upon by Concentrated Loads. We set principal instability resonance and a up Green's matrix of harmonic vibrations of a combination instability resonance of the sum circular cylindrical shell of finite length with type of two natural vibrations, each of which hinging conditions on the edges. The solution has the same circumferential wave number and is represented by a trigonometric Fourier different axial mode of vibration, are likely to series in the circumferential coordinate. The occur. (Edited author abstract) 6 Refs. In coefficients of the series are expressed in Japanese. terms of elementary functions. The response Tani, Junji; Sakai, Tatsuyoshi; Chiba, Masakatsu. of shells of infinite and finite length to Nippon Kikai Gakkai Ronbunshu C Hen v 55 n 512 Apr concentrated actions is compared. The 1989 p 870-876. solution obtained is the kernel of the integral equations of contact problems of shell 037168 Vibration Analysis of Thick Rotating vibrations. It also enables us, by using simple Prestressed Cylindrical Shells (1st Report. integration, to calculate the amplitude of The Case of Exposure to an Initial Torque). oscillation of a shell acted upon by arbitrarily Vibration analysis of thick rotating cylindrical distributed surface loads. (Author abstract) 8 shells subjected to an initial torque is Refs. described. The basic equations, including the Averbukh, A.Z.; Mavlyutov, I.G. Meeh Solids v 23 effects of the initial tensions and resultant n 51988 P 130-135. shear stresses due to rotation, torque, external pressure and axial compression load, are 037171 Free Vibrations of the Rotating derived by the Timoshenko-type shell theory. Shells of Revolution. This paper is devoted By the modified Galerkin's method, frequency to the problems of free vibrations of thin analysis is carried out for four boundary con• rotating shells. The theory of vibration of ditions (i.e., both ends (A) clamped with axial rotating shells is part of the theory of an constraint. (B) Simply supported without arbitrary rotating body and the results which axial constraint. (C) Simply supported with are valid for an arbitrary body are also valid axial constraint and (D) clamped without axial for the shells. Though numerical methods are constraint). Numerical results are compared the main approach to the investigation of the with those based on the Flugge-type shell dynamics of rotating bodies, some analytical theory and the difference between both results have been obtained for some simple theories is examined. (Author abstract) 6 Refs. bodies like rotating beams and discs. The In Japanese. mathematical theory of nonrotating thin shells Saito, Takashi; Endo, Mitsuru. Nippon Kikai Gakkai is well developed. Several of the most Ronbunshu C Hen v 55 n 512 Apr 1989 p 878-885. successful are two-dimensional theories of the Kirchoff-Love type. The aim of this paper is 037169 Vibration Analysis of Cylindrical to apply asymptotic methods to the solution of Shells Connected with Bellows. For the the eigenvalue problem for a rotating shell. purpose of decreasing the lower critical speed The authors use Novozhilov's two-dimensional

403 Excerpts from The Engineering Index Annual 1989

shell theory to obtain the equations of the inconsistencies in the mathematical analysis vibration of the shell and the theory of carried out by Evensen and also in the asymptotic integration of the differential physical behavior of the three-term model of equation to solve the eigenvalue problem for Dowell and Ventres. The comments made by these equations. 23 Refs. Prathap led to reinvestigation of the earlier Smirnov, Andrei (Leningrad Univ, Leningrad, problem in the present study. The USSR).] Appl Meeh Trans ASME v 56 n 2 Jun 1989 axisymmetric part of the assumed deflected p 423-429. shape plays an important role in the nonlinear behavior of the shell, and so two appropriate 037172 Dynamic Boundary Layer in three-term mode shapes for the transverse Problems of Vibration of Shells. Within the displacement are chosen. The modal equations framework of the three-dimensional theory, obtained by the Galerkin method are solved the authors consider a thin elastic by the fourth-order Runge-Kutta method to axisymmetric shell of revolution of arbitrary obtain the amplitude-frequency relationship. profile, that executes steady-state oscillations The numerical results based on the present under the action of an edge load. It was study and on the analysis of Evensen are established on the basis of the equations of compared with the existing experimental the classical two-dimensional theory, that for values. (Edited author abstract) 10 Refs. fixed m and increasing w the variability of the Varadan, T.K. (Indian Inst of Technology, Madras, stress-strain state of the shell increases, and India); Prathap, G.; Ramani, H.V. AIAA] v 27 n 9 there exist critical frequency values above Sep 1989 p 1303-1304. which the solution of the force-oscillation problem becomes a solution of differing 037175 Free Vibrations of Circular variability. In this paper, the authors consider Cylindrical Shells. The eigenvalue problem approximate methods of setting up solutions of the free vibrations of thin elastic circular of differing variability for the equations of cylindrical shells is a well-established classical elasticity, and consider the use of such topic in structural mechanics. All the solutions for purposes of approximate characteristic values of interest can now be investigation of forced oscillations of shells at calculated to a desired degree of accuracy as frequencies that preclude the use of the routine work with the aid of high-speed classical two-dimensional theory. 5 Refs. digital computers. A number of analytical Gol'denveizer, A.L. (Kaplunov, Yu.D.) Meeh Solids v solutions have been proposed, and they may 23 n 41988 P 146-155. help us gain good insight into the physical nature underlying the numerical data. This 037173 Spline Finite Element for paper reviews the historical background and Axisymmetric Free Vibrations of Shells of provides a unified view of the current state of Revolution. A new isoparametric element the art through asymptotic solutions recently suitable for the analysis of axisymmetric free obtained by the author. Emphasis is placed on vibrations of shells of revolution is developed the effects of the boundary conditions. in this paper. This element, which is based on (Edited author abstract) 33 Refs. classical thin shell theory, employs a set of Koga, Tatsuzo (Univ of Tsukuba, Tsukuba, Jpn). B-spline shape functions for the interpolation ]SME Int] Ser 1 v 32 n 3 Jul 1989 P 311-319. of the geometry as well as the displacements. It inherits the merits of both the finite 037176 Improved Multi-Segmental Transfer element method and spline interpolation. The Matrix Method for Closed Axisymmetric efficiency and accuracy of the proposed Shells. In literature the vibrating problem of element are illustrated by examples in the thin, elastic axisymmetric shells is modeled by paper. (Author abstract) 20 Refs. a set of ordinary differential equations, which Fan, S.C. (Nanyang Technological Inst, Singapore); are singular at closed ends. This paper Luah, M.H.] Sound Vib v 132 n 1 Jul 8 1989 P presents an improved multi-segmental transfer 61-72. matrix method to overcome the numerical difficulties resulted from the singularities. 037174 Nonlinear Free Flexural Vibration Examples are given for the calculations of of Thin Circular Cylindrical Shells. The several typical axisymmetric shells. (Author early development on the topic of nonlinear abstract) 5 Refs. vibrations of isotropic circular cylindrical Jian, Zhao (Zhong Shan Univ, Guangzhou, China); shells is well documented by Evensen. Hong-zhen, Wang; Wu-hua, Zhu. Proe Int Offshore Subsequently, Prathap pointed out some Meeh Aret Eng Symp v II (of VI), Proceedings of the

404 Excerpts from The Enaineerina Index Annual 1989

Eighth International Conference on Offshore BirIik, G.A. (Middle East Technical Univ, Ankara, Mechanics and Arctic Engineering-1989, Hague, Turk); Mengi, Y.] Sound Vib v 130 n 1 Apr 8 1989 Neth, Mar 19-23 1989. Publ by American Soc of P 69-77. Mechanical Engineers (ASME), New York, NY, USA, 1989 P 713-718. WA VE EFFECTS

VISCOELASTICITY 037179 Wave Forces on Hemicylinders. 037177 Refined Dynamic Theory for Potential solutions describing the flow about Viscoelastic Cylindrical Shells and two-dimensional marine structures on or near the ocean bottom are formulated, based on Cylindrical Laminated Composites, Part 1: Airy's wave model. The solutions for a General Theory. Through the use of a new half-cylinder and semicircular shell are technique, approximate theories are developed considered in detail and evaluated in the case for the dynamic response of viscoelastic cylindrical shells and cylindrical laminated of deep submergence. The formulation with and without flow underneath the structure is composites. The work is divided into two given and, in particular, the existence of a parts. The first part is devoted to the large difference between the two cases in. the development of the approximate theories and vertical forces is shown. The effect of the second part to the assessment. In this introducing vorticity at the edges of the shell part, first the approximate equations of a is investigated. Numerical results for single viscoelastic cylindrical shell are derived. Then, a discrete model (DM) is proposed for hemicylinders resting on the bottom and slightly raised off the bottom are presented. a composite made of viscoelastic laminae. In establishing DM, it is noted that the equations The results obtained for the wave forces are of a single shell hold also in each lamina of compared with experimental results obtained the composite. The equations of DM are for a slightly raised, open hemicylinder. completed by adding the interface continuity (Author abstract) 17 Refs. conditions to the above-mentioned equations. Chakrabarti, Subrata K. (CBI Research Corp, Finally, a continuum model (CM) is developed Plainfield, IL, USA); Naftzger, Rober A. Ocean Eng for a composite shell made of two alternating (Pergamon) v 16 n 1 1989 P 49-69. layers by using a smoothing operation. eM simplifies the determination of dynamic WIND EFFECTS behavior of composite shells when the number of laminae is large. (Edited author abstract) 037180 Stability of Wind-Loaded Cylindrical 10 Refs. Shells. Stability analysis of perfect and Mengi, Y. (Cukurova Univ, Adana, Turk); Birlik, imperfect cylindrical shells under wind pressures is performed using the finite element G.A.] Sound Vib v 130 n 1 Apr 81989 P 55-67. method. A 48 degree-of-freedom thin shell 037178 Refined Dynamic Theory for element previously developed by the present Viscoelastic Cylindrical Shells and authors is used. The element is free from Cylindrical Laminated Composites, Part 2: both shear and membrane locking and is An Application. In this study, the general capable of modelling shells with arbitrary approximate theory developed in Part 1 for imperfections. Nonlinear effects due to shells is assessed for axially symmetric elastic prebuckling rotations are taken into account. waves propagating in a dosed circular The nonlinear response is obtained using cylindrical shell (hollow rod). The spectra Riks-Wempner algorithm. Effects of the predicted by zeroth and second order imperfection amplitude and that of the approximate theories are determined for material orthotropy on the limit load points various values of shell thicknesses and the are studied. Wherever possible, the present Poisson ratios and they are compared with results are compared with existing results. A those of exact theory. It is found that the favorable agreement is observed. (Author agreement between the two is good. abstract) 17 Refs. Approximate and exact cut-off frequencies Kapania, Rakesh K. (Virginia Polytechnic Inst & match almost exactly. The approximate State Univ, Blacksburg, VA, USA); Yang, T.Y.] theory is valid for thin as well as thick shells. Wind Eng Ind Aerodyn v 28 pt 1 n 1-3 Aug 1988 These results, which are obtained without Proceedings of the 7th International Congress on using correction factors, give an indication of Wind Engineering, Held under the Auspices of the the power of the general theories proposed in International Association for Wind Engineering, Part 1. (Author abstract) 6 Refs. Aachen, West Ger,juI6-10 1987. p 281-290.

405 Selected Biblionraphy

AasJakobsen, A. 1973. Beitrag zur Theorie der Allen,]. E. Construction of long-span concrete Kugelschale auf Binzelstutzen, 22. Ingenieur arch hangar at Limestone Airforce Base. J. Archiv. ACI vol. 21 (1950): 405. Abu Ghazeleh, B.N. 1966. Analysis of plate Apeland, K. and Popov, E. V. 1962. Analysis of type prismatic structures, Ph.D. Diss. Uni• bending stresses in translation shells. Proceed• versity of California, Berkeley. ings, Colloquium on Simplified Calculation ACI Building Code Requirements for Rein• Methods. Brussels. Amsterdam: North-HoI• forced Concrete (ACI 318-89) and Com• land Publishing Company, Sept. 1961, p. 9. mentary-ACI 318R-89. ACI Committee 334. Concrete Shell Structures Baker, E. H. 1964. Analysis of symmetrically -Practice and Commentary. Proceedings, loaded sandwich cylinder. J. American Insti• ACI. (Detroit) vol. 61, no. 9 (Sept. 1964): tute Aeronautics Astronautics. Oan.). 1091-1108. --- ; Capelli, A. P.; Kovalevsky, L.; Rish, F. L.; and Verette, R. M., 1968. Shell Analysis Adler, F., and Lusher,]. K. 1967. The analysis Manual. NASA CR-912 (April). and design ofWrexham swimming pool shell Batdorf, S. B. 1974. A simplified method of roof. Proceedings, International Congress on elastic stability analysis for thin cylindrical the Application of Shells in Architecture, shells. NASA Report 874. Mexico City. Bauserfeld, W. 1963. Development of the Zeiss• Ahmad, S.; Irons, B. M., and Zienkiewicz, o. C. Dywidag Process. Shell Architecture. New 1969. Curved thick shell and membrane ele• York: Reinhold, 281-83. ments with particular reference to axi-sym• Becker, Wiliam C. E. 1955. St. Louis air termi• metric problems. Proceedings, Second Con• nal, intersecting ribs carry concrete shell ference on Matrix Methods in Structural roof. Civil Engineering no. 7: 58. Mechanics, Air Force Institute of Technol• --- . 1962. Elastic stability of orthopedic ogy, Wright-Patterson Air Force Base, Ohio shells. J. Aerospace Science vol. 29, no. 5 (Oct. 1968). Also available in AFFDL-TR- (May). 68-150 (Dec. 1969). Beles, Aurel A., and Soare, Mircea, 1964. Aimond, F. 1936. Etude statique des voiles Paraboloidul Eliptic si Hiperbolic in Con• minces in parabolodide hyperbolique travail• structii. Editura Academiei Populare Romine. lantsans flexion. Memoires, Association Inter• In Romanian. Bethlehem Steel Corp. 1968. nationale des Ponts et Charpentes (Zurich). Cable Roof Structures. Bull. 5 (Feb.). Aldstedt, E. 1969. Shell analysis using planar Bill, Max. 1969. Robert Maillart, Bridges and triangular elements. Finite Element Methods Constructions. 3 ed. New York: Frederick A. in Stress Analysis. I. Holand and K. Bell, eds. Praeger, 184. (Trondheim, Norway: TAPIR 1969), --- . 1969. Robert Maillart. 3 ed. Zurich: 255-86. Les Editions d' Architecture (Artemis).

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--- . Skew shell utilized in unusual roof. --- . Les Paraboloides Hyperboliques et les ACI. (Mar.):657 ff. Coques en Beton Arme. Aujourd'hui no. --- . 1954. Construccion. Caracas. Ouly). 23:62 ff. --- . The shell as a space encloser. Proceed- --- . Strutture e strutturalismo. Casabella ings, Conference on Thin Concrete Shells. no. 232:48 ff. MIT Oune):5 ff. --- . Weg zu einer neuen Strukturauffas• --- . Stereo-structures. Progressive Architec• sung. Bauknust und Werkform no. 9:466 ff. ture. Oune):84 ff. --- . 1985. En Defensa del Formalismo. Y --- . Structural digressions around style in Otros Escutos. Xarait Ediciones, pp. 172. architecture. Student Publications, School of Cantin, R., and Clough, R. 1968. A curved cy• Design, North Carolina State College, vol. 5, lindrical shell discrete element. AIAAJournal no. 1:18 ff. vol. 6, no. 5 (May): 1057 - 68. --- . Toward a new philosophy of struc• Carr, A. j., and Clough, R. W. 1969. Dynamic tures. Student Publications, School of De• earthquake behavior of shell roofs. Proceed• sign, North Carolina State College, vol. 5, ings, Fourth World Conference on Earth• no. 3:2 ff. quake Engineering, Santiago, Chile Oan.). --- . Warped surfaces. Proceedings, Confer• Cauchy, A. 1828. Sur l'equilibre et Ie mouve• ence on Thin Concrete Shells. MIT, June. ment d'une plaque solide. Exercise de mathi• 91 ff. matique. (10) 3. --- . 1955. Durmientes de Concrete Pre• Chetty, S. M. K., and Tottenham, H. 1964. An tensado. La Construccion Moderna. July. investigation into the bending analysis of hy• ---. Estructuras Laminares Parabolico• perbolic paraboloid shells. Indian Concrete hiperbolicas. In/ormes de la Construccion no. Journal. Bombay, vol. 38, no. 7:248-58. 76 (Dec.). Cheung, Y. K. 1969. Folded plate structures by --- . II Gusico Sinonimo della Delimita• finite strip method. Proceedings, ACSE vol. zione dello Spazio. Civilta della Machine no. 95, ST12 (Dec.):2963-79. 5:35 ff. Chinn, j. 1959. Cylindrical shell analysis simpli• --- . Structural applications of hyperbolic fied by beam method. J. ACI, Proceedings, paraboloidal shells. ACI. Oan.):397 ff. vol. 55, no. 11 (May):1l83-92. --- . Thin shell roofs for large buildings. Chronowicz, A. 1963. Reinforced concrete Consulting Engineer. (May):35 ff. roof to swimming pool. Civil Engineering --- . Toward a new philosophy of struc• and Public Works Review, London, vol. 58 tures. Student Publications, School of De• (Mar.):319-24. sign, North Carolina State College, vol. 6, Chu, K. H., and Pinjarkar, S. G. 1966. Multiple no. 1:16 ff. folded plate structures. Proceedings, ASCE --- . 1956. Iglesia de la Virgen Milagrosa. vol. 92, ST2 (Apr.):297 -321. In/ormes se la Construccion no. 86 (Dec.): 140 Clebsch, A. 1883. Theorie de I'elasticite des ff. corps soli des. Paris, Translated from the --- . Intuition as synthesis. Dimension, Stu• German, with notes by B. de St. Vanant. dent Publications, College of Architecture Clough, R. W., and Johnson, C. P. 1971. Finite and Design, University of Michigan element analysis of arbitrary thin shells. Sym• (Feb.):50 ff. posium, concrete thin shells, American Con• --- . Les Voutes Minces et I'Espace Archi• crete Institute, SP-28:333-64. tectural. L'Architecture d'Aujourd'hui no. 64: Collins, P. 1960. Antonio Gaudi. New York: 22 ff. Braziller, 24. --- . Toward a new structure. Architectural --- . 1964. Concrete shell structures, prac• Forum. (Feb.):82 ff. tice and commentary. Report of ACI Com• --- . 1957. Lezioni di Modestia. L'Architet• mittee 334, J. ACI vol. 61, no. 9 tura no. 22:218. (Sept.): 11 04. --- . 1958. Cascarones de Hormigon Ar• Connor, j. j., and Will, G. T. 1969. A mixed mado, Ingenieria Internacional Construccion. finite element shallow shell formulation. Pro• New York, June, August, Manuel del Con• ceedings, U. S.-Japan Seminar on Matrix structor. 3 ff. Methods of Structural Analysis and Design, --- . Understanding the hyperbolic para• Tokyo, (Sept.). boloid. Architectural record. Ouly): 191 ff. --- , and Brebbia, C. 1967. Stiffness ma• (Aug.):205 ff. trix for shallow rectangular shell element. --- . 1959. EI Arquitecto Felix Candela. Proceedings, ASCE vol. 93, EM5 (Oct.): Viajes. Mexico City, no. 41:22 ff. 43-65.

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--- . 1959. La Construction Moderne. Spe• concrete elements. Bull. International Asso• cial No.: Le Palais des Expositions du ciation for Shell Structures, no. 3 A-12 C.N.LT., no. 1. (Madrid). Cowan, H. J. 1961. Some applications of the use Das Gupta, N. C. 1962. Edge disturbances in a of direct model analysis in the design of ar• hyperbolic paraboloid. Civil Engineering and chitecutral structures. Journal of the Institu• Public Works Review. London, vol. 58 (Feb. tion of Engineers, Australia Ouly-Aug.). 1963):220-22. Creasy, L. R. 1961. Prestressed concrete cylin• --- . 1962. Using finite difference equa• drical tanks. New York: John Wiley & Sons. tions to find the stresses in hypar shells. Civil Cretu, Mircea. 1963. Criteria for the design of Engineering and Public Works Review. Lon• reinforced concrete shell structures and don, vol. 56 (Feb. 1961):199-201. folded plates. New Delhi: Indian Standard Dayaratnam, P., and Gerstle, Kurt H. 1964. Institution, Indian Standard 2210-1962. Buckling of hyperbolic paraboloids. Pro• Croll, J. G. A., and Scrivener, J. C. 1969. Edge ceedings, World Conference on Shell Struc• Effects in Hyperbolic Paraboloid Shells. Pro• tures, San Francisco, Oct. 1-4 1962. Wash• ceedings, ASCE vol. 95, ST3 (Mar.):457 -78. ington D.C. National Academy of Sciences• --- . Convergence of hypar finite differ• National Research Council Publication ence solutions. Proceedings, ASCE vol. 95, 1187: 289-96. ST5 (May):809-30. De Cossio, R. D. 1961. Discussion of the paper Crowley, F. X. 1969. Precast 150 ft. diameter "hyperbolic paraboloidal umbrella shells dome. J. ACI, Proceedings vol. 66, no. 9 under vertical loads" by H. P. Harrenstien. (Sept.):698 -702. J. ACI vol. 32, no. 12 Oune):1603. Csonka, P. 1955. Calculations of calotte shells DeFries-Skene, A., and Scordelis A. C. 1964. over rectangular bases. Acta Technica. Aka• Direct stiffness solution for folded plates. demiae Scientiarum Hungaricae, Budapest. Proceedings, ASCE vol. 90, ST4 (Aug.): Tomus XI, Fasciculi 3-4. 15-47. --. 1956. The buckling of spheroidal Dickson, J. N., and Brolliar, R. H. 1966. The shell curved in two directions. Acta Technica. general instability of ring-stiffened corru• Akaademiae Scientiarum Hungaricae, Buda• gated cylinders under axial compression. pest. vol. 14, no. 3-4:25-37. NASA, TND-3089 Oan.). Dischinger, Franz. 1925. Fortschritte im Bau Dabrowski, Ryszard. 1963. Analysis of pre• von Massivkuppeln. Bauingenieur no. 10: stressed cylindrical shell roofs. Journal of the 362. Also Deutsche Bauzeitung, no. 49 Structural Division, Proceedings, ASCE, ST-5 (1925). (Oct.). --- . 1927. Eine Neue Konstruktion fur Daganoff, Ilia. 1957. Der Sweigelenkbogen mit Grossmarkthallen in Leipzig. Deutsche Bau• parabelformiger Achse unter der Wirkung zeitung no. 23:161. von Schalenlasten. Bautechnik no. 2:49. ---. 1928. Schalen-und Rippenkuppein. 1958. Vorgefertigte, doppelt Handbuch fur den Eisenbetonbau. F. Em• gekrummte Schalenkonstruktionen. Proceed• perger, ed. 4 ed. vol. 6. Berlin: Ernst und ings, Second Symposium on Concrete Shell Sohn. Roof Construction, Oslo Ouly 1-3, 1957). --- . 1929. Die Theorie de Vieleckkuppein ---. 1959. Schalen und Faltwerkdacher und die Zusammenhange mit einbeschrie• aus vorgefertigten, zusammengespannten benen Rotationsschalen. Beton und Eisen nos. Stahlbetonelementen. Bauplanug no. 10:441 5,6, 8, 9:100 ff., 119 ff., 150 ff., 169 ff. ff; no. 11:511 ff. --- . 1930. Eisenbetonsc alendacher Zeiss• --- . Der Zweigelenkbogen mit kreisfor• Dywidag zur Uberdachung Weitgespannter miger Achse unter der Wirkung von Scha• Raume. Lecture, Liege, 1930. Also Tech• lenlasten. Bautechnik no. 6:235. nique des Travaux (Dec.). ---. 1961. Betrachtungen uber die Be• --- . Die Grossmarkthalle Leipzig. Verein rechnungsverfahren Rechteckiger Kugleca• Deutscher Ingenieure. Zeitschrift no. 1. lotten. Proceedings, International Collo• --- . 1932. Shells. Grosstroiizdat. quium on Simplified Calculation Methods, --- . 1935. Die strenge Theorie der Kreis- International Association for Shell Struc• zylinderschale in ihrer Anwendung auf die tures, Brussels (Sept. 4-6). Zeiss-Dywidag-Schalen. Beton und Eisen nos. Daganoff, Ilia; Hoffman, Claus; and Ruhle, 16, 18:257 ff., 283 ff. Herrmann. 1960. Shell and fold structure --- . 1936. Der Spannungszustand in af• roofs out of precast, prestressed reinforced finen Schalen und Raumfachwerken unter

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Anwendung des Prinzips des statischen Mas• sports a lavish design at record costs Oune senaugleichs. Bauingerieur nos. 23 - 28:228 10):22-37. ff. Ergauoudis, I.; Irongs, B. M.; and Zienkiewicz, --- . 1950. Neue Wege im Stahlbetonbau O. C. 1968. Cured isoparametric, "Quadri• (Bogenstaum aus Zylinderschalen). Deutscher lateral" elements for finite element analysis. Betonverein, Vortrage auf der Hauptversam• Intern. J. of Solids and Structures vol. 4 Lon• mung (14 ff.). don: Pergamon Press. --- . Schlenkuppel mit 72 m Spannweite Esquillan, Nicholas. 1952. Le hangar a deux (Mod. Projket fur die Bunaweke). Bau• nefs de 101,50 m de portee de l'Aeroport de planug-Bautechnik no. 6: 191 ff. Marignane. Annales de l'Institute Technique --- , and Finsterwalder, Ulrich. 1928. Ei• due Batiment et des Travaux Publics no. 57 senbetonschalen System Zeiss-Dywidag. (Sept.). Bauingenieur nos. 44-46:807 ff., 823 ff., --- . 1958. The design and construction of 842 ff. the shell roof of the exhibition palace of the --- . 1929. Die Frankfurter Grossmark• National Center of Industries and Technol• thalle. lement, no. 12. ogy, Paris. Cement and Concrete Associa• Distefano, N., and Torregiani, C. 1966. A sim• tion, London (Dec.). plified method to evaluate critical loads of --- . 1959. C.N.I.T. Paris. Informes de la hyperbolic paraboloidal shells. Proceedings, Construccion III (May). Symposium on Shell Structures in Engineer• Evan-Iwanowski, R. M.; Cheng, H. S.; and Loo, ing Proactive, Budapest, 1965, Epitestudo• T. C. 1962. Experimental investigations and menyi Intazet. deformation and stability of spherical shells Dong, S. B. 1966. Analysis of laminated shells subjected to concentrated loads at the apex. of revolution. Proceedings, ASCE vol. 92, Proceedings, 4th U.S. Natl. Eng. Appl. Mech.: EM6 (Dec.):135-55. 563-75. Donnell, L. H. 1934. A new theory for the buckling of thin cylinders under axial com• Feber, C. 1963. Candela: The Shell Builder. New pression and bending. Transactions of the York: Van Nostrand Reinhold. American Society of Mechanical Engineers vol. Finsterwalder, Ulrich. 1926. Die Dywidaghalle 56:108. auf der Gesolei. Bauingenieur no. 48:929. --- ,and Wan, C. C. 1950. Effect of imper• Fitch, J. R. 1968. The buckling and post-buck• fections of buckling of thin cylinders and col• ling behavior of spherical caps under con• umns under axial compression. Applied Me• centrated load. Intern. J. of Solids and Struc• chanics vol. 17, no. 1 (Mar.). tures vol. 4, no. 4(Apr.):421-46. Dubois, F. 1917, Uber die Festigkeit der Ku• Fletcher, Sir B. 1967. A History of Architecture, gelschale. Zurich: Promotionsarbeit. 17 ed. Rev. by R. A. Cordingley, New York: Charles Schribner's Sons, 198. E/AC EASE. 1969. Elastic analysis for str"uc• Flint, A. R., and Low, A. E. 1960. The con• tural engineering. Program Applications struction of hyperbolic paraboloid type shells Guide. Data Centers Division, Control Data without temporary formwork. Bull. Interna• Corporation (Aug.). tional Association for Shell Structures, Ma• --- . Elastic Analysis for Structural Engi• drid, no. 4, paper no. A-15. neering. Program User's Manual. Data Flugge, Wilhelm. 1957. Statik und Dynamic der Centers Division, Control Data Corporation Schalen Berlin: Springer-Verlag OHG. (Aug.). ---. 1960. Stresses in Shells. Berlin: Engineering News Record. 1956. Dome roof Springer-Verlag. formed on mound needs no shoring vol. 157 Fuchssteiner, Wilhelm. 1954. Die Berechnung (Sept. 27):35 ff. von Industriesc ornsteinen mit Fuchsoffnun• --- . 1957. Biggest wood dome span 300 gen. Bauingenieur no. 7. feet vol. 158 Oan. 10):32 ff. --- . 1955. Kreiszylinderschalen: Die ele• --- . 1960. For an economical roof: precast men tare Behandlung der Kampferrandstor• barrels vol. 165, no. 12 (Sept. 15):42-44. ungen. Beton-und Stahlbetonbau no. 5. --- . 1964. Flying buttress holds off thrust --- . 1960. Kreiszylinderschalen, Berech• from precast, pleated half-dome vol. 173 nung mit Polynomen. Benton-und Stahlbeton• (Nov. 19):40-42. bau no. 5. --- . 1965. Precast dome spans 202 feet --- , and Schader, Alois. 1956. Allege• vol. 174, no. 4 Oan. 8):66 - 67. meine Schalengrundgleichungen. Beton-und ---. 1976. Montreal's XXI Olympiad Stahlbetonbau no. 7.

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417 Selected Bibliography

Brussels World Fair. Philips Technical Review and Reiss, Max. 1962. Analysis of vol. 20, no. 1. Eindhoven, Netherlands: folded plates. J. Struct. Div., ASCE vol. 88 1958-1959. (Oct.).

Wacker, Rhodes, J. (ed.). 1982. Developments in thin-walled structures. London: Applied Science Publishers. Zabrowski, Robert. 1949. Hangars are what Waling, J. L.; Ziegler, Earl E.; and Kemmer, you make them. Airports and Air Carriers Harry G. 1962. Hypar shell construction by (Feb.). offset wire methods. Proceedings, World --- . 1951. Thin shell arch hockey stadium Conference on Shell Structures. Oct. 1-4, for Quebec built in ten months. Civil Engi• 1962, San Francisco. Washington D.C.: Na• neering (Oct.) tional Academy of Sciences-National Re• --- ,and Gruenwald, Ott. 1944 Monolithic search Council Publication 1187:453. concrete seaplane hangars, unique design Waller, J. H. de W., and Aston, A. C. 1953. used by East Coast Naval Air Station. Civil Corrugated concrete shell roofs. Proceedings, Engineering no. 8 (Aug.). Institution of Civil Engineers vol. 2, part 3 --- . 1954. A review of special aspects. Pro• (Aug.):153-82. ceedings, Conference on Thin Concrete Wang, L. R. L. 1966. Effects of edge restraint Shells, MIT, June. on the stability of spherical caps. J. American Zalewsky, Waclaw. 1957. Niektore nowe kon• Institute ofAeronautics and Astronautics vol. 4, strukcje Iupinowe w budownictwie przemys• no. 4 (Apr.):718-19. lowym w Polsce. Inzynieria i Budownictwo no. Wayss, G. A. 1887. Das System Monier. Berlin. 3:116 ff. Pp. 33-34 and 117 -26. --- . 1959. Vorgefertigte Stahlbetonkon• Wells, J. G. 1958. Reinforced concrete struc• struktion fur eine Textilfabrik in Kalisch. tures: flat slabs and concrete shell roofs. Bauwelt no. 47:1388 ff. M.A. thesis, School of Architecture, Univer• --- . North-light shel roofs in Poland. Con• sity of California. crete and Constructional Engineering (Apr.). Wempner, G; Oden,J. T.; and Kross, D. 1968. --- . Shell and spacial structure shapes ap• Finite-element analysis of thin-shells. Pro• plied in Poland. International Colloquium on ceedings, ASCE vol. 94, EM6 (Dec.):1273. Construction Processes of Shell Structures .. Whitney, Charles S. 1950. Wide spanning mon• Paper A-II. Madrid. olithic arches in North America. 1. Airplane --- . 1960. Hala widowiskowo-sportowa w hangars in the United States. 11. Coliseum, Katowicach. In Polish. Inzynieria i Budow• exposition palace in Quebec, Canada. La nictwo no. 4: 154 ff. Technique des Travaux (Sept.-Oct.). --- . Entwurf fur eine Mehrzweckhalle in --- . 1953. Reinforced concrete thin shell Kattowitz. Bauwelt no. 23:654 ff. structures. J. ACI (Feb.). -- . Sports hall. Interbuild (May): 12 ff. --- ; Anderson, Boyd G.; and Birnbaum, Zeiss-Dywidag. Robert and Schaefer Co. Bull. Harold. 1959. Reinforced concrete folded 138 Oan. 1932). plate construction. Structural Division, Pro• Zerna, W. 1951. Membrantheorie verallge• ceedings, ASCE vol. 85, ST8 (Oct.):15-43. meinerter Rotationsschalen. Ingenieur-Ar• Winter, G., and Pei, M. 1947. Hipped plate chive. no. 19:228. construction. J. ACI vol. 43 Oan.). --- . 1959. Uber eine nichtlineare allge• Wissler, H. 1916. Festigkeitberechnung von meine Theorie der Schalen. Proceedings, Ringflachen. Zurich: Promotions-arbeit. Symposium on Theory of Thin Elastic Shells, Delft. Yitzhaki, David. 1959. The design of prismatic Zienkiewicz, O. C. 1967. The Finite Element and cylindrical shell roofs. Amsterdam: Method in Structural and Continuum Me• North-Holland Publishing Company. chanics. New York: McGraw-HilI.

418 Index

ACI. See American Concrete Institute Army Warehouse, Columbus, Ohio, 146, 149 Acoustic wave effects, abstracts of articles on, Arslan Jadhib Tomb, Sangbast, Iran, 42, 44 361-62 Art and shell structures, 179-82 Affaita, Izydor, 74 Artificial Leather Industry building, Coswig, Agamemnon, Tomb of, Mycenae, Greece, 14 Germany, 167 Aghia Parigoritissa, Arta, Greece, 41 Aspidin, Joseph, 122 Airport hangars Astrodome, Houston, Texas, 177, 311-12, Chicago, 174, 175 313-16 Cuatro Vientos, Spain, 149, 150 Austro-Hungarian Bank, Vienna, 298 Marignane, France, 151, 153 Auxiliary members, 203-6, 208-9, 210, 211, Seattle, 192 214-15,219-20 thin shells as, 193 and ACI building codes, 345, 351 Albany Mall Meeting Center, Albany, New and barrel shells, 261-63, 267 -68 York, 193 Albert Hall, Kensington, 298 Alberti, 249 Baba Luqman Mausoleum, Sarakhs, Iran, 48 Alessi, Galeazzo, 61 Balat, A. and Maguet, 299 Alfa-Romeo Factory, Milan, 146, 148 Ballou, Louis W., 85 Alvarez Ordonez, Joaquin and Fernando, 158 Baltard, V., 298 Amati, Carlo, 83 Bank of Montreal, Montreal, 86 American Concrete Institute (ACI), 221 Baptistry, Pisa, 57 Ammann and Whitney, 152, 167, 174, 193, Baroni, Giorgio, 145, 146 220 Barrel shells, 21, 26, 99, 130-32, 211 Analysis and design Base, displacement at, and computer analysis, abstracts of articles on, 362 - 64 235-37 and ACI building codes, 347-51 Basilica of San Gaudenzio, Novara, 82 Anisotropy, abstract of article on, 364-65 Bass, L. 0., 313 Anticlastic shells, 115, 118 Baucher, Lucien-Jacques, 108 Antonelli, Alessandro, 82 Belfry, Cathedral of Ivan the Great, Moscow, Apex, displacement at, and computer analysis, 77, 79 237 Bellushi, Pietro, 163 Archimedean solids, 306, 307 Bending, abstracts of articles on, 365 Architects' Co-Partnership, 149 Berecci, Bartolomeo, 74

419 Index

Berg, Max, 143 Casa Finlandia Futura, Finland, 201, 202 Bergman, M., and Associates, 163 Castenson, George, 298 Bernini, Giovanni Lorenzo, 68, 69, 73 Cast iron domes, 83 - 84, 297 - 98 Binkley Engineering Associates, 316 Catalan vault, 100 -1 02 Bizzos, Tomb of, Ruweha, Syria, 42, 43 Catenary curves in shell design, 243, 245-46 Blasting, abstract of article on, 366 Cathedral, Pisa, 57 Blondel, jacques Fran~ois, 242 -43 Cathedral of New Norcia, Perth, Australia, B1ondel, jean-Pierre, 108 158, 159 Blount Brothers, 316 Cathedral of St. john the Divine, New York, 86 Boat building Cathedral of the Archangel Michael, Moscow, and ferrocement, 124, 125-27 77, 78 and fiber-reinforced plastic, 200 Cathedral of the Dormition, Moscow, 77, 78 Borromini, Francesco, 61, 65, 68, 69, 73 Cement, history of, 121-22 Boundary members. See Auxiliary members Centennial Hall, Breslau, Germany, 143-44 Bourse du Commerce, Paris, 298 Center for Industries and Technology, Paris, Bouvard, J. A., 299 162, 163 Bramante, Donato, 62 Ceramic domes, 105-6 Bretton Hall, Yorkshire, 298 Chapel near Cuernavaca, Mexico, 157, 158 Brodrick, C., 298 Chapel of Nuestra Senora de la Soledad, San Brunelleschi, Filippo, 58, 60, 61, 62, 72, 103, jose de Altillo, Mexico, 154, 156 214, 241 du Chateau, Stephane, 318 Bryn Mawr Rubber Factory, Wales, 149 Christian architecture, domes in, 10, 34-35 Buckling Christiansen, john V., 177, 192 abstracts of articles on, 366-70 Church, Gracanica, Yugoslavia, 41 and ACI building codes, 350 Church of Koimisis, Daphni, 40 empirical rules for, 243-45 Church of Mary, Monterrey, Mexico, 149, Bulfinch, Charles, 83 151, 153 Bunning, J. B., 298 Church of San Antonio de las Huertas, Buonarroti, Michelangelo. See Michelangelo Mexico City, 156 Burgi garden center, Camarino, Switzerland, Church of San jose Obrero, Monterrey, 170, 173 Mexico, 162, 164 Bus garage, Dusseldorf, Germany, 156 Church of Santa Monica, Mexico City, 168, 171 Byzantine architecture, domes in, 10, 35-41 Church of St. Barbara, Brooklyn, 86 Church of the Apostles, Athens, 39 Church of the Apostles, Constantinople, 39 Cable (tensegrity) domes, 322-24 Church of the Intercession of the Virgin, Cajundome, Lafayette, Louisiana, 302, 321-22 Moscow, 77, 79 Camelot, de Mailly, and Zehrfuss, 162 Church of the Miraculous Virgin. Mexico, Camoletti, Bruno, 168 154 Camoletti, Pierre, 170, 173 Church of the Nativity of Our Lady, Moscow, Camoletti House, Geneva, 170, 173 77, 78 Candela, Felix, 152, 154, 156, 157, 158, 162, Church of the Sagrada Familia, Barcelona, 183 168, 186 Church of the Transfiguration, Kizbi, Soviet and construction methodology, 104-5, 124, Union, 79, 80 343 Ciba-Geigy water purification plant, Prattelin, influence on Isler, 190 Switzerland, 170, 174 and shell design, 123, 129-30, 135, 136, Ciba Plant, canopy for, Churubusco, Mexico, 137,275 154, 155 and the Sydney Opera House, 175 Cisterns, domes as, 15 Cantilevered shells, 134-36, 137 Coal Exchange, London, 298 Capitol building, Washington, D.C., 83, 84, Coliseum, Charlotte, North Carolina, 309-10 108, 203 Composite shells, abstracts of articles on, da Caprarola, Cola, 62 370-74

420 Index

Computer aided analysis, abstract of article Dow Chemical, 197 - 200 on, 374 del Duca, Giacomo, 65 Computer aided design, abstracts of articles Dyckerhoff-Widmann KG, 156, 182 on, 374 Dywidag System, 219 Concrete, 26,100,122,176-78,259-60 abstracts of articles on, 375 and boat building, 123-27 Earle A. Chiles Center, University of Portland, and pneumatic forms, 196 Oregon, 110, III "Concrete Shell Buckling" (American Edge beams. See Auxiliary members Concrete Institute), 350 Eero Saarinen and Associates, 167 "Concrete Thin Shells" (American Concrete Eiffel, A. G., 299 Institute), 344 Elastic analysis and ACI building codes, 346, Conoidal shells, 132 - 34, 195 347 Considere, 209 Elasticity, abstracts of articles on, 381 Constillares, building in, Spain, 149, 150 Elastoplasticity, abstracts of articles on, 381-82 Constructivism, 180 - 81 Electromagnetic field effects, abstract of Control of shell structures, abstract of article article on, 382 on, 375 Energy dissipation, abstract of article on, 382 Corbeled domes, 14, 16, 18, 20, 21 Engineering Index Annual 1989, The Corrosion, abstracts of articles on, 375 - 76 (Engineering Information, Inc.), 359 da Cortona, Pietro, 65, 70 Eschmann factory, Switzerland, 170 Cosmic Rays Research Laboratory, University Esquillon, 162 of Mexico, Mexico City, 152, 153 Etruscan domed tombs, 9 Coyne System, 219 Euler's law, 307-8 Creep, abstract of article on, 376 Evans, Allen, 86 Curtis and Davis, 163, 316 Evolution Museum, Eindhoven, Netherlands, 168, 171 Exhibit Hall, Vienna, 299 Dagit, Henry D., 86 Experimental shell design, 182, 190-92 Darb-i Imam, Isfahan, Iran, 49, 50 and ACI building codes, 346, 348 Dardasht Minarets, Isfahan, Iran, 48 thin shell, Jena, Germany, 144, 145 Davazdah Imam Mausoleum, Yazd, Iran, 42, 44 Expo 86, Ontario Pavilion at, Vancouver, 304 Dean Smith Center, Chapel Hill, North Expo 67, U.S. Pavilion at, Montreal, 320 Carolina, 304, 305 Exposition Building, Turin, 156 Deaton, Charles, 203 Defects, abstract of article on, 376 Deflection, abstracts of articles on, 376-77 Factory for John Rennock and Sons, Haughley Deformation, abstracts of articles on, 377 - 80 Park, Suffolk, England, 108 Del POlO, F., Associates, 141 Failure, abstract of article on, 382 Derizet, Antoine, 70 False domes, 14, 21 Design, abstracts of articles on, 380 - 81 Falsework, 89-90, 97,101,109,178 Desret, Antonio, 70 Felix und Regula Church, Zurich, 206 Dill, R. E., 215 Ferrocement, 124, 125-27, 157 Dirigible Hangar, Orly Airport, Paris, 144 Ferstel, H. von, 298 Dischinger, Franz, 184 Fiberglass formwork, 211 Doehring, W. D., 215 Fiber-reinforced plastic shells, 200 - 202 Domenig, Gunther, 170 Field House, Montana State College, Bozeman, Dome of the Rock, Jerusalem, 42, 43, 107 108 Domes and shells, abstracts of articles on, 360 Filippone, Odette, 108 Domus Augustana, Rome, 28 - 29 Fioravanti, Rodolfo, 77 Domus Aurea, Rome, 28-29, 30 Florentine Zone, Renaissance domes of, 58-61 Dosio, Giovanni Antonio, 61 Folded plates and ACI building codes, 345 Double-shell construction, 58, 59, 214 Fontana, Carlo, 241, 242

421 Index

Fontana, Domenico, 63-65, 72, 242 Great Mosque of the Shah, Isfahan, Iran, Fontana's rules for masonry domes, 242 50-51,52 Forest Products Pavilion, Portland, Oregon, Greek Orthodox Church, Milwaukee, 154, 155 108 Grid domes, 318 Formige,j. C., 299 GT STRUDL. See Georgia Tech Structural Formwork, 97,104,145,177 Design Language plastic foam for, 197 - 200 Guastavino, Rafael, 86 pneumatic, 196 - 97 GUM Department Store, Moscow, 299 rubber membrane as, 190, 192 Gunite method, 146, 163, 195 wooden, 196,211 Gur-e Amir Mausoleum, Samarkand, Soviet Forum Baths, Pompeii, 27 Union, 49, 50 Fougner, N. K., 124 Foundry Building, Milan, 145 Hadrian Villa, Tivoli, 30, 31 Four-gable hyperbolic paraboloids, 278-83 Hardouin-Mansart, Jules, 74 Fowke, F., 298 Hardy, L., 299 Fowler, Charles, 298 Harris County Sports Stadium. See Astrodome Fracture, abstracts of articles on, 382-83 Harrison and Abramovitz, 193, 220 Framed domes, 311 Haruniyya Tomb, Tus, Iran, 46, 47 Free nodes displacement and computer Hayden Planetarium, Manhattan, 145 analysis, 237 Heat treatment, abstract of article on, 383 Freyssinet, Eugene, 144, 184, 215 Heins and La Farge, 86 Freyssinet System, 219 Helmle and Hubert, 86 Froehlich, Arthur, 174 Hershey Chocolate Company, ice hockey Fuller, R. Buckminster, 299, 300, 301-2, arena for, Pennsylvania, 192 318-20,322,323 HipOdromo, Caracas, Venezuela, 174, 176 Funicular polygons, 243, 245-46 Hiroshima Peace Center Monument, 181-82 Funthaus Church, Vienna, 298 Hisatok, T., 110 Historical masonry domes, spans of, 87 (table) Hoechel, Eric, 168 Gabellini, 124 Hoffmann, Claus, 167 Galla Placidia, Tomb of, Ravenna, 33 Holy Sepulchre, Jerusalem, 36 Galleria Umberto I, Naples, 299 Hoop forces in domes, 90 - 96 Galleria Victor Emmanuel II, Milan, 298 Hornblower and Marshall, 86 Garcia de Quinones, Andres, 76 Howells and Stokes, 86 Gas Station, Deitingen, Switzerland, 170, 172 Hoyer, E., 215-16 Gaudi, Antonio, 10, 182, 183 Huber, Hunt and Nichols, 316 Gaussian curvature, 117 Hunt, Richard Morris, 299 Geiger, David H., 302-3, 304, 305, 323 Hyperbolic paraboloids, 195, 211 Geldmeister, Charles, 298 in art, 180, 181 General Motors Technical Institute, in Candela's designs, 186 auditorium for, Warren, Michigan, 149, as conoidal surfaces, 132, 133 151 Gaudi's development of, 183 Gensert, R. M., 249 Hyperboloids, 137-42 Geodesic domes, 299-300, 301, 302, 318-20 H yperstatic domes, 204 - 6, 218 - 19 Geometry of shell design, 116, 129-30,305-8 Georgia Tech Structural Design Language (GT STRUDL), 223 lASS. See International Association for Shells Gesu Church, Rome, 63 and Spatial Structures Girard Trust Company, Philadelphia, 86 Ice houses, domes as, 14 -15 Glass and dome design, 297 - 98 Igloos, 22-23 Gonzales Reyna, Jorge, 152 Illinois State University Arena, Normal, Grand Palais, Louvet, France, 299 Illinois, 303, 323 Gran Madre di Dio, Rome, 83 II Redentore, Venice, 71

422 Index

Imamzada Sayyid Ishaq Tomb, Saveh, Iran, 46 Kresge Auditorium, Massachusetts Institute of Imamzada Yahya Mausoleum, Varamin, Iran, Technology, Cambridge, Massachussetts, 46, 47 152,154,193,209 Inelastic analysis and ACI building codes, Kuh-i Banan Tomb, Iran, 48, 49 346, 347 Information Pavilion, Brussels, 108 Institute of Arts and Sciences, Brooklyn, 85 - 86 La Clerecia Church, Salamanca, Spain, 76 Instituto Tecnico de la Construccion y del Lambot, Joseph-Louis, 124 Cemento, Constillares, Spain, 160 - 61 Lamella domes, 210, 311-18 International Association for Shells and Lardy, Pierre, 190 Spatial Structures (lASS), 221-22 Larrosa, Manuel, 157 International Exhibition Facility, New Lattice wood shells, Nara, Japan, 110 Orleans, 163, 165 Layne, Henry M., 174 International Exhibition of 1958, Phillips Le Corbusier, 159, 168 Pavilion at, Brussels, 158-59, 161 Lederer, F., 318 I Quattro libri dell'architettura (The Four Books Lenzlenger Sons Company building, on Architecture) (Palladio), 71 Switzerland, 170 Ironworks foundry, Lohr, Germany, 161-62 Lesage, 122 Islamic dome, Mimar Sinan's contributions to Les Invalides, Paris, 74 the, 53-55 Leuzinger, Hans, 146 Isler, Heinz, 170, 172, 173, 174, 190-92 Lindsay Park Sports Center, Calgary, Alberta, Isostatic domes, 204-6, 216, 217 -18 304 luvarra, Filippo, 61 Lissitzky, Elieyer, 180 Little Metropole Cathedral, Athens, 41 Lloyd and Morgan, 313 Jabal I Sang, Kerman, Iran, 45, 46 Lombardo, Pietro, 71 Jackson, P. H., 215 Lombardo, Tullio, 71 Jami Mosque, Ardistan, Iran, 44, 45 Long barrel vaults, 131,244-45,269 (table) Jami Mosque, Ashtarjan, Iran, 46, 47 Lopez Carmona, Fernando, 154, 156, 162, 168 Jami Mosque, Golpaegan, Iran, 44, 45 Lott, H. A., 313 Jami Mosque, Qazvin, Iran, 44, 46 Loudon, John Claudius, 298 Jami Mosque, Saveh, Iran, 50, 51 Lutheran church, Warsaw, 82 Jami Mosque, Varamin, Iran, 48 Jami Mosque, Zavareh, Iran, 44, 45 Jardin d'Hiver, Laeken Royal Park, Brussels, Macalloy System, 219 299 Mackenzie and Moncur, 298 Jefferson, Thomas, 84 Maderno, Carlo, 65 Johns, Slater & Howard, 108 Madison Square Presbyterian Church, New Johnson, Drake and Piper, 313 York, 86 Madonna di Loreto, Rome, 65, 67, 68 Madonna di San Biagio, Montepulciano, Italy, Kaiser Aluminum building, Honolulu, 320 63 Kalff, 168 Maeno, T., 110 Kapnikarea Church, Athens, 39 Magnel, G., 215, 219 Karaganda works, Soviet Union, 213 Magni,83 Khaidukov, G. K., 213 Maguire, C. A., and Associates, 165 Kibble, John, 299 Maillart, Robert, 146, 181, 183 Kibble Palace, Botanic Gardens, Glasgow, 298 Mail-processing facilities, Providence, Rhode Kiewitt, G. R., 313 Island, 165, 166, 167 Kiewittdomes, 311-12, 313-16 Makowsi, Z. S., 313 Kilns, domes as, 14, 15 -16 Manetti, Antonio, 60 Kingdome, Seattle, 176-78, 192, 324 Manufacture, abstracts of articles on, 383-84 Kirsis, Uldis, 249 Marcus, Henri, 313

423 Index

Market, Agadir, Morocco, 318 Nehrbass, Neil, 302 Market Hall, Algeciras, Spain, 144-45 Nervi, Pier Luigi, 136, 156, 158, 159, 163, Market Hall, Royan, France, 154 184-85 Mashhad-i Mir Buzurg Shrine, Amul, Iran, and boat design, 125 51,52 and construction strategies, 105, 178, 195 Masonry shells, 21, 22, 83, 89-92, 96-99, and the Sydney Opera House, 175 259-60 Nervi e Bartolli Construction Company, 156, spans of historical domes, 87 (table) 160 and trussed domes, 297 Network domes, 310-11 Mathematical models, abstracts of articles on, New Corn Exchange, Leeds, 298 384-85 "New Shapes for Shells" (Isler), 190 Matsushita, Fujio, 318 New York University, New York, 85 Mausoleum of Sultan Muhammad Adil Shah, Niccolini Chapel, San Croce, Florence, 61 Bijapur, India, 51, 53 Niemeyer, Oscar, 167 May-D & F Department Store, Denver, Nikken Sekkei Ltd., 325 157 -58, 159 Noise abatement, abstracts of articles on, 385 McDonald Brothers, 85 Nolan, Norman and Nolan, 316 McGuire nuclear power plant, Cornelius, Nondestructive examination, abstract of article North Carolina, 179 on, 385 McKim, Mead and White, 85, 86 Nonspherical shells, 255, 256-57 (tables) McKinley National Memorial, Canton, Ohio, Nuclear reactors, 178-79 86 Nuraghi, 16, 18-20 McSweeney, Ryan and Lee, 163 Medici Chapel, Florence, 63 Mengoni, G., 298 Obata, 142 Mesnager, 209 Oconee nuclear power plant, Seneca, South Mesopotamia, vaults and domes in, 25 - 26 Carolina, 179 Metal sheathing, 298 Octagonal Roof, Villaverde, Spain, 145, 146 Michelangelo, 63, 64, 65, 214 Odell Associates, 309 Michelozzi, 61 Olympic Games of 1988, buildings for, Seoul, Mihailescu, Mircea, 187 Korea,303,323,324 Minerva Medica, Rome, 30-32 Opera House, Sydney, Australia, 129, 136, Missouri Botanical Garden, St. Louis, 320 174-76,184 Model analysis and ACI building codes, 348 Origins of domes, 4 - 5 Mole Antonelliana, Turin, 82 Otto, Frei, 110 de Montferrand, Auguste Ricard, 298 Outdoor shelter, Sancti Spiriti, Spain, 149, 151 Moore, Walter, 313 de la Mora, Enrique, 149, 154, 156, 162, 168 Morisseau, Andre, 154 Paez, A., 141 Mosque of Gawhar Shad, Mashhad, Iran, 49, 50 Palace of the Assembly, Chandigarh, India, Mouton, William, 302, 320-22 168,171 Muller-Grah, Walter, 182 Palazzetto dello Sport, Rome, 156-57,210, Murphy and Mackey, 320 211 Mushtaquiyya'Ali Shah, Kerman, Iran, 53 Palazzo dei Congressi, E.U.R., Rome, 146, Music Pavilion, "Santa Fe" Housing Project, 148 . Mexico City, 135-36 Palazzo dello Sport, Rome, 159-60, 161 Myers, E. E., 84 Palladio, Andrea, 71, 249 Palmer and Hornbostel, 86 Palm House, Munich, 298 Nagase, T., 110 Palm House at Sefton Park, Liverpool, 298 Naramore, Bain, Brady and Johanson, 177 Pani, Aldo, 135 Nash, John, 298 Pantheon, Paris, 82, 83 Nea Moni Chios, Athens, 40 Pantheon, Rome, 29-30, 89, 102

424 Index

Paolina Chapel in Santa Maria Maggiore, Reichstag, Berlin, 301 Rome, 65 Reinforced concrete, 4, 82, 86, 124, 143, Parker, 122 193-94 Parsons, John K., and Associates, 109 Residence, Pougny, France, 168, 169 Pazzi Chapel, Florence, 60 Restaurant, Xochimilco, Mexico, 158, 160, 190 Pei, I. M., and Associates, 141, 158 Ribbed shells and ACI building codes, 345 Peller, Miklos, 249 Ricchini, Francesco, 61 Perret, Auguste, 151 Rivergate Exhibition Hall, New Orleans, 192 Pevsner, Antoine, 180, 181 Roberts and Schaefer Company, 141, 158, Pevsner, Naum, 181 192-93 Physical Education Building, De Kalb, Illinois, Robinson and Associates, 163 193 Rocco, Emanuele, 299 Piacentini, Marcello, 159 Rock-cut tombs, 13 -14 Pierson, James G., 108 Rodchenko, Alexander, 180 Planetarium, St. Louis, Missouri, 142 Rodef Sholem Synagogue, Pittsburgh, 86 Planetarium, Trenton, New Jersey, 212 -13 Roebling System, 219 Plasticity, abstract of article on, 385 Roman architecture, domes and vaults in, Plastics applications, abstracts of articles on, 26-32 386 Roman Zone, Renaissance domes of, 61-70 Platonic solids, 306, 319 Roof Structures, Inc., 311, 313 Pneumatic domes, 324-25 Rosati, Rosato, 70 Pneumatic forming, 196-97 Rosell, Guillermo, 157 Point supports for domes, 206, 207 Rossman and Partners, 109 Poleni, Giovanni, 241, 243 Rotunda, University of Virginia, Polygonal domes, 34 - 35 Charlottesville, 84-85 Polyhedra as trussed domes, 305 - 8 Royal Brighton Pavilion, 298 Ponzio, Flaminio, 65 RSG Architects, 110 Porro, Ricardo, 149 Russell, S., Hansehauer, and Schmidt, 299 della Porta, Giacomo, 63 - 65 Portinari Chapel in San Eustogio, Florence, 61 Portland Cement Association, 221 Saarinen, Eero, 149, 152, 175, 186 Posttensioning, 125 - 26, 215, 219 - 20 Saarinen, Eliel, 149 Power station, Grandval, France, 318 Saddle-type hyperbolic paraboloids, 271-77 Pozzolana, 96, 100, 122 Sado, 320 Prader and Cie., 146 Saints Martina and Luca, Rome, 65, 67 Praeger, Kavanagh and Waterbury, 177,313 Salvi, Dioti, 57 Precast shell technology, 195, 211 - 13 San Andrea, Rome, 63 Preload Company, 215 San Andrea al Quirinale, Rome, 69 Pressure effects, abstract of article on, 386 San Andrea della Valle, Rome, 65 Prestressing, 125 - 26, 141-42, 195, 215 -19 San Carlino, Rome, 67 -68,69, 89 Protestant Church, Warsaw, 76 San Carlo, Milan, 83 Pseudoshells, 23-24, 202-3 San Carlo ai Catinari, Rome, 70 San Carlo al Corso, Rome, 70 San Claudio e San Andrea dei Borgognoni, Qubab structures, 6 Rome, 70 da Sangallo, Antonio, 63 Race Track, Madrid, 146, 147 da Sangallo, Giuliano, 61 Rainaldi, 69 San Giorgio Maggiore, Venice, 71 Rastrelli, Carlo Bartolomeo, 79 San Giuseppe, Milan, 61 Ravelli, L., 156 San Ivo della Sapienza, Rome, 68, 69 "Recommendations for Concrete Shells and San Lorenzo, Florence, 60 Folded Plates" (International Association San Salvatore, Venice, 71 for Shell and Spatial Structures), 344 San Satiro, Milan, 62

425 Index

San Sebastiano, Mantua, 61 Sound insulation, abstract of article on, 386 San Sebastiano, Milan, 61 Space frames, 116,297,299-300,320-22 San Spirito, Florence, 60 Spavento, Giorgio Pietro, 71 Sant' Agnese, Rome, 68 Specchie, 20 Santa Maria dei Miracoli, Rome, 69-70 Spherical shells, dimensions for, 120 (table), Santa Maria dei Miracoli, Venice, 71 250 (tables), 252-53 (table), 254-55 Santa Maria del Fiore, Florence, 58-60, 72, (table) 89,102,103,214 Spiral Generation, 197 - 200 Santa Maria della Consolazione, Todi, Italy, Spirex Structures, Inc., 200 62-63 Sports building, Northern Arizona University, Santa Maria delle Carceri, Prato, Italy, 61 Flagstaff, 108 - 9, III Santa Maria delle Grazie, Milan, 62 Sports center, Tbilisi, Soviet Union, 213 Santa Maria di Monte Santo, Rome, 69 Sports complex, Chamonix, France, 170, 173 Santa Maria in Carignano, Genoa, Italy, 61 Sports complex, University of Northern Santissimo Nome di Maria, Rome, 70 Michigan, Marquette, 110-11 San Tommaso Villanova, Castel Gandolfo, Squinches, 207 - 8 Rome, 68 St. Andrew's Cathedral, Kiev, 79-81 Sarger, Rene, 154 St. Antony of Padova Church, Warsaw, 74 Savvestic, L., 299 St. Augustin, Paris, 298 Schaarschmidt, F., 167 St. Basil, Moscow, 41 School addition, Graz-Eggenberg, Austria, St. Casimir, Warsaw, 74 170, 174 St. Costanza, Rome, 33 School of Plastic Arts, Havana, 149, 152 St. Fosca, Torcello, Italy, 41 Schulze, 299 St. Francis de Sales Church, Philadelphia, 86 Schwedler, Johann Wilhelm, 300-301 St. Front, Perigueux, France, 41 Schwedler domes, 309 -1 0, 327 - 30 St. George, Salonica, Greece, 33 Scott, H. G., 298 St. Irene, Constantinople, 39 Senate and Chamber of Deputies, Brasilia, 167 St. Isaac's Cathedral, St. Petersburg, Soviet Sesi, 16, 18 Union, 79 Severud, Fred, Elstadt, and Kruger, 309 St. Mark's, Venice, 40 Shah Firuz, Tomb of, Sirjan, Iran, 48,49 St. Mary's Cathedral, San Francisco, 163, 166 Shah Mosque, Mashhad, Iran, 49,50 St. Mary's Cathedral, Tokyo, 168, 169, 170 Shell reinforcement and ACI building codes, St. Paul's, London, 74-76 351-54 St. Paul's Chapel, Columbia University, New Short barrel vaults, 130, 131,264-66 (tables) York, 86 Shrine of Fatima, Qum, Iran, 50, 52 St. Peter's, Rome, 58, 63-65, 66, 67, 72, Shrine of Shaykh Ni'Matallah, Mahan, Iran, 214,242 49,51 St. Petersburg Cathedral, St. Petersburg, Sicily Company, Geneva, 170, 172 Soviet Union, 298 Siegel, C., and R. Wonneberg, 162 St. Sophia, Constantinople, 36-39, 89, 102 Sigismund Chapel, Cracow, Poland, 73-74 St. Sophia, Novgorod, Soviet Union, 40 Silos, domes as, 14 St. Theodore, Athens, 40 Silverstein, Edward and Associates, 163, 316 St. Theodore, Constantinople, 41 Simon, Louis, 154 St. Theodore Stratelates, Novgorod, Soviet Sinan, Mimar, 53-55 Union, 77 Sistine Chapel in Santa Maria Maggiore, St. Theodosia, Constantinople, 41 Rome, 63 St. Vincent's Chapel, Coyoacan, Mexico, Skilling, Helle, Christiansen and Robertson, 162-63, 165 163, 177 St. Vitale, Ravenna, 39 Smithsonian Museum, Washington, D.C., 86 Stabian Baths, Pompeii, 27 Smolny Convent, St. Petersburg, Soviet Stability, abstracts of articles on, 386-88 Union, 79 State Capitol Building, Boston, 83 Souffiot, Jacques, 82 State Capitol Building, Denver, 84

426 Index

Statical analysis of structures, 300, 301 Terminal building for Trans World Airlines, Steel, abstract of article on, 388 Kennedy Airport, New York, 149, 152, Steel and dome design, 82, 86, 87 (table), 299 167, 168, 169,209 Storage shed, Ferrara, Italy, 146 Testing, abstracts of articles on, 396-97 Storrs, John W., 108 Thatched domes, 21, 22 Strain, abstracts of articles on, 388 - 89 Theiler, Otto, 170 Stresses, abstracts of articles on, 389 - 93 Theodoric, Tomb of, Ravenna, Italy, 33-34 Structural analysis, abstracts of articles on, Theory, abstracts of articles on, 397 -99 393-96 "Theory of Bridge Girder Systems" Structural behavior of shells, 89-90,122-23, (Schwedler), 300 210-11 Thermae of Agrippa, Rome, 27 conoidal domes, 95-96 Thermae of Caracalla, Rome, 30 spherical domes, 90 - 94 Thermae of Diocletian, Rome, 32 thin shells, 143 Thermal effects, abstracts of articles on, 399 Structural design, abstracts of articles on, 396 Thermoelasticity, abstracts of articles on, STRUDL II, 327 399-400 Stupas, 23-24 Thin shells, 119-20, 135, 143, 193-94 Styrofoam, 197 - 200, 202 and ACI building codes, 343, 345 Suncoast Dome, St. Petersburg, Florida, 303, computer analysis of, 223-37 323, 324 experimentation on, 144, 145, 182 Superdome, New Orleans, 176, 177, 316, 324 and ferrocement, 125 Superga, Turin, 61 Tibaldi, Pellegrino, 61 Suuronen, Matti, 201 Tile domes, 86 Sverdrup and Parcel, 316 Timber Development Association, 108 Swimming pool, Draney, France, 318 Timbrel vaulting, 100 -1 02 Swiss National Exhibition, Cement Hall at, T.M.P. Associates, 110 Zurich, 146, 148 Tombs, rock-cut, 13 -14 Symbolism of domes, 4 - 11 Tomb Tower, Lajin, Iran, 42, 44 Synclastic shells, 115, 117, 118 Toroidal shells, 153 Syon House, 298 Torroja Miret, Eduardo, 141, 144, 145, 146, 149,185,221 Trade fair building, Afghanistan, 320 Treasury of Atreus, Mycenae, Greece, 14 Tacoma Dome, Tacoma, Washington, Trosch Company factory, Switzerland, 170 109-10, III Trowbridge and Livingston, 145 Tacoma Dome Associates, 109-10 Tylman of Gameren, 74 Taillibert, R., 170 Taj Mahal, Agra, India, 53, 54 Takenaka Komuten Company, 325 Umbrella-type hyperbolic paraboloids, 283-93 Talayots, 21 UNESCO building, entrance canopy for, Paris, Talin, Vladimir Evgrafovitch, 180 136,137 Tange, Kenzo, 168, 181 Union Tank Car Company plant, Baton Tedesko, Anton, 146, 185-86, 192 Rouge, Louisiana, 320 Tempietto in San Pietro in Montorio, Rome, 62 Universal Brotherhood and Theosophical Temple of Diana, Baiae, Italy, 27 Society, San Diego, 299 Temple of Mercury, Baiae, Italy, 28 University of Illinois, Assembly Hall, Urbana, Temple of Venus, Baalbek, Syria, 32 193 Temple of Venus, Baiae, Italy, 27 University of Virginia, Charlottesville, 85 Temple of Vesta, Rome, 30 Utzon, Jorn, 136, 175 Tennis center, Heimburg, Switzerland, 170 Tensegrity, 322, 323 Terminal building, St. Louis airport, St. Louis, Vacchini, F., 158 Missouri, 152, 154, 155 Van Buren Magonigk, H., 86

427 Index

Vannoni, C., 158 Wooden domes, 86, 88 (table), 106-11,203 Varax wood domes, 110, 111 Wooden formwork, 196 Vault abutments, Blondel's rule for, 242-43 World's Columbian Exposition, administration Vaulting, 4-5,26,89,99-100,101 building for, New York, 299 Venetian Zone, Renaissance domes, 70-71 World's Fair of 1853, Crystal Palace at, New Vibrations, abstracts of articles on, 400-405 York,298 Victoria Regia House, Schoneburg Royal World's Fair of 1878, three domes at, Paris, Botanic Garden, Berlin, 299 299 da Vignola, Giacomo Barozzi, 61, 63 World's Fair of 1889, central dome for, Paris, Villa Capra (Villa Rotonda), Vicenza, Italy, 71 299 Villa Trissino, Vicenza, Italy, 71 World's Fair of 1900, Palais des Machines, Viscoelasticity, abstracts of articles on, 405 Paris, 299 Vitellozzi, Annibel, 156 Wren, Christopher, 74 Vitruvius, 249 Wright, Donald R., 197-98 Voit, A. von, 298 Wright, Frank Lloyd, 154 von Emperger's Handbuch (Dischinger), 184 Wrought iron and dome design, 297 -98 Wyatts, 122 Wyss Garden Center, Solo Thurn, Wada, M., 110 Switzerland, 170, 172 Walter, Thomas Ustick, 83 Water tower, Fedala, Spain, 141-42 Wave effects, abstract of article on, 405 Western Wood Structures, 110, III Yamasaki, Minoru, 152 White, Stanford, 85 Wieskopt and Pickworth, 145 Wilhelma Botanical Garden, Stuttgart, 298 Zanth, Ludwig von, 298 Wilson, Morris, Crain and Anderson, 313 Zimmermann, Hermann, 30 I Wind effects, abstract of article on, 405 Zimmermann domes, 311 Wind forces, 246 Zug, Szymon Bugumil, 76, 82