GEORGIAN MECHANICAL UNION
saqarTvelos meqanikosTa kavSiri
VI ANNUAL MEETING
OF THE GEORGIAN MECHANICAL UNION
saqarTvelos meqanikosTa kavSiris meeqvse yovelwliuri saerTaSoriso konferencia
BOOK OF ABSTRACTS
moxsenebaTa Tezisebi
© GGeorgian Aviation University 29.09 – 04.10 2015, TBILISI saqarTvelo saaviacio universiteti ISSN 2233-355X 29.09 – 04.10 2015, Tbilisi 2
1 ORGANIZERS: ორგანიზატორები: Georgian National Committee of Theoretical and Applied საქართველოს ეროვნული კომიტეტი თეორიულ და გამოყენებით მექანიკაში, Mechanics, Georgian Mechanical Union საქართველოს მექანიკოსთა კავშირი საქართველოს საავიაციო უნივერსიტეტი Georgian Aviation University ი. ჯავახიშვილის სახელობის თბილისის სახელმწიფო უნივერსიტეტის I. Javakhishvili Tbilisi State University ი. ვეკუას სახელობის გამოყენებითი მათემატიკის ინსტიტუტი I. Vekua Institute of Applied Mathematics ზუსტი და საბუნებისმეტყველო მეცნიერებათა ფაკულტეტი Faculty of Exact and Natural Sciences თბილისის საერთაშორისო ცენტრი მათემატიკასა და ინფორმატიკაში Tbilisi International Centre of Mathematics and Informatics საერთაშორისო სამეცნიერო კომიტეტი: SCIENTIFIC COMMITTEE: თანათავმჯდომარეები: CO-CHAIRS: ტეფნაძე სერგო (საქართველოს საავიაციო უნივერსიტეტი, საქართველო) Jaiani, George, Ivane Javakhisvili Tbilisi State University, Georgia ჯაიანი გიორგი (ი. ჯავახიშვილის სახელობის თბილისის სახელმწიფო Tepnadze, Sergo Georgian Aviation University, Georgia უნივერსიტეტი, მათემატიკის დეპარტამენტი & ი. ვეკუას სახელობის გამოყენებითი მათემატიკის ინსტიტუტი, საქართველო) COMMITTEE MEMBERS: წევრები: Altenbach, Holm (Germany) ალტენბახი ჰოლმი (გერმანია) კიკვიძე ომარი Kikvidze, Omari (Georgia) Aptsiauri, Amirani (Georgia) აფციაური ამირანი კონდრატიევა ლიდია (რუსეთი) Kipiani, Gela (Georgia) Betaneli, Archili (Georgia) ბეთანელი არჩილი კუბეჩკოვა დარია (ჩეხეთის Kvitsiani, Tarieli (Georgia) Botchorishvili, Ramazi (Georgia) ბოჭორიშვილი რამაზი რესპუბლიკა) Kondratyeva, Lidiya (Russia) Chinchaladze, Natalia (Georgia) გაბრიჩიძე გურამი მახვილაძე ნოდარი Kubeckova, Darja (Czech Republic) Dadaian, Tigran (Armenia) გიგინეიშვილი ჯონი მეუნარგია თენგიზი Makhviladze, Nodari (Georgia) Danelia, Demuri (Georgia) გულუა ბაკური ნატროშვილი დავითი Meunargia, Tengizi (Georgia) Dumbadze, Akaki (Georgia) დადაიანი, ტიგრან (სომხეთი) პატარაია დავითი Natroshvili, David (Georgia) Gabrichidze, Gurami (Georgia) დანელია დემური რაიჩიკი მარლენა (პოლონეთი) Pataraia, David (Georgia) Gigineishvili, Joni (Georgia) დუმბაძე აკაკი სმირნოვი ევგენი (რუსეთი) Rajczyk, Marlena (Poland) Gulua, Bakuri (Georgia) ვაშაყმაძე თამაზი ყიფიანი გელა Smirnov, Evgeny (Russia) Kapanadze, George (Georgia) კაპანაძე გიორგი შავლაყაძე ნუგზარი Vashakmadze, Tamazi (Georgia) Kienzler, Reinhold (Germany) კვიციანი ტარიელი ჩინჩალაძე ნატალია კინცლერი რაინჰოლდი (გერმანია) ORGANIZING COMMITTEE: საორგანიზაციო კომიტეტი: Bliadze, Seit Mikadze, Valeri, Scientific Secretary ბლიაძე სეითი ჩინჩალაძე ნატალია, Chinchaladze, Natalia, Co-Chair Kipiani, Gela, Chair გულუა ბაკური თავმჯდომარის მოადგილე Gulua, Bakuri Tsutskiridze, Vardeni მიქაძე ვალერი, სწავლული მდივანი ცუცქირიძე ვარდენი TOPICS OF THE MEETING: ყიფიანი გელა, თავმჯდომარე 1. Solid Mechanics კონფერენციის თემატიკა: 2. Fluid Mechanics 1. მყარ დეფორმად სხეულთა მექანიკა; 3. Solid-Fluid Interaction Problems 2. ჰიდროაერომექანიკა; 4. Applied Mechanics 3. დრეკად მყარ და თხევად გარემოთა ურთიერთქმედების პრობლემები; 5. Mechanics of Flying Vehicles 4. გამოყენებითი მექანიკა; 6. Related Problems of Analysis 5. საფრენი აპარატების მექანიკა; 6. ანალიზის მონათესავე საკითხები.
3 4 MATERIAL MODELING - AN ACADEMIC GAME OR A References TOOL FOR A BETTER DESIGN 1. М.Л. Акивис, В.В. Гольдберг - Тензорное исчисление, М., НАУКА, Holm Altenbach 1972 г. Otto-von-Guericke-University Magdeburg, Faculty of Mechanics 2. А. Дж. Мак-Конелл - Введение в тензорный анализ, М., Физматгиз, Magdeburg, Germany, [email protected] 1963 г. At the moment we have various possibilities to model the material behavior. The inductive way starts from simple experimental observation and step by step the generalization can be realized. This approach results in BARS AND HOSES CALCULATION the problem that the generalized equations may not satisfy the statements of the second law of thermodynamics even if the simplest case is in agreement Zurab Arkania with the second law. The deductive approach satisfies from the very Akaki Tsereteli State University beginning the second law but the procedure to get equations allowing the Kutaisi, Georgia [email protected] solution of practical problems is not trivial. There is a third approach – the rheological modeling combining the advantages of the first and second approach. All three approaches will be compared and discussed. Examples We’ve discussed static three-dimensional problems of absolute by demonstrate the advantages and disadvantages of the three approaches. flexible bars, when concentrated forces of any direction act on the bars. We’ve developed numerical method of hose shapes and determination of axial tensions in the hose. quids influence on the shape and THE EXACT EXPRESSION OF TURBULENT STRESS TENZOR We’ve researched ideal and sticky li AND CALCULATION RESULTS axial tension of the hose. It’s displayed that internal flow of the liquid doesn’t make influence on the shape of the hose. The shape of the hose is determined only by external powers. Amiran Aptsiauri We have received axial tensions formula in the hose. The method is Kutaisi National Educational University, Kutaisi, Georgia, developed for solving the static sums of complementary hoses to the flow [email protected] of liquid or air loaded with concentrated forces considering the internal flow of ideal or sticky liquid in the hose. The paper gives a solution to the problem of turbulence based on the The results allow to evaluate solidity of the bar and hose, to advisedly methods of tensor analysis. It is shown that the exact mathematical select parameters of the internal flow of the hose and liquid in it in order to expression of tensor calculus contains important information for the search raise reliability of the hose in the process of maintenance. of the turbulent stress tensor, whose definition was not possible for more than one century. It is proved that implicitly tensor is a function of the time-averaged References velocity and density, and explicitly it depends on the average velocity, 1. density and energy of turbulent fluctuations. The corresponding equations Светлицки В. А. Механика трубопроводов и шлангов м.: . are given. машиностроение, 1982, 279с Comparison of the calculated results with the available experimental data confirms the validity of the decision.
5 6 EXPERIMENTAL INVESTIGATION BEAM AT THERMO the Neumann type BVPs in the form of absolutely and uniformly convergent MECHANICAL LOADING series.
Gulbanu Baisarova*, Omar Kikvidze** References *Akaki Tsereteli state University, Kutaisi, Georgia, [email protected] 1. Khalili N., Selvadurai A.P.S.: A Fully Coupled Constitutive Model ** Akaki Tsereteli state University, for Thermo-hydro-mechanical Analysis in Elastic Media with Double Kutaisi, Georgia, [email protected] Porosity.Geophsical rResearch Letters, v.30, pp. SDE 7-1-7-3, 2003. 2. Basheleishvili M., Bitsadze L.: The basic BVPs of the theory of In this paper we consider experimental investigation of cantilevered consolidation with double porosity for the sphere. Bulletin of TICMI, beam, that is subjected to bending. The beam has rectangular cross section. 16 , n.1, 15-26 , 2012. The experimental device is presented. The beam is loaded by concentrated 3. Tsagareli I., Bitsadze L.: Explicit Solution of one Boundary Value force and temperature field. In the experiment the temperature of top and Problem in the full Coupled Theory of Elasticity for Solids with Double bottom surface of beam, and also vertical and horizontal displacement of Porosity. Acta Mechanica: Volume 226, Issue 5, 1409-1418, 2015, free end of beam are measured. All the measurements are carried out by 40 DOI: 10.1007/s00707-014-1260-8. sec. interval for both regimes: 1. The beam is acted by non homogeneous 4. I. Tsagareli, L. Bitsadze, The Boundary Value Problems in the Full temperature field, 2. The beam is acted by concentrated force and then acted Coupled Theory of Elasticity for plane with Double Porosity with a by non homogeneous temperature field. Circular Hole, Seminar of I.Vekua Institute of Applied Mathematics, The experimental results show, that displacement caused by temperature Reports, vol.. 40, 68-79, 2014. field is less than displacement caused by force. Experimental results will be 5. Basheleishvili M., Tsagareli I.: Effective solution of the basic BVPs of compared with the results of numerical calculation. the elasticity theory for a sphere. Bull.of the Academy of Sciences of the Georgian SSR, 108, 1, 41-44, 1982. References 6. Tsagareli I.: On a problem for a spherical layer. Proceedings of I.Vekua Inst. of Appl. Math., 12, 118-122 ,1983 1. Термопрочность деталей машин. /Под ред. И.А.Биргера и Б.Ф.Шорра. М.: Машиностроение, 1975.- 455 с. DYNAMIC MODELS OF LAMINATED SYSTEMS
Seit Bliadze*, Valeri Mikadze** ON SOME PROBLEMS IN THE THEORY OF THERMOELASTICITY FOR A SPHERE WITH DOUBLE *LEPL State Military Scientific Technical Center “Delta”, Tbilisi, Georgia, , [email protected] POROSITY **Georgian Aviation University, Tbilisi, Georgia, [email protected] Lamara Bitsadze Iv. Javakhishvili Tbilisi State University, I.Vekua Institute of Applied The finite element method is employed for computation of sandwich Mathematics, Tbilisi, Georgia, [email protected] shell structures. This allows to take in to consideration shear deformations with transverse deformations and inertial effects from the movement of The main goal of this paper is to consider the Dirichlet and the separate layers. Neumann type boundary value problems (BVPs) of equilibrium theory of The proposed algorithm is not connected with the formation of laminated thermoelasticity [1] for a sphere with double porosity. By using the methods finite elements, they are replaced by packages from finite element of thick developed in [2-6] we construct explicitly the solutions of the Dirichlet and and thin plates and shells, joined in nodes. The use of similar approximating
7 8 functions for forms end displacements will provide the compatibility of References package deformations, and models embedding in separate finite elements allow to evaluate stress and deformations with maximum capable approxi- 1. Nam, P.T., Larson, M., 2010. Model of nearshore waves and wave- mation. induced currents around a detached breakwater. Journal of Waterway, Port, Coastal, and Ocean Engineering 136(3), 156-176. References 2. Брегвадзе А.В., Сагинадзе И.С. Моделирование литодинамических процессов в прибрежной зоне. II Международная конференция 1. - Болотин В.В., Новичков Н.Н. Механика многослойных конструкций. М.: “Неклассические задачи механики”. 6-8.10.2012. Кутаиси, Грузия. - Машиностроение, 1980. 375с. 3. Amiran Bregvadze. Local Innovation Experience in Georgia. 2. Григолюк Э. И. Чулков П.П. Устойчивость и колебания трехслойных Engineering Aspects of Beach Formation and Coast ProtectionJean - - оболочек. М.: Машиностроение, 1973. 172 с. Monnet Programme Project EU Regional Innovation Policy as a Model for the EaP Country RegionsTbilisi 2014. 4. Krystian W. Pilarczyk, DESIGN ASPECTS OF GEOTUBES AND NUMERICAL MODELING OF SEA SHORE DYNAMIC AND ITS GEOCONTAINERS, Zoetermeer, Netherlands 30 January 1996. ENGINEERING ASPECTS
Amiran Bregvadze*, Ivane Saginadze** *Akaki Tsereteli state university, Georgia, Kutaisi, [email protected] INFLUENCE OF THE SHEAR WIND ON GENERATION OF THE **Akaki Tsereteli state university, Georgia, Kutaisi, [email protected] LARGE SCALE ZONAL FLOWS BY ULF MODES
In modern conditions more and more problems occur concerning the Khatuna Chargazia**,*** Oleg Kharshiladze*,***, destroying effects of sea shore from strong waves.Anthropological factors *Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia, threaten seashore areas. [email protected] So, it’s necessary to take right environment protecting measures which **Iv. Javakhishvili Tbilisi State University, I.Vekua Institute of Applied will be based scientifically. Nowadays engineering mentality becomes more Mathematics, Tbilisi, Georgia, and more oriented on nature, therefore new technologies are effective ways *** Iv. Javakhishvili Tbilisi State University, M. Nodia Institute of of environment protection. Nowadays it’s important to solve seashore streng Geophysics, Tbilisi, Georgia, [email protected] thening problems. The present article shows seashore processes (1;2;3)numerical modeling In the paper the features of generation of the zonal flows by magnetized Rossby waves in the shear flow driven dissipative ionosphere is considered. The modified Charney-Obykhov type equation describing the nonlinear interaction of amplitudes of five different scale modes is obtained. These (1) modes are: ultra low frequency (ULF) primary magnetized Rossby wave, two satellites of this wave, long wavelength zonal mode and large scale and using mathematical modeling, based scientifically for protecting background mode (inhomogeneous wind). The role of effects of nonlineari- seashore on base of Acetube (2;3;4). The present work is carried out for ties (scalar, vector) in formation of the large scale zonal flows by magne- Rustaveli state grant tized Rossby waves with finite amplitudes in the dissipative ionosphere is AR/22/3-109/14“geomorphological processes stability measures studied. Modified parametric approach is used. On the basis of theoretical according to Rivers: Rioni and Enguri areas hydrodynamical methods’. analysis and numerical simulation of the corresponding system for amplitu- des of the perturbations the new features of energy pumping from compa- rably small scale ULF magnetized Rossby wave and the background flow 9 10 into the large scale zonal flows and nonlinear self-organization of collective References activity of the above mentioned five modes in the ionosphere medium is revealed. Generation of the zonal flow is caused by interaction of finite 1. F. Clarelli, C. DI Russo, R. Natalini, M. Ribot, Mathematical models amplitude magnetized Rossby wave with the background shear flow. for biofilms on the surface of monuments, Applied and Industrial Dependence of the growth increment of the zonal flow on structure and Mathematics In Italy III, proceedings of SIMAI Conference 2008, velocity of the background shear flow is studied. Series on Advances in Mathematics for Applied Sciences - 82 (2009). 2. I. N. Vekua, On a way of calculating of prismatic shells (in Acknowledgement. The research was supported by Shota Rustaveli Russian), Proceedings of A. Razmadze Institute of Mathematics of National Science Foundation, Grant No. 31/14. Georgian Academy of Sciences. 21, 191-259 (1955). 3. I. N. Vekua, Shell Theory: General Methods of Construction, Pitman Advanced Publishing Program, Boston-London-Melbourne, 1985. ON SOME PROBLEMS OF BIOFILMS OCCUPYING THIN 4. N. Chinchaladze, Hierarchical models for biofilms occupying thin PRISMATIC DOMAINS prismatic domains, Bull. TICMI. 18, No. 2, 102-109 (2014).
Natalia Chinchaladze Iv. Javakhishvili Tbilisi State University, I.Vekua Institute of Applied ON ONE QUASI-STATIONARY NONLINEAR MATHEMATICAL Mathematics MODEL FOR LEAK LOCALIZATION IN THE BRANCHED GAS & Department of Mathematics of the Faculty of Exact and Natural Sciences, PIPELINE Tbilisi, Georgia [email protected], [email protected] Teimuraz Davitashvili, Givi Gubelidze, Meri Sharikadze A biofilm is a complex gel-like aggregation of microorganisms like Iv. Javakhishvili Tbilisi State University, I.Vekua Institute of Applied bacteria, cyanobacteria, algae, protozoa and fungi. They stick together, they Mathematics & Faculty of Exact and Natural Sciences, Tbilisi, Georgia, attach to a surface and they embed themselves in a self-produced [email protected], [email protected] extracellular matrix of polymeric substances, called EPS. Even if a biofilm contains water, it is mainly in a solid phase. Biofilms can develop on In the present paper pressure and gas flow rate distribution in the surfaces, which are in permanent contact with water, i.e. on solid/liquid branched pipeline on the basis of one quasi-stationary nonlinear interfaces or on different types of interfaces such as air/solid, liquid/liquid or mathematical model is investigated. For realization of this purpose the air/liquid (see [1] and references therein). system of partial differential equations describing gas quasi-stationary flow 1D and 2D problem for the biofilm occupying thin prismatic domain are in the branched pipeline was studied. We have found effective solutions of considered. 2D problem is solved using Vekuas dimension reduction these quasi-stationary nonlinear partial differential equations (pressure and methods (see, e.g., [2]-[4]). gas flow rate distribution in the branched pipeline) for leak detection in a horizontal branched pipeline. For studying the affectivity of the method Acknowledgements. The work was supported by the Consiglio quite a general test was created. Preliminary data of numerical calculations Nationale di Ricerca (Italy) and Shota Rustaveli National Science have shown efficiency of the suggested method. Some results of numerical Foundation (Georgia) within the framework of the joint project (No. 09/04) calculations defining localization of gas escape for the inclined pipeline are ”Some classes of PDE and systems with applications to mechanics and presented. The results of calculations on the basis of observation data have biology” (2012/2013). shown that the performed simulations were much closer to the results of observation.
11 12 IMPLEMENTATION OF WRF MODEL FOR THE TERRITORY OF of specific composite material for safely implementation in practice. In the CAUCASUS paper the method is presented that provides computation of aircraft composite fuselage with consideration of arising at take-off – landing Teimuraz Davitashvili*, Zurab Modebadze** oscillations and originated in material creeping. *Iv. Javakhishvili Tbilisi State University, I.Vekua Institute of Applied Mathematics, Tbilisi, Georgia, [email protected] ** Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia, [email protected] INFLUENCE OF RESULTS OF NUMERICAL ANALYSIS AND STRUCTURAL DECISION ON ARCHITECTURE OF “HILTON” In this paper we have elaborated and configured Weather Research HOTEL COMPLEX IN BATUMI Forecast - Advanced Researcher Weather (WRF-ARW) model in the GRID system for Caucasus region considering geographical-landscape character, J. Gigineishvili*, I. Timchenko**, G. Cikvaidze*** topography height, land use, soil type and temperature in deep layers, * "PROGRESI" Ltd (Engineering Center of Computer Modeling & vegetation monthly distribution, albedo and others. Porting of WRF-ARW Structural Design), 16, V.Pshavela ave, Tbilisi 0136, Georgia, tel: (+995) application to the grid was a good opportunity for running model on a larger 599 18 55 26, (+995) 577 95 33 87, E-mail: [email protected]. number of CPUs and storing large amount of data on the grid storage ** "PROGRESI" Ltd (Engineering Center of Computer Modeling & elements. The WRF was compiled on the platform Linux-x86. Simulations Structural Design), 16, V.Pshavela ave, Tbilisi 0136, Georgia, tel: (+995) were performed using a set of 2 domains with horizontal grid-point 577 49 45 11, E-mail: [email protected]. resolutions of 15 and 5 km, both defined as those currently being used for *** "PROGRESI" Ltd (Engineering Center of Computer Modeling & operational forecasts The coarser domain is a grid of 94x102 points which Structural Design), 16, V.Pshavela ave, Tbilisi 0136, Georgia, tel: (+995) covers the South Caucasus region, while the nested inner domain has a grid 599 64 41 20, E-mail: size of 70x70 points mainly territory of Georgia. Both use the default 31 vertical levels. We have studied the effect of thermal and advective-dynamic The aim of this work is to evaluate the proposed architectural and factors of atmosphere on the changes of the West Georgian climate. Some planning decision and development of more appropriate structural system of results of calculations of the interaction of airflow with complex orography the whole complex. The article considers current issues of design and of Caucasus with horizontal grid-point resolutions of 15 and 5 km are creation of reliable and optimal structures of the hotel complex «HILTON» presented. in Batumi at the same time. On the example of the complex under construction the optimal coupling between function and form, as well as strength, stability, reliability and cost of the building are considered. The ON ONE REFINED METHOD OF ANALYSIS IN CREEPING NON- first option of the hotel complex «HILTON» in Batumi was a complex of LINEAR THEORY design schemes of various high-rise buildings, located on a single foundation and bears the permanent, long-term, temporary, short-term loads Akaki Dumbadze and external factors such as: hydrostatic pressure of water, heat, wind, Georgian Aviation University, Tbilisi, Georgia, [email protected] seismic load etc. This paper discusses various options for based on the relevant computer models architectural and planning and structural features As it is known, the deformation law of composite material (ε,σ) on plane and performed analysis, as well as shows the results of these analyses. represents the curve lines that consists of two sections: first is the linear Amendments made to the structural part of the project, not only improved deformation section (within the frame of Hooke’s law) and the other – is strength characteristics of the buildings, but also had a positive influence non-linear, where Hooke’s law is not observed. For keeping at structure (beneficial effect) on the architectural appearance of the complex as a whole. (from composite material) analysis of requirements: on strength, durability Methodology. This paper is based on the submitted multi optional studies of and reliability it is necessary simultaneously that the structure is economical. the designed hotel complex «HILTON» in Batumi. The numerical The mentioned requirements are closely related with the study of properties investigations were carried out with the use of computer modeling based on 13 14 multi optional analysis of existing design solutions as well as new versions STRUCTURE FEATURES OF THE CLAMPING (RETAINING) created for the purpose of choosing the most suitable and acceptable option, WALLS OF LANDSLIDE SLOPES ON THE COMPLEX RELIEF both in terms of architectural, planning and design solutions. Findings. The numerical simulation of the complex structural system of the hotel complex Gigineshvili Joni 1*, Gedevanishvili G.K . 2 *, «HILTON» in Batumi was carried out using the software "LIRA". The Matsaberidze T.G . 3* , Goginashvili T.E . 4* , complex stress-strain state has been analyzed for different design options, 1* Engineering Centr of Computer Technology for Construction Plaining. the most appropriate configuration of both architectural and structural LTD “PROGRESI”. Address: 16 Vazha-Pshavela ave., 2 fl. Tbilisi. 0183, features of the bearing framework and foundation have been developed. As Georgia, Tel. +995 599 18 55 26., +995 32 237 10 09. E-mail a result of the application of modern computer technology numerical [email protected] www.progresi.com.ge. simulation of different options of the complex, the architectural, planning 2* Construction Plaining. “ABTektonik”. Address: 28 Pekina ave., 5 fl. and design solutions were obtained both in terms of architectural and Tbilisi. 0183, Georgia, Tel. +995 577 95 33 85., structural. Practical value. Performed stress-strain state analysis of the hotel 3* Engineering Centr of Computer Technology for Construction Plaining. complex allowed us to determine the optimal size, shape and design features LTD “PROGRESI”. Address: 16 Vazha-Pshavela ave., 2 fl. Tbilisi. 0183, of the entire complex under permanent, long-term, short-term and other Georgia, Tel. +995 599 74 44 80., +995 32 237 10 09. E-mail factors, such as the hydrostatic pressure of water, heat, wind, seismic, etc. [email protected] www.progresi.com.ge. and the optimal option was selected for external shape of the complex 4* Engineering Centr of Computer Technology for Construction Plaining. considering the structural features. LTD “PROGRESI”. Address: 16 Vazha-Pshavela ave., 2 fl. Tbilisi. 0183, . Georgia, Tel. +995 598 58 22 56., +995 32 237 10 09. E-mail Keywords: architectural and planning solutions, function, feature, computer [email protected] www.progresi.com.ge. simulation, strength, stability, reliability, numerical analysis, multi optional design, not uniform settlement. Purpose. The analysis of opportunities of use of strengthening of sloping ground and creating of landscape compositions, determination of advantage of their use in the existing environment of the city and requirements to retaining wall structural design. Methodology. Computer modeling applying soil FE of LIRA SAPR 2014 software. Results. In case of insufficient bearing capacity of a sloping ground, for structural design of the retrofitted or completely repaired structures we should discuss their reinforcing and updating on request of the modern city whose expediency should be confirmed by feasibility study. It is obvious that the choice of the effective structural solution of the clamping retaining walls is possible only on the basis of careful calculations taking into account geotechnical conditions of a foundations and construction of such structures. Complexity of such calculations and installation is that it is necessary to consider a set of various factors: real stratification of soil and sequence of loading on the basis; complicated geometry of a construction site, already built (existing) structures and a terrain topography; nonlinear properties of soil bases (work often outside a linear stage: slipping between layers, deformations at the large pulling-out loadings, etc.); an assessment of the loads arising in structural design at uneven settlements. Fully the accounting of the given factors is possible only with the use of numerical methods by consideration of spatial models for interaction of the clamping (retaining) wall and the soil 15 16 bases. Scientific novelty. The clamping (retaining) wall has the following Acknowledgment. This work was supported by SRNSF garnt FR/59/5- advantages: 1. Construction of such a wall is possible for any configuration 103/13. and height of the terrain; 2. The material consumption for construction of References such a wall is more rational. 3. Construction of such a wall doesn't require large space. 4. It gives experts various opportunities for creating unique 1. G.Khimshiashvili, Signature formulae for topological invariants, Proc. architectural forms along the length of work space. Practical importance. A.Razmadze Math. Inst. 125, 2001, 1-121 Three types of zones of a complicated terrain are allocated, where possible 2. G.Giorgadze, Quadratic mappings and configuration spaces, Banach effective use of the clamping (retaining) wall: city zone, a zone with Center Publ. 62, 2004, 73-86. negative anthropogenic impact and industrial zone. 3. G.Giorgadze, G.Khimshiashvili, Remarks on spherical linkages, Bull. Keywords: The clamping (retaining) wall, a complicated terrain Georgian Natl. Acad. Sci. (N.S.) 4, 2010, no.2, 8-12. topography, planting, creation of landscape compositions, reinforcement 4. G.Giorgadze, G.Khimshiashvili, , Remarks on bicentric polygons, Bull. rebar with a screw profile and the coupling, computer modeling, sequence of Georgian Natl. Acad. Sci. (N.S.) 7, 2013, no.3, 5-10. loading, the stress-strain state, a configuration, slope and height of a terrain. 5. G.Giorgadze, G.Khimshiashvili, Cyclic configurations of spherical polygons, Doklady Mathematics 87, 2013, 2-13, No.3, 1-4.
GEOMETRY OF CONFIGURATION SPACES OF LINKAGES AND QUADRATIC MAPPINGS KINEMATIC RESEARCH OF CRANE-TRANSPORT FACILITIES AND ROAD-CAR WORKING APPLIANCES Gia Giorgadze*, Giorgi Khimshiashvili ** *Iv. Javakhishvili Tbilisi State University, I.Vekua Institute of Applied Vazha Gogadze Mathematics, Tbilisi, Georgia, [email protected] A.Tsereteli state University, Georgia, [email protected] **Ilia State University, Tbilisi, Georgia, [email protected] In this work kinematic researching of crane-transport facilities and road- In the paper we discuss the possible characterization of configuration car working appliances are discussed. spaces of some mechanical systems. Any mechanical system M determines It’s confirmed, that certain rings of the above mentioned machines are the variety of all its possible states X which is called the configuration space connected with each-other like bones. of M. Usually a state of the system is fully determined by finitely many real When connecting it extra ties may be used. That’s why in some cases parameters, in this case the configuration space X can be viewed as a subset moving is affected by means of chinks or beforehand tension of some of the Euclidean space. Each point of X represents a state of the system and elements takes place. different points represent different states. We investigate configuration spaces of linkages, which represent a remarkable class of closed smooth manifolds, also known as polygon FREE FLOW MICRO HYDRO-ELECTRIC STATIONS spaces, using properties of quadratic mappings (see [1-2]). We calculate the Euler characteristic of configuration spaces of linkages and show that a Tamaz Gongadze configuration space X comes with the natural topology which reflects the LEPL State Military Scientific Technical Center “Delta”, technical limitations of the system. We also consider some analytical and Tbilisi, Georgia, [email protected] topological properties of configuration space of spherical and bicentric n- gons. Below various types of free flow micro hydro-electric stations are The talk is based on recent publication of authors [3-5]. considered, as long as there are many fast rivers with significant flow kinetic energy in the globe (in Georgia as well). Micro hydro-electric stations’ approximate power production is 5W÷10 kW. Micro hydro-electric stations 17 18 do not require any hydraulic works, any changes of the riverbed. Sometimes SOME RESULTS OBTAINED AND ACTIVITIES it will be necessary to make attachments to the riverbank and use improvised means (cobbles, wood around). Turbine blades are only parts George Jaiani moving in the water, no other rubbing parts will be immersed in the Iv. Javakhishvili Tbilisi State University, I.Vekua Institute of Applied water.Micro hydro-electric stations have high coefficient of efficiency, Mathematics & Department of Mathematics of the Faculty of Exact and small overall dimensions and weight. Natural Sciences, Tbilisi, Georgia [email protected], [email protected]
NORMED MOMENTS METHOD FOR NON-SHALLOW SHELLS The present talk is, in a certain sense, the speaker’s account about his main activities at the I. Javakhishvili Tbilisi State University, Georgian Bakur Gulua Mathematical Union, and Georgian Mechanical Union; besides, it is devoted Iv. Javakhishvili Tbilisi State University to his principal results obtained in the theory of Partial Differential I. Vekua Institute of Applied Mathematics Equations, mainly in the theory of degenerate ones with applications to Sokhumi State University, Tbilisi, Georgia, [email protected] cusped (tapered) elastic shells, plates, and bars. It contains also a concise survey of some two- and one-dimensional models constructed by him in the I. Vekua constructed several versions of the refined linear theory of thin fields of elastic solids and fluid-elastic solid interaction problems. and shallow shells, containing the regular processes by means of the method of reduction of 3-D problems of elasticity to 2-D ones [1]. This method for non-shallow shells in case of the geometrical and physical non-linear theory DERIVATION OF THE EQUATIONS OF ELASTIC BALANCE OF was generalized by T.Meunargia [2]. THE PLATES CONSISTING OF BINARY MIXTURE USING THE In this paper we consider non-shalow shells. By means of I. Vekua’s METHOD OF CONSECUTIVE DIFFERENTIATION normed moments method we get the approximate expression of the stress tensor which is compatible with boundary data on face surfaces. Roman Janjgava Iv. Javakhishvili Tbilisi State University, I.Vekua Institute of Applied Acknowlegment. The designated project has been fulfilled by a financial Mathematics, Tbilisi, Georgia, [email protected] support of Shota Rustaveli National Science Foundation (Grant SRNSF/FR/358/5-109/14). Any idea in this publication is possessed by the In the report we consider Green-Nagdi-Steel's model of mixture of two author and may not represent the opinion of Shota Rustaveli National isotropic elastic materials [1]. We use a method of a reduction of Vekua Science Foundation itself. called a method of consecutive differentiation [2] for a conclusion from the main equations of the above-mentioned three-dimensional model of system References of the equations of static balance of the plates consisting of binary mixture. Previously we used the method of expansion of the unknown functions by 1. Vekua, I.N. Shell Theory: General Methods of Construction. Pitman Legendre polynomials along thickness coordinate to obtain equations for Advanced Publishing Program, Boston-London-Melbourne, 1985. shallow shells [3]. 2. Meunargia, T.V. On one method of construction of geometrically and physically nonlinear theory of non-shallow shells. Proc. A. Razmadze Acknowledgement. The designated project has been fulfilled by a financial Math. Inst., 119 (1999), 133-154. support of Shota Rustaveli National Science Foundation (Grant SRNSF/FR/358/5-109/14).
19 20 References laws and between the thicknesses of a functional dependence of the form are written out. 1. Natroshvili D. G., Jagmaidze A. Ya., Svanadze M. Zh. Some problems T (t) (t) of the linear theory of elastic mixtures. TSU press, Tbilisi (1986). (in All physical characteristics of the flow are calculated. Russian) 2. Vekua, I.: Shell Theory: General Methods of Construction. Pitman References Advanced Publishing Program, 287 pp., Boston-London-Melbourne 1. Thomas A. S., Cornelius K.K. Study slotted suction boundary layer. (1985). Aerospace enjineering. 1983, vol. -107. 3. Janjgava R. Derivation of two-dimensional equation for shallow shells 1, №1, p.98 2. L.Jikidze, V.Tsutskiridze. Unsteady problem of the motion porous by means of the method of I.Vekua in the case of linear theory of elastic plate with account the falling stream of the weak conductive fluid and mixtures. Journal o Mathematical Sciences. Spr. New York, 2009, vol. -classic problems of 157, N1, 70- 78. heat transfer. International conference “Non mechanics”. Kutaisi, Georgia. Materials. Vol.II, pp.35- 42. 3. L.Jikidze, V.Tsutskiridze. Unsteady rotation problem of the motion infinite porous plate with the falling stream of the conductive fluid with UNSTEADY ROTATION PROBLEM OF THE MOTION OF account of magnetic field and heat transfer in case of variable electric INFINITE POROUS PLATE WITH THE FALLING STREAM OF conductivity. The international Scientific Conference dedicated to the THE CONDUCTIVE FLUID WITH ACCOUNT OF MAGNETIC 90th anniversary of Georgian Technical University. “Basic Paradigms FIELD AND HEAT TRANSFER IN CASE OF VARIABLE in Science and Technology Development for the 21st Century”. INJECTION VELOCITY AND ELECTRIC CONDUCTIVITY TRANSACTIONS II, 2012, pp. 56-60. 4. L.A. Dorfman. Hydrodynamic resistance and a heat transfer of rotating L. Jikidze *, V. Tsutskiridze ** bodies Fizmatgiz. 1960. Department of engineering mechanics and technical expertise of . construction, Georgian Technical University, 77, M. Kostava str, Tbilisi, 0175, Georgia Department of mathematics, Georgian Technical University, 77, M. STRENGTH OF PLATE TYPE MULTI-LAYER Kostava str, Tbilisi, 0175, Georgia STRUCTURES IN AIRCRAFTS E-mail address: [email protected], [email protected] Revaz Kakhidze By using the method of successive approximation there has been Sh. Rustaveli Batumi State University, Batumi, Georgia, studied the unsteady rotation problem of the motion infinite porous plate [email protected] with the falling stream of the conductive fluid with the components of The plate type multi-layer thin-walled structures are more and more velocity r ar, 0, z 2az , with account of magnetic field and widely applied in aircraft and missile engineering and other fields of heat transfer in case when the coefficient of electric conductivity and engineering. This is caused due to necessity of high strength and injection velocity are functions of temperature as a form- significantly reducing of structures weight. These necessary features are T T provided by application of various fillers in separate layers of multi-layer 0 1 , w 0 1 . structures. The fillers and composite materials are characterized by low T T shear stiffness that is their disadvantage [1, 2]. For determination the thickness of the dynamic and thermal boundary In the report the methodology of mentioned problem, strength layers, differential equations are obtained and their exact solutions for the numerical analysis of multi-layer plate structures is stated. particular cases when the injection velocity varies according to different
21 22 References GENERAL APPROACH OF VORTICES STUDY DUE TO GIORGI ABURJANIA’S BOOK “SELF-ORGANIZATION OF THE 1. Dumbadze, A. Mechanics of composite body. Tbilisi: Georgian Aviation NONLINEAR VORTEX STRUCTURES AND THE VORTICAL University, 2015. −292 p. TURBULENCE IN THE DISPERSIVE MEDIA” 2. Mikhailov B.K., Kipiani G.O., Moskaleva V.G. Basics of theory and stability analysis methods of three-layered plates with cuts. Tbilisi: Oleg Kharshiladze*,***, Khatuna Chargazia**,*** Metsniereba, 1991. −189 p. *Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia, [email protected] **Iv. Javakhishvili Tbilisi State University, I.Vekua Institute of Applied ON ONE PROBLEM OF THE PLANE THEORY OF ELASTICITY Mathematics, Tbilisi, Georgia, FOR CIRCULAR HOLE WITH A FINITE POLYGONAL DOMAIN *** Iv. Javakhishvili Tbilisi State University, M. Nodia Institute of Geophysics, Tbilisi, Georgia, [email protected] Giorgi Kapanadze*, Miranda Narmania** * I. Vekua Institute of Applied Mathematics, A. Razmadze Mathematical Central problem of hydrodynamics represents investigation of the Institute, Tbilisi, Georgia, [email protected] vortex dynamics. This question is most important for atmosphere and ocean **I. Vekua Institute of Applied Mathematics, University of Georgia, circulation, where the different scale vortex transfer processes are Tbilisi, Georgia, [email protected] considered. Analogous is the role of the vortex structures for investigation of the dynamics of plasma and ionosphere-magnetosphere media. Such The paper considers the problem of the plane theory of elasticity for a structures, more effectively than linear waves, can absorb free energy of circular hole with a finite polygonal domain. For the solution of the problem medium and form the strong turbulence. In the presentation general the use is made of the methods of conformal mappings and of boundary approach of G. Aburjania for investigation of the nonlinear wave processes value problems of analytic functions, and unknown complex potentials are in different dispersive physical media in neutral geophysical one as well as constructed effectively (analytically). The estimates of the solution behavior in conductive media – laboratory plasma and ionosphere is discussed. at the vicinity of angle are given. Similarity of the dynamical system in considered, problems and general mathematical tools obtained by G. Aburjania are discussed. Possibility of splitting of the vortex structures into scalar and vector ones is studied, which Acknowlegment. The designated project has been fulfilled by a financial is given in (1). Besides, the characteristic features of these structures are support of Shota Rustaveli National Science Foundation (Grant considered. As the numerical simulation shows, the main characteristics of SRNSF/FR/358/5-109/14). Any idea in this publication is possessed by the the structure dynamics and vortex interaction are determined by the author and may not represent the opinion of Shota Rustaveli National nonlinear terms included in the model equations. Due to nonlinearity of the Science Foundation itself. system of model equations, its solution represents complicated mathematical problem, which in the stationary case is given in (1). Analytical investigation of these models stimulated the numerical research of the vortex structures in non-stationary problems, which shows a good agreement of G. Aburjania’s theoretical research with numerical, satellite and laboratory experiments.
23 24 References SPECIFICITY OF UPLIFT FORCE FORMATION ON THE ANNULAR WING 1. Aburjania, G.D.: Self-Organization of the Nonlinear Vortex Structures and the Vortical Turbulence in the Dispersive Media: Kom-Kniga, Gela Kipiani*, Archil Geguchadze** Editorial URSS, Moscow (2006). Georgian Aviation University*, Akaki Tsereteli State University** E-mail: [email protected], [email protected]
ON CONSISTENT PLATE THEORIES. PARTIAL DIFFERENTIAL So it was and up to the present that the most common is such an EQUATIONS, STRESS RESULTANTS AND DISPLACEMENTS assembling of annular wing aircrafts of vertical take-off and landing, in which the uplift force forming surface shape is approached to a spherical Reinhold Kienzler* , Patrick Schneider** form, or to a ring-dome form, and where it is not possible to put down the *Bremen Institute of Mechanical Engineering (bime) center of gravity lower than geometrical center of this surface. This University of Bremen, Department of Production Engineering circumstance creates the condition of insufficient sustainability of this kind Am Biologischen Garten 2, 28359 Bremen of aircrafts. e-mail: [email protected] To solve the problem, the paper dwells on comparing the mechanical **Bremen Institute of Mechanical Engineering (bime) principles of uplift force formation of translational and centrifugal expulsion University of Bremen, Department of Production Engineering aircrafts of vertical take-off and landing with the ring-dome wing schemes, Am Biologischen Garten 2, 28359 Bremen accordingly, with respect to their aerodynamic characteristics. The e-mail: [email protected] difference between them consists in thefact that in the first case, the aerodynamic profiled wing with its front-directed frontal edge will pass Using the uniform-approximation technique in combination with the through the stationary air masses, but in the second case, the air masses pseudo-reduction method, a hierarchy of consistent plate theories is derived: moving from the center to outboard will envelop the aerodynamic profiled after the introduction of non-dimensional quantities, the strain-energy and fixed annular wing. the dual-energy densities appear as infinite power series in the plate The mentioned difference appeared to be important when analyzing the parameter that describes the relative thinness of the structure. The associated uplift force formation process. In the first case, for uplift force formation it Euler-Lagrange equations deliver a countably infinite set of PDEs, where is necessary to lift up a frontal edge of the profiled wing higher than a back each PDE is an infinite power series with respect to the plate parameter. It is edge, in order to create the so-called “angle of attack”, but in the second shown that the untruncated set of PDEs is equivalent to the problem of the case, the choice fell on making an unusual decision: the frontal edges of the three-dimensional theory of elasticity. Furthermore, an a-priori error aerodynamic profiled annular (or composed of the totality of rings) wings estimation is given for the truncated, finite and therefore tractable PDE are put down, but the centrifugal airstreams are lifted up (up-directed system. The error of the Nth-order two-dimensional theory decreases like obliquely). In the first case, there is determined the vertical direction of the the (N + 1)th-power of the characteristic plate parameter, so that a resultant force of the airstreams felt on the wing’s bottom surface and considerable gain of accuracy could be expected for higher-order theories. rebound (reflected) from it, and then it will be completely used as uplift The resulting equations of a consistent 2nd-order plate theory are used to force. assess and validate theories established in the literature. Relative position of the annular wing’s component aerodynamic profiled rings allows for higher lifting up their surfaces higher than a common geometrical center, and by that, for increasing aircraft sustainability.
25 26 generalization. After generalizing in the right part of the equation an STABILITY OF HAVING IRREGULARITIES additional term is added that contains the denominator isobaric speed of STRUCTURES IN AIRCRAFTS sound C p . This speed. the existence of which was discovered only recently Gela Kipiani*, Valeri Mikadze** is a measure of heterogeneity of the environment. At striving this velocity to *Georgian Aviation University, Tbilisi, Georgia, [email protected] infinity, generalized equation becomes an equation known today and this **Georgian Aviation University, Tbilisi, Georgia, [email protected] means that in perfectly homogeneous environment there exists just adiabatic sound velocity Cs . This situation is fundamentally changing the definition In the thin-walled structures irregularity of geometrical and physical of significant criteria such as compressibility or incompressibility parameters causes significant stress concentration and creates dangerous environment. As it turned out, these criteria, which had a purely mechanical zones of cracks or plastic deformations propagation. In most cases their load sense, take the thermodynamic sense. For example, in the thermodynamic bearing capacity will be determined due to strength conditions or buckling sense, water and iron are much more compressible materials than the air in in stress concentration zones. To other kinds of regularity violation belongs the upper atmosphere. It changed also many well-known gas and to the surface break that occurs in folded and multi-wave coverings, due to hydrodinamic relations. their impact on mode of deformation they are similar to ribs. Extremely violates the regularity cuts, breaks, holes, cracks as well other rigid inclusions of rod type [1, 2, 3]. In the report is the above EASTERNMOST BLACK SEA FORECASTING SYSTEM: THE mentioned problems on issues of structures stability in aircrafts are stated. CURRENT STATE AND PERSPECTIVES
References Avtandil Kordzadze*, Demuri Demetrashvili ** 1. Mikhailov, B.K. Plates and shells with discontinuous parameters. Iv. Javakhishvili Tbilisi State University, M. Nodia Institute of Geophysics, Leningrad: Publishing of Leningrad State University, 1980. −196 p. Tbilisi, Georgia, *[email protected], **[email protected] 2. Mikhailov, B.K., Kipiani G.O. Deformability and stability of spatial lamellar systems with discontinuous parameters. Saint-Petersburg: Large achievement of the Black Sea operational oceanography for the Stroyizdat, SPB, 1996. −442 p. last decade is the development of the Black Sea Nowcasting/Forecasting 3. Kipiani G., Mikadze V., Nikolaishvili L. Stability of plates with System that became possible as a result of scientific and technological discontinuous parameters//V International Scientific and Technical progress since the 90s of the last century. One of the components of this Conference “Modern Problems of Water Management, Environmental system is the regional forecasting system developed at M. Nodia Institute of Protection, Architect and Construction”, July 16-19, 2015, Tbilisi, Geophysics for the easternmost Black Sea, which covers the Georgian Universali, 2015, pp. 293-300. coastal zone and adjoining water area [1,2]. The regional forecasting system consists of hydrodynamic and ecological blocks. The hydrodynamic block includes M. Nodia Institute of Geophysics high-resolution 3-D regional GENERALIZED EQUATION OF CONTINUITY model of the Black Sea dynamics. The parts of the ecological block are 2-D OF MASS AND ITS CONSEQUENCES and 3-D models of spreading of polluting substances in the sea environment. The regional forecasting system provides 3 days’ forecast of main Vladimir Kirtskhalia dynamical fields – the flow, temperature and salinity with 1 km spacing, and I. Vekua Sukhumi Institute of Physics and Technology in case of accidental situations – the forecast of spreading the oil and other pollutants as well in the easternmost Black Sea water area. It is show that in the modern theory there exists the equation of Further improvement of the forecasting system is connected with continuity of mass, which is applied to any environment, it is valid only for inclusion into system the models of forecast of wind driven surface waves a homogeneous medium and in a heterogeneous environment it requires and biochemical processes. In addition, the new very high-resolution version 27 28 of the regional forecasting system will be collaborated for Adjara coastal zone and Poti water area (with horizontal grid steps 50-100 m). The NUMERICAL INVESTIGATION OF FEATURES OF THE BLACK SEA functioning of this version will be possible at the same time with the main MIXED LAYER FOR THE GEORGIAN COASTAL LINE version of the forecasting system. Thus, the complex regional forecasting system will be developed, Diana kvaratskhelia*,** Demuri Demetrashvili* which will combine the forecasting system for the Georgian coastal zone * M. Nodia Institute Geophysics of Iv. Javakhishvili Tbilisi State University; with 1 km resolution and the forecasting subsystem for Adjara and Poti **Sokhumi State University, Tbilisi, Georgia, water areas with 50-100 m resolution. [email protected]
References The upper mixed-layer of seas and oceans is one of the important water areas, the thermodynamic state of which defines many important physical, chemical or biological 1. Kordzadze A. A., Demetrashvili D. I.: Operational forecast of processes in the sea- atmosphere environment. The same can be noted concerning the hydrophysical fields in the Georgian Black Sea coastal zone within the Black Sea turbulent mixed layer, which represents the object of our investigation. ECOOP. Ocean Science 2011, 7, pp.793-803. doi:10.5194/os-7-793- 2011. It is well known that the depth of the mixed layer is generally determined 2. Kordzadze A. A, Demetrashvili D. I.: Short-range forecast of by measurements of water properties: temperature and sigma-t (density) but here hydrophysical fields in the eastern part of the Black Sea. Izvestia AN, the depth of the mixed layer and its variability are investigated by using the basin- Fizika Atmosphery i Okeana 2013, 49(6) pp. 733-745. scale numerical model of the Black Sea dynamics of M. Nodia Institute of Doi:10.7868/S0002351513060096 (in Russian). Geophysics (BSM-IG, Tbilisi, Georgia). The main object of this study is to investigate the features of the Black Sea upper mixed-layer generation for Georgian coastal line and its evolution in ON THERMAL OSCILLATIONS OF BEFOREHAND STRESSED connection with the nonstationary atmospheric circulation and thermohaline action SHELLS OF REVOLUTION, CLOSE BY THEIR FORM TO in the inner-annual time scale. Besides, how the temperature and salinity fields of the CYLINDRICAL ONES, WITH AN ELASTIC FILLER Black Sea upper layer are substantially reacted by the vertical diffusion coefficient represents the main point in our study. Therefore, the coefficient of vertical turbulent Sergo Kukudzhanov diffusion for heat and salt are tested as constant and it was parameterized by Iv. Javakhishvili Tbilisi State University, A. Razmadze Mathematical modified Oboukhov's formula. Institute Tbilisi, Georgia, [email protected] Acknowledgement: The researches were supported by the Shota Rustaveli National Science Foundation, Grant No. AR/373/9-120/12. We investigate the eigen oscillations of shells of revolution, which by their form are close to cylindrical ones with an elastic filler and under the THE CONSTANT-VELOCITY PRESSING OF A WEDGE IN AN action of meridional forces, normal pressure and heat. The shell is assumed ORTHOTROPIC HALF-PLANE to be thin and elastic. The temperature is uniformly distributed in the body of the shell. The light and sliding type filler is considered. The filler is Marina Losaberidze, David Kipiani modeled by the Winkler’s base. The shells of positive and negative Georgian Technical University; 77, Kostava st., Tbilisi 0175, Georgia Gaussian curvature are considered. We present formulas and universal curves of dependence of least frequency and form of wave formation on In the paper the problem of constant-velocity V pressing of a blunt temperature, rigidity of an elastic filler, preliminary stress, and also on the 0 sign of Gaussian curvature and amplitude of a shell deviation from a wedge in an orthotropic half-plane is considered. It must be displacement cylinder. The problem of shell stability is investigated and formulas for vector and and stress tensor , u1 u 2 x y, xy components must be determination of critical load are obtained. found, which meet the conditions: 29 30 In the present paper by means of I. Vekua’s method, the system of y differential equations for physically and geometrically non-linear theory of non-shallow shells is obtained and compared with other theories (Ressner, Koiter-Naghdi, Lurie,...). V0 Acknowlegment. The designated project has been fulfilled by a financial support of Shota Rustaveli National Science Foundation (Grant SRNSF/FR/358/5-109/14). Any idea in this publication is possessed by the author and may not represent the opinion of Shota Rustaveli National 2 +V x –Vt Science Foundation itself. t References 1. Vekua, I.N. Shell Theory: General Methods of Construction. Pitman Advanced Publishing Program, Boston-London-Melbourne, 1985. 2. Meunargia, T. On extension of the Muskhelishvili and Vekua-Bitsadze u1 1 u 2 1 ( x 1 y ) ; ( y 2 x ) ; methods for geometrically and physically nonlinear theory of non- x E1 y E 2 shallow shells. Proc. A. Razmadze Math. Inst., 157 (2011), 95-129. 1 1 u u ( 1 2 ) ; 0, when x Vt ; xy 2 y x xy
y 0, xy 0, when y 0, x Vt , where E1 and E2 are Young in main direction, and is Poisson ratio, is shear modulus, moduli 1 2 and V V0 t ctg x value must be defined in the course of evaluating the problem. The problem has been reduced to Dirichlet problem, whose solution is presented by Schwarz integral.
GENERALIZATION OF I. VEKUA’S METHOD FOR THE PHYSICALLY AND GEOMETRICALLY NON-LINEAR AND NON- SHALLOW SHELLS
Tengiz Meunargia I. Vekua Institute of Applied Mathematics of Iv. Javakhishvili Tbilisi State University Tbilisi, Georgia, [email protected]
I. Vekua constructed the linear theory of shallow shells, containing the regular processes, by means of the method of reduction of 3-D problems of elasticity to 2-D ones.
31 32 THEORETICAL BASIS OF EXPLOSIVE EXTRACTION with the help of localized potentials the boundary-transmission problems OF STONE BLOCKS can be reformulated as a localized boundary-domain integral equations (LBDIE) systems and prove that the corresponding localized boundary- Rudolf Mikhelson, Sergo Khomeriki, Marina Losaberidze, domain integral operators are invertible. Davit Khomeriki, Grigol Shatberashvili G.Tsulukidze Mining Institute Acknowlegment. This work was supported by the International Joint 7.E.Mindeli str., Tbilisi 0186, Georgia Project Grant UK-EPSRC EP/M013545/1 and by the Shota Rustaveli National Scientific Foundation Grant FR/286/5-101/13 The preservation of massif structure and decorative properties in blocks largely depends on efficiency of explosive method for extraction of high References strength and abrasivity facing stone blocks. In the paper having regard to the basic concepts of the elasticity theory 1. Chkadua O., Mikhailov S. and Natroshvili D. Localized Boundary- and the physics of explosion a new method for extraction of blocks by Domain Singular Integral Equations Based on Harmonic Parametrix directional cleaving has been formulated, which is based on the calculation for Divergence-Form Elliptic PDEs with Variable Matrix Coefficients, of initial parameters of strain wave generated in rock by blasting linear Integral Equations and Operator Theory, 76 (2013), pp. 509-547. charges of explosive and selection of explosive types and design of charge, 2. Jentsch L. and Natroshvili D. Interaction between thermo-elastic and which does not damage the stone structure. For preservation of rock natural scalar oscillation fields, Integral Equations and Operator Theory, 28 structure the use of explosive with small critical diameter and high speed of (1997), pp. 261-288. detonation is recommended. At this time the short duration impulse of 3. Werner P. Beugungsprobleme der mathematischen Akustik, Arch. explosion eliminates growth of rock massif cracks due to massif inertia. Ration. Mech. Anal., 12 (1963), pp. 155-184.
WAVE SCATTERING BY INHOMOGENEOUS ANISOTROPIC MODELING OF LIMIT PASSAGE OF BOUNDARY VALUE OBSTACLES: BOUNDARY-DOMAIN INTEGRAL EQUATION PROBLEMS ELASTICITY OF POLYGONAL PLATES BY THE APPROACH FINITE ELEMENT METHOD
David Natroshvili Giorgi Nozadze Georgian Technical University, Deprtment of Mathmatics, Tbilisi, Georgia A.Tsulukidze Mining Institute, Tbilisi, Georgia, [email protected] and Iv. Javakhishvili Tbilisi State University, I.Vekua Institute of Applied The paper considers the problem of elasticity theory forpolygonal plates Mathematics, Tbilisi, Georgia with boundary conditions of freely support by the finite element method. [email protected] For simplicity, the load given, as a concentrated perpendicular force to the plates surface at the center of the plate. The task was simulated by the We consider the time-harmonic acoustic wave scattering by a bounded software SOLID WORKS. layered anisotropic inhomogeneity embedded in an unbounded anisotropic It is shown that the boundary conditions of freely support of polygonal homogeneous medium. The material parameters and the refractive index plates in the limit passage (N∞) degrade and do not match with boundary are assumed to be discontinuous across the interfaces between conditions of freely support of respective circular plate, which is obtained inhomogeneous interior and homogeneous exterior regions. The by approximating polygonal plate. corresponding mathematical problems are formulated as boundary- transmission problems for a second order elliptic partial differential equation of Helmholtz type with discontinuous variable coefficients. We show that 33 34 References The basic integral equation and system of the integral equations has been solved by a collocation method, in particular, a method of discrete 1. Пановко Я.Г. Механика деформируемого твердого тела. М.: Наука, singularity (see [2]). Corresponding systems of the linear algebraic 1985. equations have been obtained for uniform (using rectangular quadratic 2. В. Г. Мазья, С. А. Назаров Парадоксы предельного перехода formulas) as well for non-uniformly distributed knots (with the use of в решениях краевых задач при аппроксимации гладких областей quadratic formulas of higher accuracy constructed on the knots of многоугольными. Изв. АН СССР. Сер. матем., 1986, том 50, Chebyshev polynomials). Solving the system of linear algebraic equations выпуск 6, страницы 1156–1177. and graphic interpretation was carried out by means of programming system 3. Хомасуридзе Н.Г. О некоторых предельных переходах в теории Matlab. упругости и о "парадоксе Сапонджяна" // Изв. РАН. МТТ. 2007. In the presented work for the approached solution of the above – stated № 3. С. 46-54. problems new numerical algorithms were constructed, corresponding numerical calculations were performed and the hypothetical forecast for a crack distribution in the body had been given. APPROXIMATE SOLUTION OF SOME BOUNDARY VALUE PROBLEM OF ANTIPLANE ELASTISITY THEORY BY References COLLOCATION METHOD FOR COMPOSITE BODIES 1. Papukashvili A.R. Antiplane problems of theory of elasticity for WEAKENED BY CRACKS piecewise-homogeneous orthotropic plane slackened with cracks. Bulletin of the Georgian Academy of Sciences, 169, N2, p.267-270, Archil Papukashvili, Teimuraz Davitashvili, Zurab Vashakidze Tbilisi (2004). Iv. Javakhishvili Tbilisi State University, 2. Belotserkovski S.M., Lifanov I.K. Numerical methods in the singular Faculty of Exact and Natural Sciences, integral equations and their application in aerodynamics, the elasticity I.Vekua Institute of Applied Mathematics, theory, electrodynamics,. 256 pp., Moscow, ”Nauka” (1985). Tbilisi, Georgia, [email protected], [email protected], [email protected] MODELING AND CALCULATION OF COMPLEX EXTENDED CONFIGURATION SOLID DEFORMABLE BODY BASED ON In this work research of antiplane problems of the theory of elasticity by DISCRETE PRESENTATIONS a method of the integral equations for composite (piece-wise homogeneous) orthotropic bodies weakened by cracks is studied. David Pataraia*, Edisher Coceria**, Giorgi Purceladze***, Two problems are considered. In case of the first problem the crack Rusudan Maisuradze**** spreads to the interface (the crack extends until the interface) under a right * Grigol Tsulukidze Mining Institute, Tbilisi, Georgia, angle, and in case of the second problem the crack crosses dividing border [email protected], (intersect an interface) under a right angle. The first problem is reduced to the singular integral equation which containing an immovable singularity ** l.t.d. Constudio, Tbilisi, Georgia, [email protected] (contains motionless feature), and the second problem is reduced to system *** Tbilisi Transport Company, Tbilisi, Georgia, (pair) of the singular integral equations containing an immovable [email protected] singularity, with respect to the tangent stress jumps (the characteristic **** Grigol Tsulukidze Mining Institute, Tbilisi, Georgia, function of crack expansion) (see [1]). In the above – stated problems our [email protected] main objective was research of behavior of characteristic function of In the paper the original approach of solid deformable body calculation disclosing of cracks, calculation of stress intensity factors at the ends of a is presented that is based on and applies specially developed for this purpose crack and forecasting of distribution of a crack. algorithm and discrete model [1-6]. 35 36 Area considered various aspects of this method application for such is constructed, the accuracy of that is higher on one order than classic complex configuration non-homogeneous and extended bodies modeling theory. The accordance between parametric terms and accuracy of basic part and calculation, as, for example, the space antennas, cableways, dams. of equations, forced system and initial hypothesis is also achieved. For calculation of large size bodies an approach is developed that gives the possibility to dismember the offered design algorithm and realization into a computer local network or even in the Internet. TRANSITIONS IN TAYLOR-DEAN FLOW OF A HEAT- For providing advice, support and professional assistance I am thankful CONDUCTING FLUID BETWEEN TWO ROTATING POROUS to the whole personnel of Institute of Applied Mathematics and its Director CYLINDERS Professor George Jaiani. Luiza Shapakidze References Iv. Javakhishvili Tbilisi State University, A.Razmadze Mathematical 1. Ein Beitrag zur diskreten Darstellung des Seiles. Wissenschaftliche Institute, Tbilisi, Georgia, [email protected] Arbeiten des Instituts fuer Eisenbahnwesen, Verkehrswirtschaft und Seilbahnen, Technishe Univeristaet Wien), 1981. The report presents the results of investigations of instability and 2. Calculation and design of rope systems of the ropeway (In Russian transitions of heat-conducting fluid between two porous cylinders which is Language). Mecniereba, Tbilisi, 2000 - 115 p; driven by an constant azimuthal pressure gradient acting around the 3. The calculation of rope-rod structures of ropeways on the basis of the cylinders and by rotation of cylinders. new approach, WORLD CONGRESS of O.I.T.A.F., RIO DE JANEIRO, It is assumed that the flow is under the action of a radial flow through BRAZIL, October, 2011, 24 – 27, PAPERS OF THE CONGRESS, the porous cylinder walls and a radial temperature gradient. It is http://www.oitaf.org/Kongress%202011/Referate/Pataraia.pdf demonstrated that the magnitude and the direction of applied pressure and 4. http://www.mining.org.ge/develop/pataraia-dmr/index.html temperature gradient control the characteristics of instability and transitions 5. Modeling and Calculation of Big Rarefied Space Structures. to complex regimes.of the main stationary flow. International Scientific Conference (In English language); Georgian Technical University. 206-214p; 2009. 6. Discrete model and calculation method for rope–rod structures, Problem THE SOLUTIONS OF TWO-DIMENSIONAL INTEGRO- of Mechanics / International federation for the promotion of mechanism DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS IN and machine science, (In English language), 2008 - N2 (31). THE THEORY OF VISCOELASTICITY
Nugzar Shavlakadze RESEARCH OF DEFORMABILITY OF THE Iv. Javakhishvili Tbilisi State University A. Razmadze MULTI-LAYERED ORTHOTROPIC SHELL Mathematical Institute, Georgian Technical University 68, M. Kostava St.,Tbilisi 0175, Georgia ,e-mail: [email protected] Marlena Rajczyk*, Lenka Lausova** *Czenstochowa University of Technology, Czenstochowa, Poland, The effective solutions for integro-differential equations related to [email protected] problems of interaction of an elastic thin finite inclusion with a plate, when **VŠB−Technical University of Ostrava, Ostrava-Poruba, Czech Republic, the inclusion and plate materials possess the creep property are constructed. [email protected] If the geometric parameter of the inclusion is measured along its length according to the parabolic and linear law we have managed to investigate The model of multi-layered shell is constructed that provides the the obtained boundary value problems of the theory of analytic functions orthotropy and high order factors for all layers, despite their stiffness and and get exact solutions and establish behavior of unknown contact stresses arrangement in package. The methodology of multi-layered orthotropic shell at the ends of an elastic inclusion. 37 38 Let a finite non-homogeneous inclusion be attached to the plate which AVIATION HIGH EDUCATION IN GEORGIA is in the condition of a plane deformation. It is assumed that the plate and inclusion materials possess the creep property which is characterized by the Sergi Tepnadze*, Gela Kipiani** non-homogeneity of the ageing process and have different creep measures *Georgian Aviation University, Tbilisi, Georgia, [email protected] (t ) where is the function that defines the ageing **Georgian Aviation University, Tbilisi, Georgia, [email protected] Ci (t, ) i ( )[1 e ], i ( ) process of the plate and inclusion materials; different materials age is In the paper deals with the establishment of aircraft engineering chair in (x) const and the elasto-instant deformation modulus are i order to prepare local engineering personnel for aviation higher education Besides, the lateral contraction coefficients for Ei (t) Ei const, (i 1,2). grounded on new conception. In this way based on governmental resolution (1) in structure of Georgian Technical University of aircraft engineering chair elastic deformation 2 (t) and creep deformation 2 (t, ) are the same and constant. was established. It is assumed that the inclusion has no bending rigidity, is in the uniaxial By the resolution of President of Georgia Aviation Institute was assigned stressed state and is subject only to tension, i.e. a horizontal force from Georgian Technical University and on its base was established P (x 1)H(t ) is applied to the end of the inclusion (at the point x 1) Georgian Aviation University. Issues of origination and development of 0 0 Aviation Institute and Aviation University, their present and future are at the moment of time 0 ; then only the tangential stress acts on the line discussed. of contact of the inclusion and the plate ( (x) is the Dirac function, H(t) is the unit Heaviside function). We are required to define the law of distribution of tangential contact THEORETIKAL INVESTIGATION OF TRANSFORMABLE SPASE REFLECTOR MECHANICAL SYSTEM stresses q (t, x) on the line of contact, the asymptotic behavior of these stresses at the end of the inclusion and the coefficient of stress intensity. Shota Tserodze*, Malkhaz Nikoladze** To define the unknown contact stresses we obtain the following integral *Georgian Technical University, Tbilisi, Georgia, [email protected] equation **Georgian Technical University, Tbilisi, Georgia, 2(1 2 ) 1 q(t, y)dy 1 x [email protected] 2 (1 L ) (1 L ) q (t, y)dy, 0 x 1 2 1 E2 0 y x h1 (x)E1 0 1 In the paper a new closed-chain deployable system is presented. A h q(t, y)dy P H (t ) specific feature of its structure is that, as compared with analogous 0 0 0 structures, for connecting the sections with one another it is not required to apply additional synchronization devices. Transformation mechanism where the time operators Li act on an arbitrary function in the following represents a differential lever mechanism that gives the possibility to obtain manner t the desired law of motion of a characteristic link. For the preliminary (1 L ) (t) (t) K (t , ) ( )d , investigation of the structure and making possible changes in a i i i i 0 mathematical model by ANSYS software using the Ansys Parametric
Ci (t, ) is the thickness of Design Language is constructed. The degrees of freedom of hinges are K (t, ) E , , i 1,2 h1 (x) i i i i 0 simulated in local coordinate systems and are as much as possible inclusion, h is its width. approximated to the real model. Calculations are carried out for various kinds of loads and appropriate results are obtained.
References 1. Medzmariashvili, Sh. Tserodze, V. Gogilashvili. New Variant of the 39 40 Large Deployable Ring-Shaped Space Antenna. Space brackets. The trial of applied some schemes of theory of analytical functions Commmunications 22 (2009) 41-48. and projective methods will be given. 2. Sh. Tserodze, J. Santiago Prowald, van‘t Klooster C.G.M., E. Logacheva. ”Spatial Double Conical Ring-Shaped Reflector for Space Acknowledgment. This work was supported by Rustaveli Science Based Application”. Proceedings of 33rd ESA Antenna Workshop Foundation (grant N 30/28) and budget of I.Vekua Institute of Applied “Challenges for Space Antenna Systems”. 18 - 21 October 2011. Mathematics. ESTEC, Noordwijk, The Netherlands. 3. E. Medzmariashvili, N Tsignadze, Sh. Tserodze, J. Santiago-Prowald; C. Mangenot, C.G.M. Van’t Klooster, H. Baier, M. Janikashvili. Design STUDY OF STRESS-STRAIN STATE OF of Reflector with Double Pantograph and Flexible Center. Proceedings ELLIPTICAL BODY WHIT CRACK of ESA Antenna Workshop on Large Deployable Antennas. 2-3 October 2012. ESTEC, Noordwijk, The Netherlands. Natela Zirakashvili Iv. Javakhishvili Tbilisi State University, I.Vekua Institute of Applied Mathematics, Tbilisi, Georgia, [email protected] AN ITERATIVE METHOD FOR A TIMOSHENKO TYPE DYNAMIC BEAM Boundary-value problem for the ellipse are considered, when on the elliptic border and the segment between the foci of the ellipse tangential Zviad Tsiklauri stresses, free from normal stresses are given. This task is obtained from the Department of Mathematics of Georgian Technical University, Tbilisi, corresponding problem for semi-ellipse 0 1 ,0 , when Georgia, email: [email protected] conditions of uninterrupted continuation of the solution are given at 0 and , therefore it is possible to bind the semi-ellipse as an elliptic We consider the initial boundary value problem for a nonlinear differential equation modeling dynamic state of the Timoshenko type ring, in which the tangential stresses are given on 0 and the beam. To approximate the Solution the Galerkin method, a difference conditions of uninterrupted continuation of the solution are not performed along this part, i.e. we have a crack on which the tangential stress acts. For scheme and the Jacobi iterative method are used. The error of the solving of this problem we apply a method by which the solution of iterative method is estimated. complex problems of elasticity is reduced to the solution of simple problems of elasticity [1], namely, to solution of internal and external problems of elasticity, which are easily solved by separation of variables. ON MODELING OF THERMODYNAMIC NONSHALLOW Using the MATLAB software we obtained numerical results and ELASTIC SHELLS AND APPLICATION OF COMPLEX ANALYSIS constructed 2D and 3D graphs of the distribution of displacements and stresses in body. Tamaz Vashakmadze Iv. Javakhishvili Tbilisi State University, I.Vekua Institute of Applied Reference Mathematics, Tbilisi, Georgia, [email protected] 1. Khomasuridze, N. Representation of solutions of some boundary value We consider the problem of mathematical modeling of piezoelectric, problems of elasticity by a sum of the solutions of other boundary value electrical conductivity and viscous elastic multilayer nonshallow shells by 2- problems, Georgian Mathematical Journal 10(2) (2003) 257-270. Dim von Kảrmản-Koiter type refined theories. The corresponding models represent boundary value problems for nonlinear systems of 2Dim partial integro-differential equations with Monge-Ampere operators and Poisson 41 42 Reroebisa daDSlangebis angariSi turbulentobis tenzoris zusti gantoleba da zurab arqania angariSis Sedegebi akaki wereTlis saxelmwifo universiteti quTaisi, saqarTvelo, amiran afciauri [email protected] quTaisis erovnuli saswavlo universiteti, quTaisi, saqarTvelo, Cvens mier ganxilulia absoluturad moqnili Reroe- [email protected] bis statikis samganzomilebiani amocanebi, roca Reroze moqmedeben nebismieri mimarTulebis Seyursuli Zalebi. naSromSi mocemulia turbulentobis problemis gadaw- SemuSavebulia Slangebis formebisa da SlnagSi Rer- yveta tenzoruli aRricxvis meTodebis gamoyenebiT. naC- Zuli Zalvebis gansazRvris ricxviTi meTodi. vnebia rom, tenzoruli aRricxvis maTematikuri gantole- gamokvleulia idealuri da blanti siTxeebis Siga bebi Seicaven umniSvnelovanes informacias imisaTvis, ra- nakadebis gavlena Slangis formaze da RerZul Zalvebze. Ta moZebnili iqnas turbulenturi Zabvebis is tenzori, naCvenebia, rom siTxis Siga nakadi Slangis formaze gav- romlis gansazRvrac ver xerxdeboda saukuneze meti xnis lenas ar axdens. Slangis forma ganisazRvreba mxolod ganmavlobaSi.Ndamtkicebulia, rom aracxadi saxiT, tenzo- gare ZalebiT. ri warmoadgens drois mixedviT saSualo siCqarisa da miRebulia SlangSi RerZuli Zalvebis formula. simkvrivis gradientebis funqcias, xolo, cxadi saxiT, SemuSavebulia gareSe Seyursuli ZalebiT datvirTu- tenzori SeiZleba ganisazRvros rogorc saSualo siCqa- li, siTxis an haeris nakadebTan urTierTqmedi Slangebis ris, simkvrivisa da pulsaciebis energiis funqcia. moce- statikis amocanebis amoxsnis meTodi SlangSi idealuri mulia Sesabamisi gantolebebi. an blanti siTxis Siga nakadis gaTvaliswinebiT. Catarebuli gaangariSebebis Sedareba arsebul eqsperi- miRebuli Sedegebi saSualebas iZlevian SevafasoT mentalur monacemebTan adasturebs amonaxsnis marTebu- Reros da Slangis simtkice, mizanmimarTulad mivudgeT lobas. Slangis da SlangSi siTxis Siga nakadis parametrebis SerCevas da amiT avamaRloT Slangis saimedooba misi Lliteratura eqsploataciis dros. 1. М.Л. Акивис, В.В. Гольдберг - Тензорное исчисление, М., НАУКА, literatura 1972 г. 2. А. Дж. Мак-Конелл - Введение в тензорный анализ, М., Физматгиз, 1. Светлицки В. А. Механика трубопроводов и шлангов м.: 1963 г. машиностроение, 1982, 279с.
43 44 Zelis eqsperimentaluri kvleva Termodrekadobis Teoriis zogierTi amocana Termomeqanikuri datvirTvisas orgvari forovnobis mqone sferosaTvis
Ggulbanu baisarova*, omar kikviZe** Llamara biwaZe *akaki wereTlis saxelmwifo universiteti iv. javaxiSvilis saxelobis Tbilisis saxelmwifo quTaisi, saqarTvelo, [email protected] universiteti, **akaki wereTlis saxelmwifo universiteti i. vekuas saxelobis gamoyenebiTi maTematikis instituti, quTaisi, saqarTvelo, [email protected] Tbilisi, saqarTvelo, [email protected]
naSromSi ganxilulia konsoluri Zelis pirdapiri naSromis mizania Termodrekadobis Teoriis statikis Runva Termomeqanikuri datvirTvisas. Zelis ganivi kveti dirixles da neimanis tipis amocanebis ganxilva orgvari marTkuTxaa. warmodgenilia eqsperimentaluri stendi, sa- forovnobis mqone sferosaTvis [1]. [2-5]-Si ganxiluli dac Zeli itvirTeba Seyursuli ZaliT Tavisufal bolo- meTodebis gamoyenebiT agebulia dirixles da neimanis ze, xolo qveda zedapiris Sua nawili xurdeba specia- tipis amocanebis amonaxsnebi absoluturad da Tanabrad luri mowyobilobiT. eqsperimentSi izomeba Zelis zeda krebadi mwkrivebis saxiT. da qveda zedapirebis temperaturebi gaxurebis ubanze, literaturა aseve Tavisufali bolos vertikaluri da horizonta- luri gadaadgilebebi. Ggazomvebi Sesrulebulia 40 wm.-is 1. Khalili N.,Selvadurai A.P.S.: A Fully Coupled Constitutive Model intervaliT Termomeqanikuri datvirTvis Semdegi reJime- for Thermo-hydro-mechanical Analysis in Elastic Media with Double bisaTvis: 1. Zelze moqmedebs mxolod araerTgvarovani Porosity.Geophsical rResearch Letters,v.30,pp. SDE 7-1-7-3 , 2003. temperaturuli veli, 2. Zelze modebulia Seyursuli 2. Basheleishvili M., Bitsadze L.: The basic BVPs of the theory of Zala da Semdeg qveda zedapiris Sua nawili xurdeba. consolidation with double porosity for the sphere. Bulletin of TICMI, eqsperimentis SedegebiT dadgenilia, rom cvladi tem- 16 , n.1, 15-26 , 2012. peraturuli veliT gamowveuli vertikaluri gadaadgile- 3. Tsagareli I., Bitsadze L.: Explicit Solution of one Boundary Value bebi gacilebiT mcirea meqanikuri datvirTviT gamowveul Problem in the full Coupled Theory of Elasticity for Solids with Double gadaadgilebebze. Sedegebi adastureben Teoriuli kvle- Porosity. Acta Mechanica: Volume 226, Issue 5, 1409-1418 ,2015, visas daSvebuli hipoTezis samarTlianobas. eqsperimentis DOI: 10.1007/s00707-014-1260-8. Sedegebi Sedarebuli iqneba ricxviTi gaangariSebiT miRe- 4. I. Tsagareli, L. Bitsadze, The Boundary Value Problems in the Full bul SedegebTan. Coupled Theory of Elasticity for plane with Double Porosity with a Circular Hole, Seminar of I.Vekua Institute of Applied literatura Mathematics, Reports, vol.. 40, 68-79, 2014. 5. Basheleishvili M., Tsagareli I.: Effective solution of the basic BVPs of 1. Термопрочность деталей машин. /Под ред. И.А.Биргера и the elasticity theory for a sphere. Bull.of the Academy of Sciences of Б.Ф.Шорра. М.: Машиностроение, 1975.- 455 с. the Georgian SSR, 108, 1, 41-44, 1982. 6. Tsagareli I.: On a problem for a spherical layer. Proceedings of I.Vekua Inst. of Appl. Math., 12, 118-122 ,1983
45 46 fenovani sistemebis dinamikuri modelebi lema. romelsac safrTxes uqmnis talRebisa da dinebebis zemoqmedeba sanapiro areebze da anTropologiuri faqto- seiT bliaZe*, valeri miqaZe** rebi. aRniSnulidan gamomdinare, gasatarebelia mecnie- *ssip saxelmwifo samxedro samecniero-teqnikuri rul safuZvelze damyarebuli swori garemos dacviTi centri „delta“, RonisZiebebi. bolo dros sainJinro azrovneba sul ufro Tbilisi, saqarTvelo, [email protected] xdeba bunebaze orientirebuli, ris gamoc axali teqno- ** saqarTvelos saaviacio universiteti, Tbilisi, logiebi warmogvidgeba, rogorc garemos dacvis efeqturi saqarTvelo, [email protected] saSualeba, romelmac amJamad mniSvnelovani gamoyeneba hpova zRvis sanapiro zolis aRdgena-gamagrebis proble- garsisebri sendviC konstruqciebis angariSisaTvis ga- mis gadawyvetaSi. moiyeneba sasrul elementTa meTodi, rac saSualebas iZ- winamdebare statiaSi ganxilulia zRvis sanapiro pro- leva gaTvaliswinebul iqnas Zvris deformacia ganivi de- cesebis (1;2;3) ricxviTi modelireba formaciebiT da calkeuli fenebis moZraobis inerciuli efeqtebi. SemoTavazebuli algoriTmi ar aris dakav- Sirebuli laminirebuli sasruli elementebis formi- rebasTan, isini Caenacvlebian sqeli da Txeli firfitis (1) da garsis sasrul elementebs. msgavsi aproqsimirebuli da maTematikuri modelirebis mecnierulad dasabuTebuli funqciebis gamoyeneba formebisa da gadaadgilebebisaTvis gamoyeneba zRvis sanapiro zolis dacva-aRdgenisTvis uzrunvelyofs deformaciebis Tavsebadobas, rac saSua- ACEtube (2;3;4) teqnologiis safuZvelze. lebas iZleva Sefasdes Zabvebi da deformaciebi maqsima- naSromi Sesrulebulia rusTavelis gamoyenebiTi lurad miaxloebuli analitikuri angariSis SedegebTan. kvlevebisaTvis saxelmwifo grantisAAR/22/3-109/14 geomor- fologiuri procesebis stabilizaciis RonisZiebebi mdi- literaturა nareebis rionis da enguris SesarTav akvatoriebSi da ma- Ti gaangariSebis hidrodinamikuri meTodebi farglebSi. 1. Болотин В.В., Новичков Н.Н. Механика многослойных конструкций. - М.: Машиностроение, 1980. -375с. literatura 2. Григолюк Э. И. Чулков П.П. Устойчивость и колебания трехслойных оболочек.- М.: Машиностроение, 1973.-172 с. 1. Nam, P.T., Larson, M., 2010. Model of nearshore waves and wave- induced currents around a detached breakwater. Journal of Waterway, Port, Coastal, and Ocean Engineering 136(3), 156-176. zRvis sanapiro zolis dinamikis ricxviTi 2. Брегвадзе А.В., Сагинадзе И.С. Моделирование литодинамических modelireba da misi sainJinro aspeqtebi процессов в прибрежной зоне. II Международная конференция “Неклассические задачи механики”. 6-8.10.2012. Кутаиси, Грузия. amiran bregvaZe*, ivane saRinaZe** 3. AmiranBregvadze.Local Innovation Experience in Georgia. akaki wereTlis saxelmwifo universiteti, saqarTvelo, Engineering Aspects of Beach Formation and Coast ProtectionJean quTaisi [email protected],** Monnet Programme Project EU Regional Innovation Policy as a Model akaki wereTlis saxelmwifo universiteti, saqarTvelo. for the EaP Country RegionsTbilisi 2014 4. Krystian W. Pilarczyk,DESIGN ASPECTS OF GEOTUBES AND Tanamedrove pirobebSi sul ufro mkafiod dgeba napi- GEOCONTAINERS, Zoetermeer, Netherlands 30 January 1996 rebis talRebis damangreveli moqmedebisgan dacvis prob- 47 48 saxsruli meqanizmebis da amwe-satransporto da sagzao manqanebis kvadratuli asaxvebis geometria samuSao aRWurvilobis kinematikuri kvleva
gia giorgaZe*, giorgi ximSiaSvili** vaJa gogaZe *i.vekuas gamoyenebiTi maTematikis instituti, akaki wereTlis saxelmwifo universiteti, quTaisi, [email protected] saqarTvelo, [email protected] **ilias saxelmwifo universiteti, [email protected] amwe-satransporto da sagzao manqanebis samuSao aRWur- moxsenebaSi ganvixilavT zogierTi meqanikuri sistemis vilobebi warmoadgens rTul sivrcul Rerovan sistemebs, konfiguraciuli sivrcis erT-erT SesaZlo daxasiaTebas. romelTa calkeuli rgolebi saxsruladaa dakavSirebuli nebismieri M meqanikuri sistemis yevla SesaZlo mdgoma- erTmaneTTan da mimarTva xdeba hidrocilindrebis saSua- reobaTa X sivrce, romelsac M-is konfiguraciuli sivr- lebiT. cnobilia, rom aRniSnul manqanebSi rgolebis Seer- ce ewodeba, qmnis algebrul mravalsaxeobas. ZiriTadad, TebisaTvis umetesad gamoyenebulia cilindruli saxsrebi, sistemis mdgomareoba srulad xasiaTdeba sasruli romelTaTavis uflebis xarisxi erTis tolia. rig SemTx- raodenobis parametrebis saSualebiT, am SemTxvevaSi Seg- vevaSi calkeuli rgolebi sferuli saxsrebiTaa dakavSi- viZlia CavTvaloT, rom figuraciuli sivrce aris evkli- rebuli, romelTaTavis uflebis xarisxi samis tolia. dur sivrceSi Cadgmuli mravalsaxeoba. X-is nebismiri mizan Sewonilia aRniSnuli manqanebSi gamoyenebul iqnas wertili aris sistemis garkveuli mdgomareba da gansxva- ormagi cilindruli saxsrebi, romelTaTavis uflebis vebul wertilebs Seesabameba gansxvavebuli mdgomareo- xarisxi oris tolia. ormagi cilindruli saxsrebis gamo- bebi. yeneba zrdis manqanis funqcionalur daniSnulebas, amar- Cven ganvixilavT saxsruli meqanizmebis konfigu- tivebs konstruqcias da zrdis manqanis mwarmoeblobas, raciul sivrces, romelic gluvi mravalsaxeobebis ga- konstruqciis simtkicesa da xangamZleobas. morCeuli klasia da kidev cnobilia rogorc mravalku- amwe-satransporto da sagzao manqanebis samuSao aRWur- Txedebis konfiguraciuli sivrce, amasTan gamoviyenebT vilobis struqturulma kvlevam aCvena, rom rig SemTxve- kvadratuli asaxvis Tvisebebs. Cven gamoviTvliT saxs- vebSi aRniSnul konstruqciebSi adgili aqvs zedmeti bmebis ruli meqanizmebis konfiguraciuli sivrcis eileris maxa- arsebobas, ris gamoc rgolebis moZraoba xdeba saxsrebSi siaTebels da vaCvenebT, rom sivrcis topologia teqnikur arsebuli RreCoebis meSveobiT an liTonis konstruqciebis SezRudvebs adebs meqanikur sistemas. ganvixilavT agreTve winaswari daZabuli mdgomareobiT, rac moiTxovs konst- sferuli da bicentruli mravalkuTxedebis ruqciis damzadebis sizustes, amcirebs manqanis simtkicesa konfiguraciuli sivrceebis topologiur da analizur da saimedoobas. Tvisebebs. amitom mizanSewonilia Seiqmnas iseTi racionaluri konstruqciebi, romlebsac ar gaaCniaT zedmeti bmebi. TviT- madloba. winamdebare naSromi Sesrulebuli iyo SoTa regulirebadia da ar iwvevs samuSao aRWurvilobis ele- rusTavelis erovnuli samecniero fondis mxardaWeriT. mentebis winaswar daZabul mdgomareobas. granti FR/59/5-103/13.N literatura
1. gogaZe v. m. sapatento modeli “TviTsacleli” saqarT- velos inteleqtualuri sakuTrebis erovnuli centri “saqpatenti”, 2009 #11 (279), gverdi 20
49 50 2. gogaZe v. m. gogaZe g. buldozeris samuSao aRWurvi- loba. patenti #5633 gamogoneba Tbilisi 2012 madloba. winamdebare naSromi Sesrulebuli iyo SoTa 3. gogaZe v. m. gogaZe g. skreperis samuSao aRWurviloba. rusTavelis erovnuli samecniero fondis mxardaWeriT patenti #5634 gamogoneba Tbilisi 2012 (granti SRNSF / FR / 358 / 5-109 / 14). 4. gogaZe v. m. gogaZe g. cicxviani satvirTveli. patenti #5696 gamogoneba Tbilisi 2012 literaturა 5. gogaZe v. m. gogaZe m. paWkoria b. Canglebiani satvi- rTveli. ganacxadi gamogonebaze #AP2014013372, 2014 1. Vekua, I.N. Shell Theory: General Methods of Construction. Pitman Advanced Publishing Program, Boston-London-Melbourne, 1985. 6. gogaZe v. m. gogaZe m. iremaZe l. Avtogreideri samuSao 2. Meunargia, T.V. On one method of construction of geometrically and AP2014013370, aRWurviloba. ganacxadi gamogonebaze. # physically nonlinear theory of non-shallow shells. Proc. A. Razmadze 2014 Math. Inst., 119 (1999), 133-154.
normirebul momentTa meTodi kavkasiis teritoriisTvis amindis sakvlevi aradamreci garsebisaTvis saprognozo modelis realizaciis Sesaxeb bakur gulua iv. javaxiSvilis saxelobis Tbilisis saxelmwifo Teimuraz daviTaSvili*, zurab modebaZe** universiteti *iv. javaxiSvilis saxelobis Tbilisis saxelmwifo i. vekuas saxelobis gamoyenebiTi maTematikis instituti universiteti, soxumis saxelmwifo universiteti, Tbilisi, saqarTvelo, i. vekuas saxelobis gamoyenebiTi maTematikis instituti, [email protected] Tbilisi, saqarTvelo, [email protected] ** iv. javaxiSvilis saxelobis Tbilisis saxelmwifo sazogadod, garsebis dazustebuli Teoriis ageba xor- universiteti, Tbilisi, saqarTvelo, [email protected] cieldeba samganzomilebiani drekadobis Teoriis ganto- lebaTa sistemis reduqciiT. akad. i. vekuas SromebSi miRe- warmodgenil naSromSi kavkasiis teritoriisTvis Cven buli iyo gantolebaTa sistema cvalebadi sisqis Txeli SevimuSaveT da CavtvirTeT amindis sakvlevi saprognozo da damreci garsebisaTvis, anu sisqis mimarT ucvleli modeli (WRF-ARW) GRID sistemaSi, romelic iTvaliswi- geometriis mqone garsebisaTvis [1]. igive meTodi nebda garemos geografiul maxasisTeblebs, topografiul geometriulad da fizikurad arawrfivi aradamreci gar- simaRleebs, niadagis tipebs da maT temperaturul monace- sebis SemTxvevaSi ganzogadebulia prof. T. meunargias mebs, mcenareuli safaris yovelTviur ganawilebas, mier [2]. dedamiwis albedos da a.S. amindis sakvlevi saprognozo mocemul naSromSi ganxilulia aradamreci garsebi. i. modeli (WRF-ARW) CatvirTul iqna linuqs-86 platformis vekuas normirebul momentTa meTodis gamoyenebiT miRe- gamoyenebiT. modeluri gaTvlebi ganxorcielebul iqna bulia garsis pireulebze sasazRvro pirobebTan SeTanx- horizontalurad erTmaneTSi Cadgmuli 15 da 5km badeebis mebuli Zabvis tenzoris miaxloebiTi gamosaxuleba nebi- saSualebiT. uxeSi bade zomebiT 94x102 faravda mTlianad 0 1 N samxreT kavkasiis regions, xolo masSi Cadgmuli bade smieri veqtoruli velebisaTvis u , u,..., u , romlebic zomebiT 70x70 gankuTvnili iyo saqarTvelos teritori- warmoadgenen saZiebeli u veqtoris momentebs. isTvis. Oorive bade vertikaluri mimarTulebiT Seicavda 31 dones. Cven SeviswavleT atmosferos Termuli da 51 52 adveqciuri faqtorebis efeqti dasavleT saqarTveloSi cocvadobis arawrfiv TeoriaSi gaangariSebis mimdinare klimaturi cvlilebis fonze. mocemul erTi dazustebuli meTodis Sesaxeb naSromSi warmodgenilia zogierTi gamoTvlebis Sedegebi romlebic Sesrulebul iqna erTmaneTSi Cadgmuli 15 da akaki dumbaZe 5km badeebis saSualebiT. saqarTvelos saaviacio universiteti, Tbilisi, saqarTvelo, [email protected]
erTi arawrfivi kvazistacionaruli rogorc cnobilia kompozituri masalis deformirebis maTematikuri modelis Sesaxeb ganStoebis mqone kanoni (ε,σ) – sibrtyeSi warmoadgens mrud wirs, romelic gazsadenSi gaJonvis adgilmdebareobis ori ubnisagan Sedgeba: pirveli – wrfivi deformirebis aRmosaCenad ubania (hukis kanonis farglebSi), xolo meore – ara- wrfivi, sadac daculi ar aris hukis kanoni. imisaTvis, Teimuraz daviTaSvili, givi gubeliZe, meri SariqaZe. rom konstruqciis (kompozituri masalisgan) gaangariSebi- iv. javaxiSvilis saxelobis Tbilisis saxelmwifo sas daculi iyos moTxovnebi: simtkiceze, xangamZleobasa universitetis i. vekuas saxelobis gamoyenebiTi da saimedoobaze, saWiro aris amasTanave is, rom kons- maTematikis instituti, zusti da sabunebismetyvelo truqcia iyos ekonomiuri. aRniSnuli moTxovnebi mWidrod mecnierebaTa fakulteti, Tbilisi, saqarTvelo, aris dakavSirebuli konkretuli markis kompozituri [email protected], [email protected] masalis Tvisebebis SeswavlasTan, raTa SesaZlebeli iyos misi usafrTxod danergva ama Tu im konstruqciaSi. moxse- mocemul naSromSi erTi arawrfivi kvazistacionaruli, nebaSi gadmocemulia meTodi, romlis gaTvaliswinebiT maTematikuri modelis safuZvelze Seswavlilia ganSto- gaangariSebulia kompozituri fiuzelaJi TviTmfrinavis ebis mqone gazsadenSi nakadis wnevisa da xarjis gana- afrena-daSvebisas warmoqmnili rxevebisa da masalaSi gan- wileba. am miznis misaRwevad Seswavlilia erTi arawrfivi viTarebuli cocvadobis gaTvaliswinebiT. kerZowarmoebuliani diferencialur gantolebaTa sis- tema, romelic aRwers gazis arastacionarul moZraobas ganStoebis mqone milsadenSi. napovnia am gantolebaTa Termodinamiuri drekadi garsebis sistemis efeqturi amonaxsni (wnevisa da gazis nakadis modelirebisa da analizur funqciaTa Teoriis xarjis ganawileba milsadenSi) SemdgomSi gazsadenSi gamoyenebis Sesaxeb gaJonvis adgilmdebareobis aRmoCenis mizniT. winaswarma ricxviTma gaTvlebma aCvena SemoTavazebuli meTodis efeq- Tamaz vaSaymaZe turoba. naSromSi mocemulia zogierTi ricxviTi Tvlis iv. javaxiSvilis saxelobis Tbilisis saxelmwifo Sedegebi, romlebic adekvaturia dakvirvebis masalebiT universiteti, i. vekuas saxelobis gamoyenebiTi miRebul SedegegebTan. maTematikis instituti, Tbilisi, saqarTvelo, [email protected]
ganixileba Termodinamiuri struqturebis maTematiku- ri modelirebis sakiTxi organzomilebiani fon karman- koiteris tipis dazustebuli TeoriebiT piezoeleqtru- li, eleqtrogamtari da blanti drekadi fenovani ara- damreci garsebisaTvis. miiReba sasazRvro amocanebi
53 54 kerZo warmoebulian integro-diferencialur gantole- MATLAB-is programuli uzrunvelyofis gamoyenebiT baTa sistemisaTvis; maTi nawili warmoadgens monJ-ampe- miRebulia ricxviTi Sedegebi da agebulia sxeulSi risa operatorisa da puasonis frCxilebis Sesabamisi ga- gadaadgilebebisa da Zabvebis ganawilebis Sesabamisi 2D mosaxulebebs, romelTa gaTvaliswinebiT gadmocemuli და 3D grafikebi. iqneba analizur funqciaTa Teoriisa da proeqciuli me- Todebis zogierTi sqemis gamoyenebis cda. literaturა madloba. winamdebare naSromi Sesrulebuli iyo rusTa- 1. Khomasuridze, N. Representation of solutions of some boundary value velis samecniero fondis grantisa 30/28 da i. vekuas gamo- problems of elasticity by a sum of the solutions of other boundary value yenebiTi maTematikis institutis sabiujeto finansirebaTa problems, Georgian Mathematical Journal 10(2) (2003) 257-270. xelSewyobiT. drekadobis brtyeli Teoriis erTi bzariani elifsuri sxeulis daZabul- amocanis Sesaxeb mravalkuTxa deformirebuli mdgomareobis Seswavla xvrelis mqone wriuli arisaTvis
naTela ziraqaSvili giorgi kapanaZe*, miranda narmania** iv. javaxiSvilis saxelobis Tbilisis saxelmwifo * i.vekuas saxelobis gamoyenebiTi maTematikis instituti. universiteti, a.razmaZis saxelobis maTematikis instituti, i. vekuas saxelobis gamoyenebiTi maTematikis instituti, [email protected] Tbilisi, saqarTvelo, [email protected] **saqarTvelos universiteti, Tbilisi, saqarTvelo,
ganixileba sasazRvro amocana elifsisaTvis, rodesac ganxilulia drekadobis brtyeli Teoriis amocana mra- elifsur sazRvarze da elifsis fokusebs Soris mona- valkuTxa xvrelis mqone wriuli arisaTvis. amocanis amosax- kveTze mocemulia mxebi Zabvebi, xolo normaluri snelad gamoyenebulia konformul asaxvaTa da analizur Zabvebisgan Tavisufalia. es amocana miiReba naxevarelif- funqciaTa sasazRvro amocanebis meTodebi da saZiebeli sisaTvis 0 1 ,0 Sesabamisi amocanisgan, ro- kompleqsuri potencialebi agebulia efeqturad (analizuri desac 0 da -ze mocemulia amonaxsnis uwyvetad formiT). moyvanilia amonaxsnebis Sefasebebi kuTxeebis wveroTa maxloblobaSi. gagrZelebis pirobebi, amitom SesaZlebelia naxevar elifsis Sekvra mTlian elifsur rgolad, romelSic madloba. winamdebare naSromi Sesrulebuli iyo SoTa 0 -ze mocemulia mxebi Zabva da am monakveTze ar sru- rusTavelis erovnuli samecniero fondis mxardaWeriT ldeba amonaxsnis uwyvetad gagrZelebis pirobebi, e.i. (granti SRNSF / FR / 358 / 5-109 / 14). gvaqvs bzari, romelzec moqmedebs mxebi Zabva. am amocanis amosaxsnelad gamoiyeneba meTodi, romliTac drekadobis Teoriis rTuli amocanebis amoxsna daiyvaneba martivi amocanebis amoxsnaze [1], kerZod, drekadobis Teoriis Siga da gare amocanebis amoxsnaze, romlebic martivad ixsneba cvladTa gancalebis meTodiT.
55 56 firfitis tipis mravalfeniani Savi zRvis Sereuli fenis Taviseburebebis konstruqciebis simtkice safren aparatebSi ricxviTi kvleva saqarTvelos sanapiro zonisaTvis revaz kaxiZe SoTa rusTavelis saxelobis baTumis saxelmwifo diana kvaracxelia*, demuri demetraSvili** universiteti, baTumi, saqarTvelo, [email protected] *iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti, m. nodias geofizikis instituti, Tbilisi firfitis tipis mravalfeniani Txelkedliani konst- **soxumis saxelmwifo universiteti, Tbilisi, ruqciebi sul ufro farTod gamoiyeneba aviamSeneb- saqarTvelo, [email protected] lobaSi, raketebis mSeneblobaSi da teqnikis sxva dar- gebSi. yovelive es konstruqciebis maRali simtkicisa da zRvebisa da okeaneebis zeda Sereuli fena warmoadgens maTi wonis sagrZnobi Semcirebis aucileblobiTaa gamow- wylis erTerT mniSvnelovan ares, romlis Termo- veuli. am aucilebeli Taviseburebebis erToblioba uzru- dinamikuri mdgomareoba gansazRvravs mraval mniSvnelo- nvelyofilia mravalfeniani konstruqciebis calkeuli van fizikur, qimiur da biologiur procesebs zRva-atmos- fenebisaTvis sxvadasxva Semavseblebis gamoyenebiT. Semav- ferul garemoSi. igives Tqma SeiZleba Savi zRvis turbu- seblebi da kompoziciuri masalebi xasiaTdebian Zvris lenturi Sereuli fenis Sesaxeb, romelic warmoadgens dabali sixistiT, rac maTi uaryofiTi Tvisebaa [1, 2]. kvlevis mTavar sagans. moxsenebaSi gadmocemulia aRniSnuli problemis, mra- cnobilia, rom Sereuli fenis siRrme ZiriTadad gani- valfeniani firfitovani konstruqciis simtkicis ricxvi- sazRvreba wylis Tvisebebis SefasebebiT: temperaturisa Ti analizis meTodika. da simkvrivis, magram Cvens SemTxvevaSi Sereuli fenis siRrme da misi cvalebadoba Seswavlilia Savi zRvis literatura dinamikis ricxviTi modelis gamoyenebiT, romelic SemuSavda m. nodias geofizikis institutSi (BSM-IG). 1. dumbaZe, a. kompozituri tanis meqanika. Tbilisi: saqar- kvlevis mTavar sagans warmoadgens Savi zRvis zeda Tvelos saaviacio universiteti, 2015. −292 gv. Sereuli fenis warmoqmnis Taviseburebebisa da misi evo- 2. Михайлов Б.К., Кипиани Г.О., Москалева В.Г. Основы теории и luciis Seswavla saqarTvelos sanapiro zonisaTvis ara- методы расчёта на устойчивость трёхслойных пластин с разрезами. stacionaruli atmosferul cirkulaciasTan mimarTebaSi Тбилиси: Мецниереба, 1991. −189 c. da Termoxalinuri zemoqmedebis gaTvaliswinebiT Sida wliur droiT masStabebSi. agreTve, kvlevis mTavar aspeqts warmoadgens vertikaluri difuziis koeficientis mniSvnelovani zegavlena Savi zRvis zeda fenis tempera- turul da marilianobis velebze. amasTanave, vertika- luri difuziis koeficientis siTbosa da marilianobis- Tvis CaTvlilia mudmivad da misi parametrizeba ganxor- cielda obuxovis modificirebuli formulis mixedviT.
madloba. winamdebare naSromi Sesrulebuli iyo SoTa rusTavelis erovnuli samecniero fondis grant No. AR/373/9-120/12. mxardaWeriT.
57 58 masis uwyvetobis ganzogadoebuli eleqtromagnituri talRis gabneva T –s magvar gantolebada misi Sedegebi samkapas rezonatorul nawilSi moTavsebul cilindrze, rodesac misi aRgzneba xdeba vladimer kircxalia sxvadasxva mxridan ilia vekuas saxelobis soxumis fizika-teqnikis instituti firani kobiaSvili naCvenebia, rom Tanamedrove TeoriaSi arsebuli masis Teoriul da gamoyenebiT meqanikaSi saqarTvelos uwyvetobis gantoleba, roelsac iyeneben nebismieri gare- erovnuli komitetis wevri. mosTvis, samarTliania mxolod erTgvarovani garemos SemTxvevaSi da araerTgvarovani garemosTvis saWiroebs Temis aqtualoba ganpirobebulia radioeleqtronuli da komunikaciuri sistemebis ganviTarebis Tanamedrove ganzogadoebas. ganzogadoebis Semdeg gantolebas marjvena tendenciebiT, romlebic sul ufro da ufro mzard moT- mxares emateba wevri, roelic mniSvnelSi Seicavs beris izo- xovnebs uyenebs rogorc mTlianad sistemebs, aseve maT barul siCqares C p . igi warmoadgens garemos araerTgvarov- konstruqciul gadamcem da mimReb traqtebs elementebis nobis zomas da misi arseboba sul axlaxans iqna aRmoCenili. efeqturobisa da eleqtromagnituri Tavsebadobis am siCqaris usasrulobisken miswrafebisas gantoleba gazrdis TvalsazrisiT. ganixileba sworkuTxa talRgamtarebis segmentebisgan gadadis masis uwyvetobis dRes cnobil gantolebaSi, rac Sedgenili samkapas rezonatorul nawilSi ganTavsebuli imas niSnavs, rom idealurad erTgvarovan garemoSi arsebobs wriuli ganivi kveTis mqone metaluri cilindris mkacri bgeris mxolod adiabaturi siCqare Cs . es garemoeba Zireu- eleqtrodinamikuri Teoria, rodesac sistemis aRgzneba lad cvlis iseTi umniSvnelovanesi kriteriumebis ganmar- xdeba ganmStoeblis nebismieri Stos mxridan. tebas, rogorebicaa garemos kumSvadoba an ukumSvadoba. Semotanilia e.w. kvebis logikuri mamravlis cneba, aRmoCnda, rom es kriteriumebi, romelTac qondaT wminda romelic migvaniSnebs xdeba Tu ara sistemis kveba fiqsi- rebuli Stos mxridan [2,4]. Cawerilia sruli velis meqanikuri azri, iZenen Termodinamikur azrs. ase magaliTad, gamosaxulebebi TiToeuli arisaTvis. Tavdapirvelad Termodinamikiuli TvalsazrisiT wyali da rkina gacilebiT rezonatorul nawilSi veli warmodgeba uwyveti velis ufro kumSvadi nivTierebebia, vidre haeri atmosferos zeda saxiT (radgan am arisaTvis ucnobia sakuTari talRuri fenebSi. garda amisa, icvlebian cnobili aero da hidro- ricxvebi). siaxle mdgomareobs imaSi, rom eleqtruli dinamikuri Tanafardobebi. velis daZabulobis veqtoris tangencialuri mdgenelis uwyvetobis pirobis gamoyenebis Semdeg xdeba velis Cawera diskretul speqtrad, naSTTa Teoriis, Jordanis lemis da koSis Teoremis gamoyenebiT [1,3]. aseTi saxiT Cawerili velisaTvis metalur cilindrze sasazRvro pirobis realizaciis Sedegad miRebul wrfiv algebrul gantolebaTa usasrulod dualur sistemaSi matriculi elementebisa da Tavisufali wevrebis gamosaxulebebSi miiReba ganSlad mwkrivTa jami, amitom saWiroa velis mimarT garkveuli manipulaciebis Catareba, rac xerxdeba rezonatorul nawilsa da gverdiT Stoebs Soris warmo-
59 60 saxviT zedapirebze eleqtruli velis tangencialuri hidrodinamikuri da ekologiuri blokebisagan. hidrodi- mdgenelis uwyvetobis pirobis realizaciis Sedegad. namikuri blokis ZiriTadi birTvia geofizikis institu- tis maRali garCevisunarianobis mqone Savi zRvis dinami- literatura: kis regionuli maTematikuri modeli. ekologiuri blo- kis Semadgeneli nawilebia zRvis garemoSi damaWuWyiane- 1. S. L. Prosvirnin, L.N. Litvinenko, V. N. Kochin, G.V. Kekelia, P.G. bel nivTierebaTa gavrcelebis ori da samganzomilebiani Kobiashvili. The characteristics of the short vibrator loaded with disks. maTematikuri modelebi. regionuli prognozis sistema "Radiophysics and radio astronomy" Radio-astronomical institute NAN saSualebas iZleva gamovTvaloT zRvis aRmosavleT akva- of the Ukraine.2011. toriaSi ZiriTadi dinamikuri velebis – dinebis, tempera- 2. K.V.Kotetishvili, G.Sh. Kevanishvili, G.V.Kekelia, I.G.Kevanishvili, turisa da marilianobis 3 dRiani prognozi 1 km sivr- G.G.Chikhladze, and P.G.Kobiashvili . To the electrodynamic theory of ciTi garCevisunarianobiT, xolo sagangebo situaciebis an antenna grutings formed by the eqvidisnancly located active dipoles . dros viwinaswarmetyveloT agreTve zRvaSi CaRvrili JAE, vol.13 , num 3. Athens Greece, 2011, 13p. navTobisa da sxva minarevebis gavrcelebis areebi da 3. Kekelia G.V., Kobiashvili F.G., Kipiani D.O. To the question on the koncentraciebi. considerable decrease of the time of numerical count in the problem of regionuli prognozis sistemis Semdgomi srulyofa scattering the electromagnetic waves on the cylindrical heterogeneity in dakavSirebulia zRvis Relvianobis prognozisa da bioqi- the resonator part of the waveguide tee. GEN, N2, 2009, p. 25-28. miuri procesebis modelebis CarTvasTan prognozul 4. Alavidze M.V., Kekelia G.V., Shavlakadze N. N., Kobiashvili P.G. The sistemaSi. garda amisa, SemuSavdeba prognozuli sistemis strict calculation of four-port waveguide branching. GEN, N 4, 2009, p. gacilebiT maRali garCevisunarianobis mqone versia, 45-52. romelic gamoyenebuli iqneba aWaris sanapiro zonisa da q. foTis akvatoriisaTvis (sivrciTi bijiT 50-100 m). am versiis funqcionireba SesaZlebelia mxolod ZiriTad aRmosavleT Savi zRvis prognozuli sistema: versiasTan erToblivad. amgvarad, Seiqmneba kompleqsuri mimdinare mdgomareoba da perspeqtivebi operatiuli regionuli prognozis sistema, romelic gaa- erTianebs 1 km garCevisunarian prognozul sistemas avTandil korZaZe*, demuri demetraSvili** mTlianad saqarTvelos sanapiro zonisaTvis, da 50-100 m iv. javaxiSvilis saxelobis Tbilisis saxelmwifo garCevisunarian prognozul qvesistemas aWaris sanapiro universiteti, m. nodias geofizikis instuti, Tbilisi, zonisa da q. foTis akvatoriisaTvis. saqarTvelo, *[email protected] , **[email protected] literaturა bolo aTeul weliwadSi Savi zRvis operatiuli okeanografiis udidesi miRwevaa Savi zRvis diagnozisa 1. Kordzadze A. A., Demetrashvili D.I.: Operational forecast of da prognozis sistemis SemuSaveba, rac SesaZlebeli hydrophysical fields in the Georgian Black Sea coastal zone within the gaxda im samecniero-teqnologiuri progresis Sedegad, ECOOP. Ocean Science 7, pp.793-803. doi:10.5194/os-7-793- rac daikvirveba gasuli saukunis 90-iani wlebidan. am 2011(2011). sistemis erT-erTi komponentia m. nodias geofizikis ins- 2. Кордзадзе А. А., Деметрашвили Д. И.: Краткосрочный прогноз titutSi SemuSavebuli Savi zRvis regionuli prognozis гидрофизических полей в восточной части Чёрного моря. Изв. sistema Savi zRvis aRmosavleT nawilisaTvis, romelic РАН, Физика атмосферы и океана. 2013, т. 49, № 6, c. 733-745. moicavs saqarTvelos sanapiro zonas da mis mimdebare akvatorias [1, 2]. regionuli prognozis sistema Sedgeba
61 62 winaswar daZabuli, drekad Semavsebliani , , komponentebi, romlebic akmayofileban piro- cilindrul formasTan miaxloebuli brunviTi x y xy garsebis Termorxevebi bebs: y sergo kukujanovi iv. javaxiSvilis saxelobis Tbilisis saxelmwifo
universiteti, V0 a. razmaZis maTematikis instituti, Tbilisi, saqarTvelo, [email protected]
ganxilulia sakuTari rxevebi drekad Semavsebliani x cilindrul formasTan miaxloebuli brunviTi garsebisa, –Vt 2 +Vt romelzec moqmedebs normaluri wneva, meridianuli Zale- bis gavlena da gacxeleba. ganxilulia Txeli da dre- kadi garsebi. temperatura Tanabrad ganawilebulia gar- sis sxeulSi. msubuqi Semavsebeli igulisxmeba sriala ti- pis. Semavsebelis modulireba xdeba vinkleris fuZiT. gan- u1 1 ; u 2 1 ; (x 1 y ) ( y 2 x ) xilulia rogorc dadebiTi, aseve uaryofiTi gausis x E1 y E 2 simrudis mqone garsebi. moyvanilia formulebi da univer- 1 1 u1 u 2 ; ; ( ) xy 0, roca x Vt y 0, xy 0, roca saluri mrudebi umciresi sixSireebisa da talRaTa xy 2 y x warmoqmnis formebisaTvis, romlebic damokidebulia tem- y 0, x Vt , sadac E1 da E2 iungis modulebia mTavari mimar- peraturaze, drekadi Semavseblis sixisteze, winaswar TulebiT, da – puasonis koeficienti, – Zvris moduli, daZabulobaze, gausis simrudis niSansa da cilindruli 1 2 formidan garsis gadaxris amplitudaze. agreTve ganxi- xolo V V0 t ctg x sidide unda ganisazRvros amocanis lulia mdgradobis sakiTxi da moyvanilia formulebi msvlelobaSi. amocana dayvanilia dirixles amocanaze, rom- kritikuli ZalebisTvis. lis amonaxsni warmodgenilia Svarcis integraliT.
orTotropul naxevarsibrtyeSi solis mudmivi siCqariT Cawneva
marina losaberiZe, daviT yifiani saqarTvelos teqnikuri universiteti 0175, saqarTvelo, Tbilisi, kostavas 77
naSromSi ganxilulia orTotropul naxevarsibrtyeSi blagvi solis mudmivi V0 siqariT Cawnevis amocana. saZiebe- lia gadaadgilebis veqtoris u1 da u 2 da Zabvis tenzoris
63 64 i. vekuas meTodis ganzogadeba afeTqebiTi energiis gamoyenebiT qvis blokebis fizikurad da geometriulad mopovebis Teoriuli safuZvlebi arawrfivi da aradamreci garsebisaTvis r. mixelsoni, s. xomeriki, m. losaberiZe, d. xomeriki, Tengiz meunargia g. SatberaSvili iv. javaxiSvilis saxelobis Tbilisis saxelmwifo grigol wulukiZis samTo instituti, Tbilisi, universitetis i. vekuas saxelobis gamoyenebiTi saqarTvelo maTematikis instituti Tbilisi, saqarTvelo, [email protected] maRali simtkicisa da abraziulobis mosapirkeTebeli qvis blokebis mosapoveblad afeTqebis energiis gamoyenebis i. vekuas mier agebuli iyo damreci garsebis wrfivi meTodis efeqturobaze didadaa damokidebuli blokebSi ma- Teoria, romelic Seicavs drekadobis 3-ganzomilebiani sivis struqturis da dekoratiuli Tvisebebis SenarCuneba. amocanebis 2-ganzomilebian amocanebze dayvanis e.w. regu- naSromSi drekadobis Teoriisa da afeTqebis fizikis larul process. am meTodis gamoyenebiT miRebulia ara- ZiriTad debulebebze dayrdnobiT Camoyalibebulia mosa- damreci garsebis fizikurad da geometriulad arawrfivi pirkeTebeli qvis masivis mimarTuli gapobiT blokebis mopo- Teoriis 2-ganzomilebiani gantolebaTa sistema da Seda- vebis axali meTodi, romelic efuZneba feTqebadi nivTiere- rebulia sxva dazustebul TeoriebTan (reisneri, koiteri- bis wrfiv muxtebis afeTqebiT qanSi generirebuli ZabvaTa nagdi, lurie,...). talRis sawyisi parametrebis gaTvlas, feTqebadi nivTi- madloba. winamdebare naSromi Sesrulebuli iyo SoTa erebis tipebisa da qvis struqturis aradamazianebeli mux- rusTavelis erovnuli samecniero fondis mxardaWeriT tis konstuqciis SerCevas. qanis bunebrivi struqturis (granti SRNSF / FR / 358 / 5-109 / 14). SenarCunebis mizniT rekomendebulia mcire krizisuli diametrisa da detonaciis maRali siCqaris mqone feTqebadi literaturა nivTierebebis gamoyeneba. am dros afeTqebis mcire xangr- Zlivobis impulsi gamoricxavs qanis masivis inerciis 1. Vekua, I.N. Shell Theory: General Methods of Construction. Pitman xarjze masSi arsebuli bzarebis zrdas. Advanced Publishing Program, Boston-London-Melbourne, 1985. 2. Meunargia, T. On extension of the Muskhelishvili and Vekua-Bitsadze literatura methods for geometrically and physically nonlinear theory of non- shallow shells. Proc. A. Razmadze Math. Inst., 157 (2011), 95-129. 1. Г.Си, Г. Либовиц. Математическая теория хрупкого разрушения. Сборник «Разрушение», Т.2., Москва, «Мир» 1975, стр. 2. Дж. Райс. Математические методы в механике разрушения. Сборник «Разрушение», т.2, Москва, «Мир», 1975, стр. 204-335. 3. Д.Н. Климова. Задача динамики горных пород, Изд. Ленинградского университета, 1985, 128 с. 4. Р.Э. Дашко. Механика горных пород, Москва, «Недра», 1987. 264 с. 5. Ф.А. Баум, Л.П. Орленко, К.П. Станюкович, В.П. Челышев, Б.И. Шехтер. Физика взрыва. Изд. 2-у перераб и доп, Москва, «Недра», 1975, 704 с.
65 66 6. А.Н. Ханукаев. Энергия волн напряжений при разрушении пород Divergence-Form Elliptic PDEs with Variable Matrix Coefficients, взрывом. Москва, госгортехиздат, 1962, 198 с. Integral Equations and Operator Theory, 76 (2013), pp. 509-547. 7. А.Н. Ханукаев. Физические процессы при отбойке горных пород 2. Jentsch L. and Natroshvili D. Interaction between thermo-elastic and взрывом. Москва, «Недра», 1974. 224 с. scalar oscillation fields, Integral Equations and Operator Theory, 28 8. Р.В. Михельсон. Условия качественного оконтуривания горных (1997), pp. 261-288. пород взрывом линейных зарядов ВВ. Tbilisi, samTo Jurnali 3. Werner P. Beugungsprobleme der mathematischen Akustik, Arch. N2(27), 2011, gv.84–87. Ration. Mech. Anal., 12 (1963), pp. 155-184. talRaTa gabneva araerTgvarovani anizotropuli mravalkuTxa firfitebis drekadobis Teoriis winaRobis mier: sasazRvro-sivrculi amocanis zRvruli gadasvlis sasazRvro gantolebebis meTodi pirobebis modelireba sasrul elementTa meTodis gamoyenebiT daviT natroSvili saqarTvelos teqnikuri universiteti; giorgi nozaZe i. vekuas saxelobis gamoyenebiTi maTematikis instituti, a. wulukiZis samTo instituti, Tbilisi, saqarTvelo. Tbilisi, saqarTvelo, [email protected] [email protected]
naSromSi ganxilulia akustikuri talRebis gabnevis naSromSi ganxilulia da amoxsnili wesieri mraval- maTematikuri amocanebi, rodesac amreklavi winaRoba kuTxa firfitebis drekadobis amocana Tavisufali dayrd- warmoadgens anizotropul araerTgvarovan garemos. ganxi- nobis sasazRvro pirobiT sasrul elementTa meTodis lulia SemTxveva, rodesac fizikuri parametrebi gamoyenebiT 3 ganzomilebiani dasmis SemTxvevaSi. simar- wyvetilia erTgvarovani da arerTgvarovani nawilebis tivisaTvis ganxilulia firfitis zedapirisadmi marTobu- gamyof zedapirze. amocanebi Seswavlilia axlad damu- li datvirTva Seyursuli Zalis saxiT firfitis centrSi. Savebuli sasazRvro-sivrculi lokalizebuli gantole- amocanis modelireba ganxorcielda Solid Work -is prog- bebis Teoriis gamoyenebiT, romelic dafuZnebulia loka- ramul garemoSi. lizebuli parametriqsis saSualebiT agebuli ganzoga- naCvenebia, rom mravalkuTxedebis Tavisufali dayrd- debuli potencialebisa da maTi Sesabamisi integraluri nobis sasazRvro piroba ganicdis gadagvarebas kuTxis da fsevdo diferencialuri operatorebis Tvisebebze. wertilebis ricxvis matebasTan erTad zRvruli gadas- damtkicebulia Sesabamisi transmisiis amocanebis amonax- vlis dros (N∞) da ar Seesabameba aproqsimaciiT miRe- snTa arsebobisa da erTaderTobis Teoremebi rxevis para- metris nebismieri mniSvnelobisaTvis. buli saTanado wriuli firfitis Tavisufali dayrdno- bis sasazRvro pirobas. madloba. winamdebare naSromi Sesrulebuli iyo didi britaneTis UK-EPSRC EP/M013545/1 da SoTa rusTavelis Lliteratura fondis FR/286/5-101/13 grantebis finansuri mxardaWeriT. 1. Пановко Я.Г. Механика деформируемого твердого тела. М.: Наука, literatura 1985 2. В. Г. Мазья, С. А. Назаров Парадоксы предельного перехода 1. Chkadua O., Mikhailov S. and Natroshvili D. Localized Boundary- в решениях краевых задач при аппроксимации гладких областей Domain Singular Integral Equations Based on Harmonic Parametrix for 67 68 многоугольными. Изв. АН СССР. Сер. матем., 1986, том 50, sabaziso integralur gantolebas, aseve integralur выпуск 6, страницы 1156–1177 gantolebaTa sistemas vxsniT kolokaciis, kerZod diskre- 3. Хомасуридзе Н.Г. О некоторых предельных переходах в теории tul gansakuTrebulobaTa meTodiT (ix. [2]). Sesabamisi упругости и о "парадоксе Сапонджяна" // Изв. РАН. МТТ. 2007. wrfiv algebrul gantolebaTa sistemebi miRebuli gvaqvs № 3. С. 46-54 rogorc Tanabrad daSorebul (marTkuTxedebis kvadratu- ruli formulis gamoyenebiT), aseve araTanabrad daSore- buli kvanZebis SemTxvevaSi (CebiSevis kvanZebze agebuli bzarebiT Sesustebuli Sedgenili sxeulisTvis umaRlesi sizustis kvadraturuli formulebis gamoye- drekadobis antibrtyeli Teoriis zogierTi nebiT). wrfiv algebrul gantolebaTa sistemis amoxsna, sasazRvro amocanis miaxloebiTi amoxsna amonaxsnis grafikuli interpretacia xorcieldeboda kolokaciis meTodiT programuli sistema Matlab-is gamoyenebiT. warmodgenil naSromSi zemoaRniSnuli amocanebis arCil papukaSvili, Teimuraz daviTaSvili, zurab vaSakiZe miaxloebiTi amoxsnisTvis gamowerilia axali saTvleli iv. javaxiSvilis saxelobis Tbilisis saxelmwifo algoriTmebi, Catarebulia Sesabamisi ricxviTi gaTvlebi universiteti, da gakeTebulia bzaris gavrcelebis Sesaxeb hipoTeturi zust da sabunebismetyvelo mecnierebaTa fakulteti, i. vekuas saxelobis gamoyenebiTi maTematikis instituti, prognozi. Tbilisi, saqarTvelo, [email protected], [email protected], literaturა [email protected] 1. Papukashvili A.R. Antiplane problems of theory of elasticity for naSromSi warmodgenilia bzarebiT Sesustebuli Sed- piecewise-homogeneous orthotropic plane slackened with cracks. genili (ubnobriv-erTgvarovani) orTotropiuli sxeule- Bulletin of the Georgian Academy of Sciences, 169, N2, p.267-270, bis SemTxvevaSi drekadobis Teoriis antibrtyeli amoca- Tbilisi (2004). nebis kvleva integralur gantolebaTa meTodiT. vixilavT 2. Belotserkovski S.M., Lifanov I.K. Numerical methods in the singular or amocanas. Ppirveli amocanis SemTxvevaSi bzari gamo- integral equations and their application in aerodynamics, the elasticity dis gamyof sazRvarze (bzari vrceldeba gamyof sazRvram- theory, electrodynamics. 256 pp., Moscow, ”Nauka” (1985). de) marTi kuTxiT, xolo meore amocanis SemTxvevaSi bzari kveTs gamyof sazRvars marTi kuTxiT. pirveli amocana miiyvaneba uZravi gansakuTrebulobis Semcvel singularul integralur gantolebaze, xolo meore amo- cana uZravi gansakuTrebulobis Semcvel singularul integralur gantolebaTa sistemaze (wyvilze) mxebi Zab- vebis naxtomebis (bzaris gaxsnis maxasiaTebeli funqcie- bis) mimarT (ix. [1]). zemoaRniSnul sakvlev amocanebSi Cveni ZiriTadi mizani iyo Segveswavla bzaris gaxsnis ma- xasiaTebeli funqciis yofaqveva, bzaris boloebSi daZa- bulobis intensiurobis koeficientebis gamoTvla da bza- ris gavrcelebis Sesaxeb prognozis gakeTeba.
69 70 rTuli gavrcobili konfiguraciis myari 3. The calculation of rope-rod structures of ropeways on the basis of the deformirebadi tanis modelireba da gaangariSeba new approach, WORLD CONGRESS of O.I.T.A.F., RIO DE diskretuli warmodgenis safuZvelze JANEIRO, BRAZIL, October, 2011, 24 – 27, PAPERS OF THE CONGRESS, daviT pataraia*, ediSer woweria**, http://www.oitaf.org/Kongress%202011/Referate/Pataraia.pdf giorgi furcelaZe***, rusudan maisuraZe**** 4. http://www.mining.org.ge/develop/pataraia-dmr/index.html * grigol wulukiZis samTo instituti, Tbilisi, 5. Modeling and Calculation of Big Rarefied Space Structures. saqarTvelo, [email protected]; International Scientific Conference (In English language); Georgian ** S.p.s. konstudio, Tbilisi, saqarTvelo, Technical University. 206-214p; 2009. [email protected] ; 6. Discrete model and calculation method for rope–rod structures, Problem of Mechanics / International federation for the promotion of *** Tbilisis satransporto kompania, Tbilisi, mechanism and machine science, (In English language), 2008 - N2 saqarTvelo, [email protected] ; (31). **** grigol wulukiZis samTo instituti, Tbilisi, saqarTvelo, [email protected]
samuSaoSi warmodgenilia myari deformirebadi tanis saaviacio umaRlesi ganaTleba saqarTveloSi gaangariSebis originaluri midgoma, romelic efuZneba da iyenebs am mizniT specialurad damuSavebul diskre- sergo tefnaZe*, gela yifiani** tul modelsa da algoriTms [1-6]. *saqarTvelos saaviacio universiteti, Tbilisi, [email protected] ganxilulia am meTodis gamoyenebis sxvadasxva aspeqte- saqarTvelo, bi iseTi rTuli konfiguraciis araerTgvarovani da gav- **saqarTvelos saaviacio universiteti, Tbilisi, rcobili tanebis modelirebisa da gaangariSebisas, rogo- saqarTvelo, [email protected] ricaa, magaliTad, kosmosuri antenebi, bagirgzebi, kaS- xlebi. moxsenebaSi gadmocemulia adgilobrivi sainJinro kad- didi zomis tanebis gasaangariSeblad damuSavda mid- rebis momzadebis mizniT TviTmfrinavmSeneblobis kaTed- goma, romlis saSualebiTac SesaZlebelia SemoTavazebu- ris daarsebidan, axali koncepciis safuZvelze saaviacio li saTvleli algoriTmis danawileba da realizacia umaRlesi ganaTlebis Camoyalibebis Sesaxeb. Tu rogor kompiuterebis lokalur qselSi an sulac internetSi. Seiqmna saqarTvelos teqnikuri universitetis struqtura- gaweuli konsultaciebisaTvis, mxardaWerisa da profe- Si samTavrobo dadgenilebis safuZvelze TviTmfrinavmSe- siuli TanadgomisaTvis did madlobas vuxdiT gamoyenebi- neblobis kaTedris bazaze saaviacio-samecniero institu- Ti maTematikis institutis koleqtivsa da mis direqtors ti. profesor giorgi jaians. saqarTvelos prezidentis gadawyvetilebiT saaviacio institutis gamoyofa saqarTvelos teqnikuri universite- tidan da mis bazaze “saqarTvelos saaviacio universi- literaturა teti”-s Camoyalibeba. aRniSnulia saaviacio institutis da saaviacio universitetis aRmocenebis da ganviTarebis 1. Ein Beitrag zur diskreten Darstellung des Seiles. Wissenschaftliche Arbeiten des Instituts fuer Eisenbahnwesen, Verkehrswirtschaft und sakiTxebi, awmyo da momavali. Seilbahnen, Technishe Univeristaet Wien), 1981. 2. Calculation and design of rope systems of the ropeway (In Russian Language). Mecniereba, Tbilisi, 2000 - 115 p; 71 72 Tavisufaldinebadi mikrohesebi talRovan gadaxurvebSi, daZabul mdgomareobaze gavleniT isini wiboebis analogiurebi arian. Tamaz RonRaZe gansakuTrebiT Zlier arRveven regularobas Wrilebi, ssip saxelmwifo samxedro samecniero-teqnikuri centri texvebi, xvretebi, bzarebi, agreTve Reroebis tipis sxva- „delta“, Tbilisi, saqarTvelo, dasxva xisti CanarTebi [1, 2, 3]. moxsenebaSi gadmocemulia [email protected] zemoT aRniSnuli problemebis Sesaxeb safren aparatebSi konstruqciebis mdgradobis sakiTxebze. ganxilulia Tavisufaldinebadi mikrohesebis nair- saxeobebi, radganac swrafi mdinareebi, romelTa dinebis literatura kinetikuri energia yuradsaRebia, mravladaa msoflioSi 1. Михайлов, Б.К. Пластины и оболочки с разрывными параметрами. (saqarTveloSic). mikrohesebis savaraudo simZlavre 50vt- Ленинград: Издательство ЛГУ, 1980. СССР −196 c. ÷10kvt. ar moiTxovs araviTar hidronagebobes, araviTar 2. Михайлов Б.К., Кипиани Г.О. Деформированность и устойчивость derivaciebs. saWiro iqneba zogjer napirebze Camagreba da пространственных пластинчатых систем с разрывными saxeldaxelo saSualebebi (riyis qva, iqve arsebuli xe). параметрами. Санкт-Петербург: Стройиздат СПБ, 1996. −442 c. wyalSi moZraobs mxolod turbinis frTebi. aranairi sxva 3. Kipiani G., Mikadze V., Nikolaishvili L. Stability of plates with moxaxune detalebi wyalSi araa CaZiruli. maTTvis damaxa- discontinuous parameters//V International Scientific and Technical Problems of Water Management, Environmental siaTebelia energiis gamoyenebis didi koeficienti; mcire Conference “Modern Protection, Architect and Construction”, July 16-19, 2015, Tbilisi, gabaritebi da Sesabamisad mcire wona. Universali, 2015, pp. 293-300.
safren aparatebSi araregularulobis mqone rgolur frTaze amwevi Zalis konstruqciebis mdgradoba formirebis specifika
gela yifiani*, valeri miqaZe** gela yifiani, arCil geguCaZe *saqarTvelos saaviacio universiteti, Tbilisi, saqarTvelos saaviacio universiteti , akaki wereTlis saqarTvelo, [email protected] saxelmwifo universiteti ** saqarTvelos saaviacio universiteti, Tbilisi, [email protected], [email protected] saqarTvelo, [email protected] Tavidanve ase warimarTa da dRemde upiratesad gavrce- Txelkedlian konstruqciebSi geometriuli da fizi- lebulia wriuli an rgoluri formis frTebiani verti- kuri parametrebis araregularoba iwvevs Zabvebis mniSvne- lovan koncentracias da qmnis bzarebis an plastikuri kaluri afrena-dafrenis safreni aparatebis iseTi kompaneba, deformaciebis gavrcelebis saSiS zonebs. umetes SemTxve- romelSic amwevi Zalis maformirebeli (muSa) zedapiris vaSi maTi mzidunarianoba ganisazRvreba simtkicis pirobe- forma uaxlovdeba sferuls, an rgolur-gumbaTovans da ar biT an Zabvebis koncentraciis zonaSi mdgradobis dakarg- uxerxdeba simZimis centris daweva am zedapiris geomet- viT. regularobis darRvevis sxva saxeebs miekuTvneba riuli centrze ufro dabla. es garemoeba warmoSobs aseTi zedapiris texva, rasac adgili aqvs naoWovan da mraval- tipis safreni aparatebis mdgradobis arasakmaris pirobas.
73 74 problemis gadasawyvetad statiaSi Sedarebulia winsv- gadasvlebi or forovan cilindrs Soris liT moZravi klasikuri da centridanuli gaqreviT vertika- siTbogamtari siTxis teilor-dinis dinebaSi luri afrena-dafrenis rgolur-gumbaTovan frTiani sqeme- bis safreni aparatebis amwevi Zalis formirebis meqanikuri luiza SafaqiZe principebi Sesabamisad, aerodinamikis gaTvaliswinebiT. maT iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti, a.razmaZis maTematikis instituti, Soris gansxvaveba mdgomareobs imaSi, rom pirvel SemTxve- [email protected] vaSi aerodinamikur profiliani frTa moZraobisadmi fron- Tbilisi, saqarTvelo, talurad mimarTuli wina wiboTi gaivlis uZrav haeris maseb- moxsenebaSi warmodgenilia aramdgradobebi da gadasv- Si, xolo meore SemTxvevaSi - centridan gareT moZravi aeris lebi or forovan cilindrs Soris siTbogamtari siTxis masebi garsSemouvlian centrisken mimarTul aerodinamikur dinebaSi, romelic gamowveulia cilindrebis gaswvriv profilian uZrav rgolur frTas. moqmedi mudmivi azimuturi wnevis gradientisa da cilin- aRniSnuli gansxvaveba mniSvnelovani aRmoCnda amwevi drebis brunviT. Zalebis formirebis procesis analizis dros. pirvel SemTx- igulisxmeba, rom siTxis dinebaze moqmedebs radia- vevaSi amwevi Zalis formirebisaTvis saWiroa wina nawiburis nuli dineba forovani cilindrebis kedlebis mimarTu- maRla aweva ukanasTan SedarebiT, raTa Seiqmnas e.w. „Setevis lebiT da radianuli temperaturuli gradienti. naCvene- kuTxe“, xolo meore SemTxvevaSi arCevani SeCerebulia araor- bia, rom moqmedi wnevis gradientis sidide da misi mimar- dinarul gadawyvetaze: aerodinamikur profiliani Tuleba, aseve temperaturuli gradienti SesamCnev gav- rgoluri (an rgolebis erTobliobiT Sedgenili) frT(eb)is lenas axdens ZiriTadi stacionaruli dinebis aramdgra- wina nawibur(eb)i daweulia, xolo haeris centridanuli dobaze da rTuli reJimebisaken gadasvlaze. nakadebi - aRmavali (daxrilad zemoT mimarTuli). pirvel SemTxvevaSi frTis qveda zedapirze dacemuli da asxletili wanacvlebiTi qaris gavlena didmasStabiani uds (areklili) haeris nakad(eb)is tolqmedi Zala daxrilia, modebis mier zonaruli dinebebis generaciaze xolo amwev Zalas qmnis misi vertikaluri mdgeneli, xolo meore SemTxvevaSi, rgoluri frT(eb)is zemoaRniSnuli spe- xaTuna Cargazia**,*** oleg xarSilaZe*,*** cifiuri ganlagebiT, frTis qveda zedapirze dacemuli da *iv. javaxiSvilis saxelobis Tbilisis saxelmwifo asxletili (areklili) haeris nakad(eb)is tolqmed Zalas universiteti, Tbilisi, saqarTvelo, ganesazRvreba vertikaluri mimarTuleba da igi srulad [email protected] iqneba gamoyenebuli amwev Zalad. **iv. javaxiSvilis saxelobis Tbilisis saxelmwifo wriuli frTis Semadgeneli aerodinamikur profiliani universiteti, rgolebis urTierTganlageba iZleva maTi zedapirebis i. vekuas saxelobis gamoyenebiTi maTematikis instituti, saerTo geometriuli centris simZimis centrze ufro maRla Tbilisi, saqarTvelo, awevisa da amiT safreni aparatis mdgradobis gazrdis *** iv. javaxiSvilis saxelobis Tbilisis saxelmwifo SesaZleblobas. universiteti, m. nodias geofizikis instituti, Tbilisi, saqarTvelo, [email protected]
warmodgenil moxsenebaSi ganxilulia damagnitebuli rosbis talRis mier didmasStabiani zonaluri dinebebis 75 76 generacia araerTgvarovan wanacvlebiT dinebebiT marTul biofilmi romelsac ukavia disipaciur ionosferoSi. miRebulia modificirebuli Txeli prizmuli areebi Carni-obuxovis tipis gantoleba, romelic aRwers xuTi natalia CinCalaZe sxvadasxva masStabis modis arawrfiv urTierTqmedebas. es i. javaxiSvilis saxelobis Tbilisis saxelwifo modebia: ultra dabali sixSiris (uds) damagnitebuli univeristetis rosbis talRa, misi ori sateliti, grZeltalRovani zo- i. vekuas saxelobis gamoyenebiTi maTematikis instituti & naluri moda da didmasStabiani fonuri wavnacvlebiTi zust da sabunebismetyvelo mecnierebaTa fakultetis dineba (araerTgvarovani qari). Seswavlilia arawrfivo- maTematikis departamenti bebis (skalaruli, veqtoruli) efeqtebis gavlena sasrul [email protected], [email protected] amplitudiani damagnitebuli rosbis talRis mier didmas- Stabiani zonaluri dinebebis formirebaze disipaciur biofilmi aris gelis msgavsi agregati, romelic Sed- geba baqteriebis msgavsi mikroorganizmebisagan. miuxe- ionosferoSi. gamoyenebulia modificirebuli parametru- davad imisa, rom biofilmi Seicavs siTxes isini SeiZleba li midgoma. SeSfoTebebis amplitudebis Sesabamisi ganto- ganxilul iqnas, rogorc myari struqtura. biofilmi lebaTa sistemis Teoriuli analizisa da ricxviTi SeiZleba warmoiSvas sxvadasxva garemos gamyof zeda- modelirebis bazaze gamovlenilia SedarebiT mciremas- pirebze, magaliTad, myari sxeulisa da siTxis sakontaqto Stabiani uds rosbis talRebidan da fonuri dinebidan zedapirze an airisa da myari sxeulis, an airisa da didmasStabian zonalur dinebebSi energiis gadatanis siTxis gamyof zedapirze da a.S. (ix. [1] da iq miTiTebuli axali Taviseburebebi da zemoT aRniSnuli xuTi modis literatura). winamdebare moxseneba exeba erT da organzomilebian arawrfivi TviTorganizacia ionosferul garemoSi. zona- amocanebs, roca biofilms ukavia Txeli prizmuli are. luri dinebebis generacia ganpirobebulia sasrulo organzomilebiani amocanis ganxilvisas gamoyenebulia amplitudiani damagnitebuli rosbis talRis urTierT- vekuas ierarqiuli meTodebi (ix., mag., [2]-[4]). qmedebiT fonur wanacvlebiT dinebasTan. Seswavlilia zonaluri dinebebis gaZlierebis inkrementis damokide- madloba. winamdebare naSromi Sesrulebuli iyo CNR buleba fonuri wanacvlebiTi dinebis struqturasa da (italia) da SoTa rusTavelis erovnuli samecniero siCqaris sidideze. fondis (saqarTvelo) erToblivi samecniero proeqtis (No. 09/04) ”Some classes of PDE and systems with applications to mechanics madloba. winamdebare naSromi Sesrulebuli iyo SoTa and biology” (2012/2013) farglebSi. rusTavelis erovnuli samecniero fondis grant No. 31/14. mxardaWeriT. literatura
1. F. Clarelli, C. DI Russo, R. Natalini, M. Ribot, Mathematical models for biofilms on the surface of monuments, Applied and Industrial Mathematics In Italy III, proceedings of SIMAI Conference 2008, Series on Advances in Mathematics for Applied Sciences - 82 (2009)
77 78 2. I. N. Vekua, On a way of calculating of prismatic shells (in 2. Sh. Tserodze, J. Santiago Prowald, van‘t Klooster C.G.M., E. Russian), Proceedings of A. Razmadze Institute of Mathematics of Logacheva. ”Spatial Double Conical Ring-Shaped Reflector for Space Georgian Academy of Sciences. 21, 191-259 (1955) Based Application”. Proceedings of 33rd ESA Antenna Workshop 3. I. N. Vekua, Shell Theory: General Methods of Construction, Pitman “Challenges for Space Antenna Systems”. 18 - 21 October 2011. Advanced Publishing Program, Boston-London-Melbourne, 1985 ESTEC, Noordwijk, The Netherlands. 4. N. Chinchaladze, Hierarchical models for biofilms occupying thin 3. E. Medzmariashvili, N Tsignadze, Sh. Tserodze, J. Santiago-Prowald; prismatic domains, Bull. TICMI. 18, No. 2, 102-109 (2014) C. Mangenot, C.G.M. Van’t Klooster, H. Baier, M. Janikashvili. Design of Reflector with Double Pantograph and Flexible Center. Proceedings of ESA Antenna Workshop on Large Deployable Antennas. 2-3 October transformirebadi kosmosuri refleqtoris 2012. ESTEC, Noordwijk, The Netherlands meqanikuri sistemis Teoriuli kvleva
SoTa weroZe*, malxaz nikolaZe** iteraciuli meTodi timoSenkos *saqarTvelos teqnikuri universiteti, Tbilisi, tipis dinamiuri ZelisaTvis saqarTvelo, [email protected] ** saqarTvelos teqnikuri universiteti, Tbilisi, z. wiklauri saqarTvelo, [email protected] saqarTvelos teqnikuri universiteti, maTematikis departamenti, [email protected] moxsenebaSi warmodgenilia axali Caketil jaWviani ganSladi sistema. analogiuri struqturebisagan misi ganxilulia sawyis-sasazRvro amocana arawrfivi dife- konstruqcia gamoirCeva imiT, rom mezobeli seqciebis rencialuri gantolebisaTvis, romelic aRwers timoSenkos SesaerTeblad ar saWiroebs damatebiT sinqronizaciis mo- wyobilobebs. misi gasaSleli meqanizmi warmoadgens dife- tipis dinamiuri Zelis mdgomareobas. miaxloebiTi amonax- rencirebul berketul meqanizms, romelic iZleva snis misaRebad gamoyenebulia: galiorkinis meTodi, sxvao- saSualebas miviRoT maxasiaTebeli rgolis moZraobis sa- biani sqema da iakobis iteraciuli meTodi. Sefasebulia ite- surveli kanoni. konstruqciis winaswari gamokvleviT da raciuli meTodis cdomileba. aucilebeli Sesworebebis SetaniT agebulia maTematikuri modeli ANSYS programiT Ansys Parametric Design Language–is gamoyenebiT. saxsrebis Tavisuflebis xarisxi modeli- rebulia adgilobriv koordinatTa sistemaSi da maqsi- malurad miaxloebulia realur modelTan. gaangariSeba Catarebulia datvirTvis sxvadasxva SemTxvevisaTvis da miRebulia Sesabamisi Sedegebi.
literatura
1. Medzmariashvili, Sh. Tserodze, V. Gogilashvili. New Variant of the Large Deployable Ring-Shaped Space Antenna. Space Communications 22 (2009) 41-48.
79 80 grigalebis kvlevis erTiani midgoma giorgi li arawrfivi wevrebi. gantolebaTa sistemis arawrfivo- anburjanias wignSi “arawrfivi grigaluri bis gamo misi amoxsnisas warmoiqmneba rTuli maTematiku- struqturebisa da grigaluri turbulentobis ri problemebi, romelTa amoxsna stacionarul SemTxve- TviTorganizeba dispersiul garemoSi” vebSi mocemulia g. aburjania wignSi. am modelebis anali- oleg xarSilaZe*,*** xaTuna Cargazia**,*** zurma kvlevebma moaxdina grigaluri struqturebis aras- *iv. javaxiSvilis saxelobis Tbilisis saxelmwifo tacionaluri amocanebis ricxviTi kvlevebis stimulire- universiteti, Tbilisi, saqarTvelo, ba, ramac aCvena g. aburjanias Teoriuli kvlevebis kargi [email protected] Tanxvedra ricxviT, Tanamgzavrul da laboratoriul **iv. javaxiSvilis saxelobis Tbilisis saxelmwifo eqsperimentebTan. universiteti, i. vekuas saxelobis gamoyenebiTi literaturა maTematikis instituti, Tbilisi, saqarTvelo, *** iv. javaxiSvilis saxelobis Tbilisis saxelmwifo 1 Aburjania, G.D.: Self-Organization of the Nonlinear Vortex Structures universiteti, m. nodias geofizikis instituti, Tbilisi, and the Vortical Turbulence in the Dispersive Media: Kom-Kniga, saqarTvelo, [email protected] Editorial URSS, Moscow (2006).
hidrodinamikis centralur amocanas warmoadgens gri- galis dinamikis Seswavla. gansakuTrebiT es sakiTxi mniS- zogierTi miRebuli Sedegi da aqtivoba vnelovania atmosferosa da okeanis cirkulaciis prob- lemebSi, sadac ganixileba sxvadasxva masStabebis griga- giorgi jaiani lebis gadatanis amocana. analogiuria grigaluri struq- i. javaxiSvilis saxelobis Tbilisis saxelwifo turebis roli plazmisa da ionosferul-magnitosferul univeristetis i. vekuas saxelobis gamoyenebiTi maTematikis garemos dinamikis SeswavlisaTvis. aseT struqturebs ufro efeqturad, vidre wrfiv talRebs, SeuZliaT gare- instituti & zust da sabunebismetyvelo mecnierebaTa mos Tavisufali energiis STanTqma da Zlieri turbulen- fakultetis maTematikis departamenti tobis Camoyalibeba. moxsenebaSi ganxilulia g. aburja- [email protected], [email protected] nias erTiani midgoma sxvadasxva dispersiul fizikur ga- remoSi arawrfivi talRuri procesebis SeawavlisaTvis, winamdebare moxseneba, garkveuli azriT, warmoadgens rogorc neitralur geofizikur garemoSi, aseve gamtar momxseneblis angariSs misi ZiriTadi aqtivobebis Taobaze garemoSi – laboratoriul plazmasa da ionosferoSi. i. javaxiSvilis saxelobis Tbilisis saxelmwifo universi- ganxilulia aRniSnuli amocanebis Sesabamisi dinamikur tetSi, saqarTvelos maTematikosTa kavSirsa da saqarTve- gantolebaTa sistemis msgavseba da g. aburjanias mier Ca- los meqanikosTa kavSirSi; garda amisa is eZRvneba mis Ziri- moyalibebuli erTiani maTematikuri aparati. Seswavlilia Tad Sedegebs kerZowarmoebulian diferencialur, umTavre- grigaluri struqturebis skalarul da veqtorul struq- sad gadagvarebul, gantolebaTa TeoriaSi da maT gamoyene- turebad dayofis SesaZlebloba, rac mocemulia abur- bebs wamaxvilebuli drekadi garsebis, firfitebisa da janias wignSi, aseve aseTi struqturebis damaxasiaTebeli ReroebisaTvis. is Seicavs agreTve drekadi myari sxeulebi- Taviseburebani. rogorc ricxviTma kvlevebma aCvena, saTvis da siTxisa da drekadi myari sxeulebis urTierTqme- struqturebis dinamikisa da grigalebis urTierTqmedebis debis amocanebisaTvis avtoris mier agebul zogierT or da ZiriTad maxasiaTeblebs gansazRvravs gantolebaSi Semava- erTganzomilebian modelis mokle mimoxilvas. 81 82 usasrulo forovani firfitis gamtari siTxis binaruli narevisgan Sedgenili firfitebis damcemi nakadiT brunvis arastacionaruli drekadi wonasworobis gantolebebis miReba amocana magnituri velisa da siTbogadacemis mimdevrobiTi gawarmoebis meTodiT gaTvaliswinebiT cvladi gamoJonvis siCqarisa da eleqtrogamtareblobis SemTxvevaSi roman janjRava iv. javaxiSvilis saxelobis Tbilisis saxelmwifo l.a. jiqiZe , v.n. cucqiriZe universiteti, i. vekuas saxelobis gamoyenebiTi sainJinro meqanikisa da mSeneblobis teqnikuri maTematikis instituti, Tbilisi, saqarTvelo, eqspertizis departamenti, saqarTvelos teqnikuri [email protected] universiteti, saqarTvelo, 0175, Tbilisi, m. kostavas 77 maTematikis departamenti, saqarTvelos teqnikuri moxsenebaSi ganixileba ori izotropuli drekadi universiteti, saqarTvelo, 0175, Tbilisi, m. kostavas 77 masalis narevis e. w. grin-nagdi-stilis modeli [1]. aRniS- nuli samganzomilebiani modelis ZiriTadi gantolebe- mimdevrobiTi miaxloebis meTodiT Seswavlilia siC- bidan binaruli narevisgan Sedgenili firfitebisTvis qaris ar, 0, 2az komponentebis mqone gamtari statikuri wonasworobis gantolebaTa sistemis misaRebad r z gamoyenebulia i. vekuas reduqciis meTodi, romelsac is siTxis damcemi nakadiT usasrulo forovani firfitis mimdevrobiTi gawarmoebis meTods uwodebs [2]. Aadre, brunvis arastacionaruli amocana magnituri velisa da damreci garsebisTvis Sesabamisi gantolebebis misaRebad siTbogadacemis gaTvaliswinebiT, roca eleqtrogamtareb- gamoyenebuli iyo saZiebeli sidideebis sisqis mimarT lobis koeficienti da gamoJonvis siCqare warmoadgenen leJandris polinomebad gaSlis meTodi [3]. temperaturaze damokidebul T T saxis 0 1 , w 0 1 T T madloba. naSromi Sesrulebulia SoTa rusTavelis funqciebs. erovnuli samecniero fondis finansuri mxardaWeriT dinamikuri da siTburi sasazRvro fenaTa sisqeebis (granti SRNSF/FR/358/5-109/14). gansasazRvravad miRebulia Sesabamisi diferencialuri gantolebebi da Cawerilia maTi zusti amoxsnebi zogierT literaturა kerZo SemTxvevaSi, rodesac gamoJonvis siCqare icvleba sxvadasxva kanoniT da sasazRvro fenaTa sisqeebs Soris
1. Natroshvili D. G., Jagmaidze A. Ya., Svanadze M. Zh. Some problems arsebobs T (t) (t) saxis damokidebuleba. of the linear theory of elastic mixtures. TSU press, Tbilisi (1986). (in gamoTvlilia dinebis yvela fizikuri maxasiaTebeli. Russian) 2. Vekua, I.: Shell Theory: General Methods of Construction. Pitman Advanced Publishing Program, 287 pp., Boston-London-Melbourne (1985). 3. Janjgava R. Derivation of two-dimensional equation for shallow shells by means of the method of I.Vekua in the case of linear theory of elastic mixtures. Journal o Mathematical Sciences. Spr. New York, 2009, vol. 157, N1, 70- 78.
83 84 C O N T E N T S J. Gigineshvili , G. Gedevanishvili, T. Matsaberidze, T. Goginashvili Structure features of the clamping (retaining) walls of landslide slopes H. Altenbach on the complex relief 16 Material modeling - an academic game or a tool for a better design 5 G. Giorgadze, G. Khimshiashvili A. Aptsiauri Geometry of configuration spaces of linkages and quadratic mappings 17 The exact expression of turbulent stress tenzor and calculation results 5 V. Gogadze Z. Arkania Kinematic research of crane-transport facilities and road-car working Bars and hoses calculation 6 appliances 18 G. baisarova, O. kikvidze T. Gongadze Experimental investigation beam at thermo mechanical loading 7 Free flow micro hydro-electric stations L. Bitsadze 18 On some problems in the theory of thermoelasticity for a sphere with B. Gulua Normed moments method for non-shallow shells double porosity 7 19 S. Bliadze, V. Mikadze G. Jaiani Some results obtained and activities Dynamic models of laminated systems 8 20 A. Bregvadze, I. Saginadze R. Janjgava Numerical modeling of sea shore dynamic and its engineering aspects Derivation of the equations of elastic balance of the plates consisting 9 of binary mixture using the method of consecutive differentiation Kh. Chargazia, O. Kharshiladze 20 Influence of the shear wind on generation of the large scale zonal L. Jikidze, V. Tsutskiridze flows by ulf modes Unsteady rotation problem of the motion of infinite porous plate with 10 the falling stream of the conductive fluid with account of magnetic N. Chinchaladze field and heat transfer in case of variable injection velocity and On some problems of biofilms occupying thin prismatic domains 11 electric conductivity 21 T. Davitashvili, G. Gubelidze, M. Sharikadze R. Kakhidze On one quasi-stationary nonlinear mathematical model for leak Strength of plate type multi-layer structures in aircrafts localization in the branched gas pipeline 22 12 G. Kapanadze, Miranda Narmania T. Davitashvili, Z. Modebadze On one problem of the plane theory of elasticity for a circular hole Implementation of WRF model for the territory of caucasus 13 with a finite polygonal domain 23 A. Dumbadze O. Kharshiladze, Kh. Chargazia On one refined method of analysis in creeping non-linear theory 13 General approach of vortices study due to Giorgi Aburjania’s book J. Gigineishvili, I. Timchenko, G. Cikvaidze “self-organization of the nonlinear vortex structures and the vortical Influence of results of numerical analysis and structural decision on turbulence in the dispersive media” 24 architecture of “hilton” hotel complex in batumi 14 R. Kienzler, P. Schneider On consistent plate theories. Partial differential equations, stress resultants and displacements 25 G. Kipiani, A. Geguchadze Specificity of uplift force formation on the annular wing 26
85 86 G. Kipiani, V. Mikadze L. Shapakidze Stability of having irregularities structures in aircrafts 27 Transitions in taylor-dean flow of a heat-conducting fluid between V. Kirtskhalia two rotating porous cylinders 38 Generalized equation of continuity of mass and its consequences 27 N. Shavlakadze A. Kordzadze, D. Demetrashvili The solutions of two-dimensional integro-differential equations and Easternmost Black Sea forecasting system: the current state and their applications in the theory of viscoelasticity 38 perspectives 28 S. Tepnadze, G. Kipiani S. Kukudzhanov Aviation high education in Georgia 40 On thermal oscillations of beforehand stressed shells of revolution, Sh. Tserodze, M. Nikoladze close by their form to cylindrical ones, with an elastic filler 29 Theoretikal investigation of transformable spase reflector mechanical D. Kvaratskhelia D. Demetrashvili system 40 Numerical investigation of features of the Black Sea mixed layer for the Z. Tsiklauri Georgian coastal line 30 An iterative method for a timoshenko type dynamic beam 41 M. Losaberidze, D. Kipiani T. Vashakmadze The constant-velocity pressing of a wedge in an orthotropic half-plane 30 On modeling of thermodynamic nonshallow elastic shells and T. Meunargia application of complex analysis 41 Generalization of I. Vekua’s method for the physically and N. Zirakashvili geometrically non-linear and non-shallow shells 31 Study of stress-strain state of elliptical body whit crack 42 R. Mikhelson, S. Khomeriki, M. Losaberidze,D. Khomeriki, G. Shatberashvili Theoretical basis of explosive extraction of stone blocks 33 D. Natroshvili Wave scattering by inhomogeneous anisotropic obstacles: boundary- domain integral equation approach 33 G. Nozadze Modeling of limit passage of boundary value problems elasticity of polygonal plates by the finite element method 34 A. Papukashvili, T. Davitashvili, Z. Vashakidze Approximate solution of some boundary value problem of antiplane elastisity theory by collocation method for composite bodies weakened by cracks 35 D. Pataraia, E. Coceria, G. Purceladze, R. Maisuradze Modeling and calculation of complex extended configuration solid deformable body based on discrete presentations 36 M. Rajczyk, L. Lausova Research of deformability of the multi-layered orthotropic shell 37
87 88 s a r C e v i r. kaxiZe. firfitis tipis mravalfeniani konstruqciebis simtkice safren aparatebSi 57 d. kvaracxelia, d. demetraSvili. Savi zRvis Sereuli z. arqania. Reroebisa daDSlangebis angariSi 43 fenis Taviseburebebis ricxviTi kvleva saqarTvelos a. afciauri. turbulentobis tenzoris zusti gantoleba sanapiro zonisaTvis 58 da angariSis Sedegebi 44 v. kircxalia. masis uwyvetobis ganzogadoebuli gantoleba g. baisarova, o. kikviZe. Zelis eqsperimentaluri kvleva da misi Sedegebi 59 Termomeqanikuri datvirTvisas 45 f. kobiaSvili. eleqtromagnituri talRis gabneva T–s l. biwaZe. Termodrekadobis Teoriis zogierTi amocana magvar samkapas rezonatorul nawilSi moTavsebul orgvari forovnobis mqone sferosaTvis cilindrze, rodesac misi aRgzneba xdeba sxvadasxva 46 mxridan s. bliaZe, v. miqaZe. fenovani sistemebis dinamikuri 60 modelebi a. korZaZe, d. demetraSvili. aRmosavleT Savi zRvis 47 prognozuli sistema: mimdinare mdgomareoba da a. bregvaZe, i. saRinaZe. zRvis sanapiro zolis dinamikis perspeqtivebi ricxviTi modelireba da misi sainJinro aspeqtebi 61 47 s. kukujanovi. winaswar daZabuli, drekad Semavsebliani g. giorgaZe, g. ximSiaSvili. saxsruli meqanizmebis da cilindrul formasTan miaxloebuli brunviTi garsebis kvadratuli asaxvebis geometria Termorxevebi 49 63 v. gogaZe. amwe-satransporto da sagzao manqanebis samuSao m. losaberiZe, d. yifiani. orTotropul naxevarsibrtyeSi aRWurvilobis kinematikuri kvleva solis mudmivi siCqariT Cawneva 50 63 b. gulua. normirebul momentTa meTodi aradamreci T. meunargia. i. vekuas meTodis ganzogadeba fizikurad da garsebisaTvis geometriulad arawrfivi da aradamreci garsebisaTvis 51 65 T. daviTaSvili, z. modebaZe. kavkasiis teritoriisTvis r. mixelsoni, s. xomeriki, m. losaberiZe, d. xomeriki, amindis sakvlevi saprognozo modelis realizaciis g. SatberaSvili. afeTqebiTi energiis gamoyenebiT qvis Sesaxeb blokebis mopovebis Teoriuli safuZvlebi 52 66 T. daviTaSvili, g. gubeliZe, m. SariqaZe. erTi arawrfivi d. natroSvili. talRaTa gabneva araerTgvarovani kvazistacionaruli maTematikuri modelis Sesaxeb anizotropuli winaRobis mier: sasazRvro-sivrculi ganStoebis mqone gazsadenSi gaJonvis adgilmdebareobis gantolebebis meTodi aRmosaCenad 67 53 g. nozaZe. mravalkuTxa firfitebis drekadobis Teoriis a. dumbaZe. cocvadobis arawrfiv TeoriaSi gaangariSebis amocanis zRvruli gadasvlis sasazRvro pirobebis erTi dazustebuli meTodis Sesaxeb modelireba sasrul elementTa meTodis gamoyenebiT 54 68 T. vaSaymaZe. Termodinamiuri drekadi garsebis a. papukaSvili, T. daviTaSvili, z. vaSakiZe. bzarebiT modelirebisa da analizur funqciaTa Teoriis Sesustebuli Sedgenili sxeulisTvis drekadobis gamoyenebis Sesaxeb 54 antibrtyeli Teoriis zogierTi sasazRvro amocanis miaxloebiTi amoxsna kolokaciis meTodiT n. ziraqaSvili. bzariani elifsuri sxeulis daZabul- 69 deformirebuli mdgomareobis Seswavla 55 d. pataraia, e. woweria, g. furcelaZe, r. maisuraZe. rTuli g. kapanaZe, m. narmania. drekadobis brtyeli Teoriis erTi gavrcobili konfiguraciis myari deformirebadi tanis amocanis Sesaxeb mravalkuTxa xvrelis mqone wriuli modelireba da gaangariSeba diskretuli warmodgenis arisaTvis 56 safuZvelze 71 89 90 s. tefnaZe, g. yifiani. saaviacio umaRlesi ganaTleba The selection and presentation of material and opinion expressed in saqarTveloSi 72 this publication are the sole responsibility of the authors concerned. T. RonRaZe. Tavisufaldinebadi mikrohesebi 73 g. yifiani, v. miqaZe. safren aparatebSi araregularulobis mqone konstruqciebis mdgradoba 73 g. yifiani, a. geguCaZe. rgolur frTaze amwevi Zalis formirebis specifika 74 l. SafaqiZe. gadasvlebi or forovan cilindrs Soris Technical editorial board: M. Tevdoradze siTbogamtari siTxis teilor-dinis dinebaSi 76 M. Sharikadze x. Cargazia, o. xarSilaZe. wanacvlebiTi qaris gavlena didmasStabiani uds modebis mier zonaruli dinebebis Cover Designer: S. Chaduneli generaciaze 76 n. CinCalaZe. biofilmi romelsac ukavia Txeli prizmuli areebi 78 S. weroZe, m. nikolaZe. transformirebadi kosmosuri refleqtoris meqanikuri sistemis Teoriuli kvleva 79 teqnikuri saredaqcio kolegia: m. TevdoraZe z. wiklauri. iteraciuli meTodi timoSenkos tipis m. SariqaZe dinamiuri ZelisaTvis 80 o. xarSilaZe, x. Cargazia. grigalebis kvlevis erTiani garekani Sesrulebulia sofo Cadunelis mier midgoma giorgi anburjanias wignSi “arawrfivi grigaluri struqturebisa da grigaluri turbulentobis TviTorganizeba dispersiul garemoSi” 81 g. jaiani. zogierTi miRebuli Sedegi da aqtivoba 82 r. janjRava. binaruli narevisgan Sedgenili firfitebis drekadi wonasworobis gantolebebis miReba mimdevrobiTi saqarTvelos saaviacio universiteti gawarmoebis meTodiT 83 0144 Tbilisi, qeTevan wamebulis, 16 l. jiqiZe, v. cucqiriZe. usasrulo forovani firfitis gamtari siTxis damcemi nakadiT brunvis arastacionaruli Ketevan Tsamebuli Tbilisi 0144 amocana magnituri velisa da siTbogadacemis Tel (+995 32) 277 52 78 gaTvaliswinebiT cvladi gamoJonvis siCqarisa da Facebook.com/ssu.edu.ge eleqtrogamtareblobis SemTxvevaSi 84 www.ssu.edu.ge
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