Towards the Design of a Multispar Composite Wing

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Article Towards the Design of a Multispar Composite Wing

Dimitrios Stamatelos 1,* and George Labeas 2

1 Laboratory of Strength of Materials, Department of Aeronautical Sciences, Aeronautical Engineering Section, Hellenic Air Force Academy, Dekelia Air Force Base, 13671 Attica, Greece 2 Laboratory of Technology and Strength of Materials, Department of Mechanical Engineering and Aeronautics, University of Patras, 26500 Rion, Greece; [email protected] * Correspondence: [email protected]

Received: 2 March 2020; Accepted: 7 April 2020; Published: 9 April 2020

Abstract: In the pursuit of a lighter composite wing design, fast and effective methodologies for sizing and validating the wing members (e.g., spar, ribs, skins, etc.) are required. In the present paper, the preliminary design methodology of an airliner main composite wing, which has an innovative multispar configuration instead of the conventional two-spar design, is investigated. The investigated aircraft wing is a large-scale composite component, requiring an efficient analysis methodology; for this purpose, the initial wing sizing is mostly based on simplified Finite Element (FE) stress analysis combined to analytically formulated design criteria. The proposed methodology comprises three basic modules, namely, computational stress analysis of the wing structure, comparison of the stress–strain results to specific design allowable and a suitable resizing procedure, until all design requirements are satisfied. The design constraints include strain allowable for the entire wing structure, stability constraints for the upper skin and spar webs, as well as bearing bypass analysis of the riveted/bolted joints of the spar flanges/skins connection. A comparison between a conventional (2-spar) and an innovative 4-spar wing configuration is presented. It arises from the comparison between the conventional and the 4-spar wing arrangement, that under certain conditions the multispar configuration has significant advantages over the conventional design.

Keywords: composite wing; structural wing design; multispar arrangement; design criteria

1. Introduction The application of composite materials in primary aeronautical structures is progressively increasing, e.g., about 25% of the AIRBUS A380 aircraft (A380 Innovation: https://www.airbus.com/ aircraft/passenger-aircraft/a380/innovation.html#materials (accessed on 21 February 2020)) is produced of composites (mainly the rear fuselage, central wing box, horizontal and vertical tail plane), while the next aircraft generation is expected to have about 50% of composite materials on its structure. To fully exploit the advantages of composite material design, apart from other developments, investigations on the possible advantages of non-conventional design configurations is essential. In the pursuit of a lighter composite wing design, fast and effective methodologies for sizing and validating the wing members (e.g., spar, ribs, skins, etc.) are required. The increase of the computer power, as well as the constant development of the numerical methods (e.g., FE methods) allowed researchers to explore different wing structural configurations [1] that deviate from the traditional wing design, which is based on the experience gained so far. Most of the wing studies focus on the wing structural optimization, in order to determine the lightest and strongest internal wing structure. Characteristic studies are carried out, by several researchers, by employing optimization routines regarding the stiffened panels [2–5], the position of the spars and ribs [6,7]. Furthermore, topology optimization is frequently employed to determine the optimum

Computation 2020, 8, 24; doi:10.3390/computation8020024 www.mdpi.com/journal/computation Computation 2020, 8, 24 2 of 14 location of certain structural components under static and aeroelastic loads [8,9]. Additionally, a lot of work has been accomplished for the solution of local structural problems, e.g., buckling issues or lay-up optimization [10–17], aeroelasticity, flutter [18], local optimization of panels or areas with cut-outs [19–21] for obtaining lighter designs. The aforementioned studies refer to a 2-spar arrangement only and to some specific structural problems, while the advantages that can be obtained by accommodating additional spar (more than two) in the wingbox as well as the design methodology that has to be followed is not exhaustively covered. Some of the most relevant but limited studies in the field of multispar wing structures are briefly mentioned hereafter. Snell et al. studied in [13] possible advantages of a metallic multispar configuration with composite skin by determining the optimum skin lamination in a small structural section only. A study carried out by Watson et al. [22] investigates a multispar configuration by considering only the buckling of skin, with semi-analytical methods, as a constraint, while for the rest of the members no additional failure criteria are adopted. Aston et al. in [23] developed a methodology for conservatively designing a multispar wing, and the focus of this work is to achieve fast design results rather than obtaining optimized member sizing. Herbeck developed a design methodology for sizing a wing structure by having as design criteria the buckling of skin and ribs, as well as bolted joints behavior [24]. Despite all of the above, Herbeck applied the methodology to a conventional 2-spar composite configuration only, while multispar configurations are not studied. Another work [25], focusing on the optimization of stiffened panels of a metallic wing box using buckling constraints and fatigue, is aiming to determine a lighter design. A significant contribution is offered by Stamatelos and Labeas in [26], who showed that multispar configurations can lead to lighter designs than the respective conventional under certain circumstances. Their investigation is based on the methodology presented hereafter. More recently, Moors et al. completed a study [27] which found that multispar designs can be lighter if combined with the appropriate number of stiffeners. In the latest work, local buckling of stiffeners (crippling) is also considered as a design constraint but the bearing bypass behavior is not taken into account. According to the aforementioned literature review the wing members, during the preliminary design phase, are usually sized based on stress–strain criteria in order to have fast iterations, therefore simplified FE models are utilized for this design stage. On the contrary, during the detail design phase, fine FE models are necessary so that wing members are sized, among others, against buckling and study their bearing bypass behavior. In the present paper, an innovative methodology for the preliminary member sizing of a wing structure is proposed, which considers (a) stress strain criteria, (b) global buckling criteria for the stiffened skin and spar webs, as well as (c) bearing bypass analysis for the bolted joints. To this end, the member sizing of the preliminary design phase can become more accurate, since criteria from the detail design phase are considered. It is essential to note that the proposed sizing methodology requires simple FE models, so the time for the completion of each iteration is relatively small. Eventually, by adopting the proposed methodology, the accuracy of the member sizing, during the preliminary design phase, can be increased. Moreover, the efficiency of the proposed methodology enables the fast, preliminary sizing of an innovative 4-spar composite wing layout. The 4-spar composite wing layout is then compared to a conventional 2-spar configuration in order to examine if multispar configurations demonstrate potential advantages, such as, stronger and stiffer structural arrangement, possibility of skin thickness reductions, or enhancement of their bearing bypass behavior. The reason for demonstrating the generic design methodology proposed for multispar configurations in the case of a 4-spar wing is simply because a 3-spar arrangement partially exists in some conventional wings, usually as a false spar; apparently, the method can be easily adopted for any other multispar wing configuration. Although, metallic multispar arrangements (e.g., delta wing) are usually used in supersonic military aircraft, where super critical airfoils are required, a composite multispar wing for commercial aircraft has not been studied so far. Computation 2020, 8, 24 3 of 14

The ﬂow chart of Figure1 illustrates the di ﬀerent stages of the design optimization process, which have been followed in the present paper, for the initial sizing of an airliner composite multispar Computation 2020, 8, x FOR PEER REVIEW 3 of 14 wing structure.

Wing parametric Finite Element model development

Stress / Strain analysis

Design allowable check

Modification of YES skin thickness NO Allowable Composite Wing flange areas, satisfied Final Sizing joint details, etc

Figure 1. Flow chart of the multispar composite wing design process.

The parametricFigure numerical 1. Flow Finite chart Element of the multispar (FE) models composite of a 2-sparwing design and a process. 4-spar wing configuration have been developed using ANSYS FE code [28] and they are presented in Section2. The models The parametric numerical Finite Element (FE) models of a 2-spar and a 4-spar wing are based on a 70% scaling of the basic geometrical configuration of an AIRBUS A330 aircraft. The configuration have been developed using ANSYS FE code [28] and they are presented in Section 2. computational models are fully parametric with respect to the main geometrical details, such that the The models are based on a 70% scaling of the basic geometrical configuration of an AIRBUS A330 determination of stress, strain and displacement of numerous wing structural variations is calculated as aircraft. The computational models are fully parametric with respect to the main geometrical details, function of varying sizing parameters (i.e., thickness or area); in that way, optimization of the structural such that the determination of stress, strain and displacement of numerous wing structural variations sizing is achieved. The FE results are introduced in a sizing routine, which includes an integrated set is calculated as function of varying sizing parameters (i.e., thickness or area); in that way, of design constraints for sizing the entire composite wing. optimization of the structural sizing is achieved. The FE results are introduced in a sizing routine, The design constrains, as explained in Section3, are similar to those proposed in Herbeck’s which includes an integrated set of design constraints for sizing the entire composite wing. work [24], with some modifications and additions, which mainly refer to stiffened panel buckling The design constrains, as explained in Section 3, are similar to those proposed in Herbeck’s work analysis and bearing bypass calculations. The wing numerical stress analysis, as well as the sizing [24], with some modifications and additions, which mainly refer to stiffened panel buckling analysis routine, are iterated until all design constrains are satisfied, i.e., the corresponding Reserve Factors and bearing bypass calculations. The wing numerical stress analysis, as well as the sizing routine, are (RFs) must have values greater than unity. iterated until all design constrains are satisfied, i.e., the corresponding Reserve Factors (RFs) must The optimized wing designs arise by applying two different variations of the iterative optimization have values greater than unity. procedure, as further explained in Section4. The comparison of the 2-spar and the 4-spar wing (Section4), The optimized wing designs arise by applying two different variations of the iterative demonstrates that the 4-spar configuration can have a mass reduction of 1.6% to 6.3%, indicating that optimization procedure, as further explained in Section 4. The comparison of the 2-spar and the 4- multispar designs can be potentially used in future airliner composite wing constructions. spar wing (Section 4), demonstrates that the 4-spar configuration can have a mass reduction of 1.6% 2.to Description6.3%, indicating of the that Computational multispar designs Analysis can be Model potentially used in future airliner composite wing constructions. A composite wingbox comprising the exact geometry of an AIRBUS A330 airliner wing, scaled at2. Description 70% of its original of the Computational size, is considered Analysis for the Model present study. The length of the analyzed wing is 21 m (wing span of 44.95 m), with a total wing area of 94 m2. The wing geometry modeled is kept as simpleA ascomposite possible wingbox for both configurations,comprising the i.e.,exact the geometry conventional of an 2-sparAIRBUS and A330 the 4-sparairliner configuration. wing, scaled Despiteat 70% of the its fact original that the size, number is considered and the for position the present of the study. ribs in The conjunction length of with the theanalyzed number wing of spars is 21 2 willm (wing reveal span more of advantages 44.95 m), with for a a multispar total wing configuration, area of 94 m the. The location wing ofgeometry the ribs modeled is kept constant is keptfor as bothsimple configurations. as possible for The both main configurations, reasons for this i.e., assumption the conventional is, firstly, 2-spar the needand the for 4-spar reducing configuration. the number ofDespite optimization the fact parameters,that the number secondly, and the to position make more of the evident ribs in the conjunction effect and with benefit the of number any additional of spars sparswill reveal in the more wingbox advantages and, thirdly, for a multispar the fact that configuration, the final rib the position location in aof wing the ribs structure is kept altersconstant as thefor designboth configurations. progresses, since The the main ribs arereasons also positionedfor this assumption to pick up concentratedis, firstly, the loads need from for landingreducing gears, the powerplants,number of optimization actuators, formation parameters, of fuelsecondly, tanks boundariesto make more etc. evident the effect and benefit of any additional spars in the wingbox and, thirdly, the fact that the final rib position in a wing structure alters as the design progresses, since the ribs are also positioned to pick up concentrated loads from landing gears, powerplants, actuators, formation of fuel tanks boundaries etc. The FE models mainly comprise two or four main spars, (spar flanges and spar webs are modeled explicitly), the upper and lower skins (covers) and the ribs, as presented in Figure 2a,b and c. The mesh density of the FE model, is determined through a convergence study, where the vertical displacement is monitored in order to obtain an adequate mesh density for the wing structure.

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ComputationThe 2020 FE models, 8, x FORmainly PEER REVIEW comprise two or four main spars, (spar ﬂanges and spar webs are modeled4 of 14 explicitly), the upper and lower skins (covers) and the ribs, as presented in Figure2a–c. The mesh density of the FE model, is determined through a convergence study, where the vertical displacement Computation 2020, 8, x FOR PEER REVIEW 4 of 14 is monitored in order to obtain an adequate mesh density for the wing structure.

(a) (b) (c)

Figure 2. (a) Outer geometry of the wing; (b) inner 2-spar wing structure; (c) inner 4-spar wing structure. (a) (b) (c)

‘ShellFigureFigure 181’ 2.2. ( (aaelement)) OuterOuter geometry geometrytype ofof the theof theANSYS wing; wing; (b )element inner(b) inner 2-spar li brary2-spar wing structure;iswing used structure; for (c) innerthe (skin,c 4-spar) inner rib wing 4-sparand structure. spar-web wing panels.structure. The spar flanges are modeled using the ‘Link8’ element type, which is a 3-D spar element ‘Shell 181’ element type of the ANSYS element library is used for the skin, rib and spar-web panels. with uniaxial tension-compression behavior and has three degrees of freedom at each node. The The spar‘Shell flanges 181’ element are modeled type usingof the the ANSYS ‘Link8’ element element li type,brary which is used is afor 3-D the spar skin, element rib and with spar-web uniaxial entire FE model of the 2-spar and 4-spar configurations comprises approximately 40,000 and 43,000 panels.tension-compression The spar flanges behavior are modeled and has threeusing degreesthe ‘Link8’ of freedom element at type, each which node. Theis a entire3-D spar FE modelelement of elements, respectively. A detail of the FE model discretization in the lower side, which shows the FE withthe 2-spar uniaxial and tension-compression 4-spar configurations comprisesbehavior and approximately has three degrees 40,000 and of 43,000freedom elements, at each respectively. node. The mesh around the access holes area is shown in Figure 3a. It must be mentioned that all geometrical entireA detail FE of model the FE of model the 2-spar discretization and 4-spar in configurations the lower side, comprises which shows approximately the FE mesh 40,000 around and the 43,000 access input of the model is introduced in the FE model parametrically (skin and web thickness, flange areas, elements,holes area respectively. is shown in A Figure detail3 a.of the It must FE model be mentioned discretization that allin the geometrical lower side, input which of shows the model the FE is bolt-hole dimensions, etc.), in order to enable variations of these parameters during the optimization meshintroduced around in the FEaccess model holes parametrically area is shown (skin in andFigu webre 3a. thickness, It must be flange mentioned areas, bolt-hole that all geometrical dimensions, procedure. Each skin panel is divided to five areas, at each of which a different thickness value may inputetc.), inof orderthe model to enable is introduced variations in ofthe these FE model parameters parametrically during the (skin optimization and web thickness, procedure. flange Each areas, skin be assigned, i.e., the skin panel thickness is assumed to vary chordwise to allow weight reduction, as bolt-holepanel is divided dimensions, to five etc.), areas, in order at each to ofenable which vari aations different of these thickness parameters value may during be assigned,the optimization i.e., the shown in Figure 3b. The FE model’s boundary conditions comprise fixing of all degrees of freedom procedure.skin panel thicknessEach skin ispanel assumed is divided to vary to chordwisefive areas, toat alloweach of weight which reduction, a different as thickness shown in value Figure may3b. in the wing root. beThe assigned, FE model’s i.e., boundarythe skin panel conditions thickness comprise is assumed fixing to of vary all degrees chordwise of freedom to allow in weight the wing reduction, root. as shown in Figure 3b. The FE model’s boundary conditions comprise fixing of all degrees of freedom in the wing root.

(a) (b)

Figure 3. (a) Discretization of lower skin in the area of access holes; (b) chordwise panel thickness Figurevariation 3. (a (right).) Discretization(a) of lower skin in the area of access holes; (b) chordwise(b) panel thickness variation (right). The material system is not a design variable in the current study. The apparent material properties Figure 3. (a) Discretization of lower skin in the area of access holes; (b) chordwise panel thickness of theThe composite material lay-upsystem appliedis not area de achievedsign variable using in the the Classical current Lamination study. The Theory; apparent for bothmaterial spars variation (right). propertiesand ribs, of the the apparent composite elasticity lay-up applied modulus are values achieved are Eusing11 = theE22 Classica= 51,953l Lamination MPa, shear Theory; modulus foris bothG12 spars= 25,772 and MParibs, the and apparent Poisson’s elasticity ratio is νmodulus12 = 0.398; values in a are similar E11 = way,E22 = 51,953 the respective MPa, shear values modulus for the The material system is not a designν variable in the current study. The apparent material iscovers G12 = 25772 are E11 MPa= 75,026 and Poisson’s MPa, E22 =ratio30,335 is MPa,12 = 0.398; G12 =in15,573 a similar MPa way, and νthe12 =respective0.4366. values for the properties of the composite lay-up applied are achieved using theν Classical Lamination Theory; for coversAs are the E11 present= 75026 studyMPa, E aims22 = 30335 to a preliminary MPa, G12 = 15573 comparison MPa and of 2-12 and= 0.4366. 4-spar wings, only the most both spars and ribs, the apparent elasticity modulus values are E11 = E22 = 51,953 MPa, shear modulus importantAs the present and critical study wing aims loading to a preliminary scenario hascomparison been selected of 2- and for the4-spar analysis; wings, it only comprises the most the is G12 = 25772 MPa and Poisson’s ratio is ν12 = 0.398; in a similar way, the respective values for the importantaerodynamic and liftcritical and wing drag loading pressures, scenario as well has as been the selected weight offor the the powerplant. analysis; it comprises All secondary the covers are E11 = 75026 MPa, E22 = 30335 MPa, G12 = 15573 MPa and ν12 = 0.4366. aerodynamicloading conditions, lift and drag such pressures, as landing as gearwell loads,as the weight secondary of the aerodynamic powerplant. loads,All secondary etc. are loading ignored. As the present study aims to a preliminary comparison of 2- and 4-spar wings, only the most conditions, such as landing gear loads, secondary aerodynamic loads, etc. are ignored. The above- important and critical wing loading scenario has been selected for the analysis; it comprises the described FE models are used to perform a linear static analysis with the use of ANSYS FE solver, aerodynamic lift and drag pressures, as well as the weight of the powerplant. All secondary loading from which the stresses, strains and displacements all over the wing structure are calculated. conditions, such as landing gear loads, secondary aerodynamic loads, etc. are ignored. The above- described FE models are used to perform a linear static analysis with the use of ANSYS FE solver, 3. Composite Wing Design Allowable from which the stresses, strains and displacements all over the wing structure are calculated.

3. Composite Wing Design Allowable

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The above-described FE models are used to perform a linear static analysis with the use of ANSYS FE solver, from which the stresses, strains and displacements all over the wing structure are calculated.

3. Composite Wing Design Allowable In order to perform an initial structural sizing of the wing components, the obtained static analysis results are compared to the respective allowable values, in order to check if the members’ sizing fulfil the design constraints. All structural elements of the wing, i.e., spar flanges, spar webs, skin panels and ribs are checked for satisfying the strain allowable, which ensures that no material failure will occur. In order to achieve a conservative design, the strain allowable of the current material system is set to 6000 µ for tension, 6000 µ for compression and 7000 µ for shear loading. The strain allowables − are set to have these values after following AIRBUS-UK guidelines, so that certain damage tolerance principles are met. Apart from the aforementioned strain allowable, other specific design constrains should be fulfilled. The upper skin panels, which are under compression loading due to the wing bending arising from the aerodynamic lift load, are additionally sized and verified with respect to buckling under compression, shear, and compression–shear interaction. The spar webs are additionally sized according to buckling under shear, bending and shear–bending interaction. Finally, a bearing bypass analysis is performed for the flange-web and flange-skin connection areas. Wing ribs are additionally sized according to Brazier loading, i.e., rib crashing due to wing bending. The rib number and sizing does not affect significantly the total mass of the wing, as their total mass is less than 10% of the total wing mass; considering also the reasons mentioned in Section2, the rib number is kept constant for both 2- and 4-spar layouts. The implementation of the various design constrains for each structural element of the composite wing is described in detail hereafter.

3.1. Upper and Lower Skin Panels It is well known that the upper cover of a wing is subjected to compressive and shear loads, which may lead to panel buckling. For this reason, the upper wing panels are additionally sized with respect to compressive and shear bucking, as well as to their interaction. Determination of the critical buckling load of stiffened panels requires modelling of the different, complex stiffener geometry, as well as the skin stiffener interface. However, in the phase of initial and preliminary design, modelling of the stiffener geometry and its connection to the skin would result to a large-scale computational model, requiring significantly increased model development and solution effort. Furthermore, changing the design parameters and performing iterations with such a large-scale numerical model is rather impractical. Thus, to simplify the wing’s FE model, the stiffeners are not included in the panel’s FE model in a discrete way, but their stiffness is smeared into the entire panel geometry, as shown in Figure4, in a way that their e ffect in buckling response is efficiently considered. According to AIRBUS-UK guidelines, it is assumed during the stiffness smearing process that the stiffeners are blade shaped with a pitch of 200 mm, which is rather typical for such aircraft wing size. Consequently, the calculation of the critical buckling load of stiffened composite panels can be performed using unstiffened panel analytical formulations [29–32]. It is also worth mentioning that, during the preliminary design phase for the buckling analysis of the panels, simply supported boundary conditions are assumed for all of their edges. This is a common assumption for this design phase, so that a relatively conservative member sizing can be obtained, as well as for simplicity reasons. In reality and in full-scale experimental tests though, the boundary conditions of the panels are elastically restrained, hence, simply supported panels are meaningless to be experimentally tested in later stages of the design. Consequently, the validation of the proposed buckling solution, which refers to simply supported panels, is obtained with the use of FE methods. Furthermore, the methodology is revised by AIRBUS-UK for its applicability. Of course, during the experimental study of the structure, where large scale components are tested, Computation 2020, 8, 24 6 of 14 the modelling approach differentiates with the one presented hereafter. For completeness purposes, representativeComputation 2020 experimental, 8, x FOR PEER studies REVIEW are also mentioned for large scale aircraft structures [336 –of35 14] and for rotorcrafts [36,37].

Nx Nx Ny Ny

Homogeneous plate with equivalent stiffness z Nx Ny Nx Ny

y x

Figure 4. Homogenization of a stiffened panel by smearing stiffeners. Figure 4. Homogenization of a stiffened panel by smearing stiffeners. In the present analysis, the critical buckling compressive load is calculated using the analytical In the present analysis, the critical buckling compressive load is calculated using the analytical solution of Equation (1) [31]; solution of Equation (1) [31]; D0 Ncr = (1) α2λ = (1) " eq eq eq ! eq ! # D D D 2 4 D 4 2 11 2 12 66 α 2 α 22 n π m + 2 + 2 n + D0 D0 D0 b b D0 m2 λ = +2 +2 + (2) 2 2 = Ny α n (2) 1 + N b m 1 + x 3 E11t eq = Equations (1) and (2), D0 12(1 ν ν ) , Dij are the components of the equivalent bending stiffness Equations (1) and (2), = 12 21 , D are the components of the equivalent bending matrix. The equivalent bending stiff−ness matrix yields using an energy approach. In more detail, by stiffness matrix. The equivalent bending stiffness matrix yields using an energy approach. In more equating the strain energy and the work done by the compressive forces of the stiffened panel with the detail, by equating the strain energy and the work done by the compressive forces of the stiffened respective energy of an equivalent homogeneous panel (no stiffeners), the equivalent bending stiffness panel with the respective energy of an equivalent homogeneous panel (no stiffeners), the equivalent termsbending can be calculated.stiffness terms Furthermore, can be calculated. in Equations Furthermore, (1) and in Equations (2), α is the (1) lengthand (2), of the is the unloaded length of edge of thethe panel unloaded and R edgeis the of panel’sthe panel aspect and ratio. is the Npanel’sx, Ny aspectare the ratio. uniform , distributed are the uniform load distributed applied to the panel’sload edges applied as shown to the panel’s in Figure edges4. asm ,shownn are thein Figure number 4. of, buckling are the number half waves of buckling and their half valueswaves are determinedand their to values result are the determined minimum to critical result bucklingthe minimum load criticalNcr. buckling load . At eachAt each design design optimization optimization step, step, th thee skin skin panels panels may may fulfil fulfil or not or fulfil not the fulfil buckling the buckling or the strain or the strainallowable. allowable. In Ineither either case, case, the the panel panel skin skin thickness thickness should should be properly be properly resized resized locally locally before beforea a consequentconsequent iterative iterative solution solution of of th thee entire entire structural structural model model is executed. is executed. The element The thickness element should thickness be suitably increased in case the panel load is higher compared to the critical buckling load; on the should be suitably increased in case the panel load is higher compared to the critical buckling load; contrary, it must be decreased in cases that the RF is much higher than unity, such that in the on the contrary, it must be decreased in cases that the RF is much higher than unity, such that in the subsequent iterations the RF approaches unity. In the present optimization procedure, the introduced subsequentresizing iterations rules distinguish the RF betweenapproaches the possible unity. In failur thee present types. For optimization the case of buckling procedure, constraint, the introduced panel resizingthickness rules distinguish recalculation between () follows the possible the rule: failure types. For the case of buckling constraint, panel thickness recalculation (ti+1) follows the rule: (3) =q 4 4 ti ti+1 = /RFi (3) Equation (3) arises from Equations (4) and (5), which express the RFs of two subsequent Equationiterations (3)() arisesand (+1 from). EquationsThe RF of (4)the and iteration (5), which is express and theis calculatedRFs of two as subsequent a function of iterations the th (i) andapplied (i + 1). load The RF andof thepaneli thicknessiteration is, RFas:i and is calculated as a function of the applied load Pi and panel thickness ti, as: = = (4)  3  Ncr  t  RF = i = f  i  (4) i N P  Similarly the RF of the sequential iteration (+1i ) is giveni by the first part of Equation (5).

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Similarly the RF of the sequential iteration (i + 1) is given by the ﬁrst part of Equation (5).

 3   4  Ncr  t   t  = i+1 =  i+1  =  i+1  RFi+1 f  t  f   (5) Ni+1 P i /t  Pi ti  i × i+1 × Equation (3) yields from the substitution of Equation (4) to Equation (5) and solving with respect to panel thickness ti+1. The iterative procedure is performed until an optimum sizing is achieved, which apparently is succeeded when a RF of one (RF f inal = 1) is achieved. The critical shear buckling load of the spar webs and the upper skin panels is estimated by Equation (6), [32]; the analytical buckling solutions are valid for long panels loaded in shear:   4 D D3 8.125 + 5.05 , 1  b2 11 22 θ θ N =  ≥ (6) xycr  p  4 D (D + D ) + + 2  b2 22 22 2 66 11.7 0.532θ 0.938θ , θ < 1

√D11D In Equation (6), θ = 22 and b is the lateral dimension of the plate. D12+2D66 Finally, to avoid panel buckling due to interaction of compression and shear loading, the individual buckling RFs for compression and shear (Equations (7) and (8)) are combined according to Equation (9) [38] as follows:

Nxcr RFcomp = (7) Nx

Nshearcr RFshear = (8) Nshear 1 1 + = 1 (9) RFcomp 2 RFshear

In Equations (7)–(9), RFcomp and RFshear are the RF for compression and shear buckling, respectively. Buckling is not an applicable sizing criterion for the lower skin, simply because it is basically loaded in tension. Therefore, the axial strain allowable of the panels governs their sizing. As already mentioned, the allowable tensile strain level used is 4500 µ.

3.2. Wing Main Spar The investigated wing designs comprise 2- and 4-main spar layouts. Each spar consists of the upper and lower spar flanges, which are connected by the spar web. The main driving factor for the spar web’s sizing is buckling under shear loading, which is calculated by Equation (6). However, in-plane bending buckling and the interaction of shear and in-plane bending buckling are also considered. For in-plane bending buckling, a closed form analytical solution is proposed [39] as given in Equation (10). p 2 2 Bendcr = KBendπ D11D22/b (10)

Where in Equation (10),

(D12 + 2D66) KBend = 13.425 + 10.499β and, β = √D11D22

The above buckling formulae for shear and in-plane bending buckling are limited to infinitely simply supported long plates, a requirement which is fulfilled in the case of the long spar webs. The interaction of shear and in-plane bending buckling is treated using the RF approach of Equations (7)–(9) of Section1 properly modified. Computation 2020, 8, 24 8 of 14 Computation 2020, 8, x FOR PEER REVIEW 8 of 14

3.3.Computation Bolted3.3. Bolted and 2020 Riveted,and 8, x FORRiveted PEER Joint JointREVIEW Areas Areas 8 of 14

3.3.1.3.3.3.3.1. Bolted Bearing Bearing and Bypass Riveted Bypass Joint Analysis AnalAreasysis of the of Jointthe Joint Areas Areas

3.3.1.The BearingThe upper upper Bypass and and lower Anal lowerysis skins of skins the are Joint boltedare Areas bolted to the to sparthe spar flanges, flanges, but evenbut even the bestthe best fastened fastened joints joints in in composite materials can still impose a loss in strength of about half the basic material allowable [40]. compositeThe upper materials and canlower still skins impose are bolted a loss to in the strength spar flanges, of about but halfeven the thebasic best fastened material joints allowable in [40]. Incomposite general,In general, fastener materials fastener holes can holesstill are impose subjected are subjected a loss to in the strength to combined the combinedof about effects half effects of the bearing basic of bearingmaterial loads ( F loadsallowablebearing () and [40]. loads ) and that loads bypassIn thatgeneral, the bypass hole fastener the (Fbypass holeshole), (are as illustratedsubjected), as illustrated to inthe Figure combined in5. Figure The effects ratio 5. of The ofbearing bearingratio loadsof tobearing ( bypass to) load bypassand loads depends load depends on thethat stion ffbypass nessthe stiffness ofthe the hole joint of( the configuration. ),joint as illustrated configuration. As in the Figure joint As 5. isthe The loaded joint ratio by isof Floadedbearingtot, the toby bearing bypass , bypasstheload bearing depends ratio bypass remains ratio nearlyonremains the constant stiffness nearly untilof theconstant joint joint damage configuration. until joint develops. damage As the Therefore, jointdevelops. is loaded the Therefore, joint by area, the ofthe the jointbearing spar area flangesbypass of the ratio to spar the flanges skins to shouldremainsthe beskins nearly considered should constant be for considereduntil bearing joint ordamage for net-section bearing develops. or failures net-section Therefore, [41–43 the failures]. joint area [41–43]. of the spar flanges to the skins should be considered for bearing or net-section failures [41–43].

= =

Figure 5. Bolted joint bearing bypass load transfer schematically represented. FigureFigure 5. Bolted 5. Bolted joint bearing joint bearing bypass loadbypass transfer load schematically transfer schematically represented. represented. The bearing bypass analysis is the final constrain considered in the present design. The important geometricTheThe characteristicsbearing bearing bypass bypass of analysis the jointanalysis is area the is arefinal the bolt co finalnstrain diameter co nstrainconsidered (d), bolt considered pitchin the (4 dpresent) andin the spar design. present flange The thicknessdesign. The important geometric characteristics of the joint area are bolt diameter (), bolt pitch (4) and spar (tfl).important The joint bearing geometric and bypasscharacteristics loads, required of the joint as input area for are the bolt bearing diameter bypass (), analysis, bolt pitch are ( extracted4) and spar flange thickness (). The joint bearing and bypass loads, required as input for the bearing bypass fromflange the FE thickness model solution. (). The In joint parallel, bearing experimentally and bypass loads, obtained required failure as envelopes input for arethe constructed bearing bypass analysis, are extracted from the FE model solution. In parallel, experimentally obtained failure basedanalysis, on joint are geometrical extracted andfrom material the FE data. model It issolution consequently. In parallel, checked experimentally if the applied bearingobtained and failure envelopes are constructed based on joint geometrical and material data. It is consequently checked if bypasstheenvelopes applied loads bearing satisfy are constructed and the strengthbypass based loads requirements. satisfyon joint the geometrical strength The extracted requirements. and material values The fromdata. extracted theIt is FE consequently values model, from as well checked as if thethe calculatedthe FE applied model, parameters asbearing well asand forthe bypass plottingcalculated loads the paramete finalsatisfy failurers the for st envelope,plottingrength requirements.the are final illustrated failure The envelope, in extracted the flow-chart are values of from Figureillustratedthe6. FE The inmodel, details the flow-chart ofas thewell process of as Fi gurethe implementation calculated6. The details paramete of in the the process casers for of implementation theplotting current the composite infinal the casefailure wing of the envelope, joints are are describedcurrentillustrated composite in the in next the wing paragraphs.flow-chart joints are ofdescribed Figure in6. theThe next details paragraphs. of the process implementation in the case of the current composite wing joints are described in the next paragraphs.

FE Model Solution FE Model Solution Extracted values from FE model Shear Flow Area of Flanges Flange Axial Load Extracted values from FE model Shear Flow Area of Flanges Flange Axial Load Calculated Bolt Diameter Spar Flange Bearing Bypass parameters Thickness loads loads Calculated Bolt Diameter Spar Flange Bearing Bypass Bolt Pitch parameters Thickness loads loads

Failure Envelop Bolt PitchFailure Envelop Final Check

Failure EnvelopFigure 6. 6. FlowFlow chart chart of ofthe the bearing bearingFailure bypass bypass Envelo bolted bolted jointp Final analysis. joint Check analysis.

3.3.2.3.3.2. Geometrical Geometrical ConfigurationConfiguration of of the the Joint Joint Figure 6. Flow chart of the bearing bypass bolted joint analysis. AA double double row of of bolts bolts in inthe thespanwise spanwise direction direction is considered is considered for both wing for both configurations. wing configurations. The Thecomplete complete determination determination of the joint of the geometrical joint geometrical configuration configuration requires definition requires of the definition bolt diameter of the bolt 3.3.2. Geometrical Configuration of the Joint diameter(), bolt (pitchd), bolt and pitch the andspar theflange spar thickness flange thickness(). The bolts (tfl). are The equally bolts are spaced equally with spaced a pitch withof 4 a, pitch of 4dfollowing, followingA boltingdouble bolting empirical row empirical of bolts guidelines, in guidelines, the whichspanwise whichensure direction that ensure unreasonable is that considered unreasonable failures for willboth failures be wing avoided. willconfigurations. beThe avoided. The Thebolt boltcomplete diameters diameters determination are allowed are allowed to ofva rythe to in vary joint the inspanwise geometrical the spanwise direction. configuration direction. requires definition of the bolt diameter

(), bolt pitch and the spar flange thickness (). The bolts are equally spaced with a pitch of 4,

following bolting empirical guidelines, which ensure that unreasonable failures will be avoided. The bolt diameters are allowed to vary in the spanwise direction.

Computation 2020, 8, 24 9 of 14

The bolt diameter is calculated according to the inequality of Equation (11). For the present wing design, titanium bolts are selected with an allowable shear strength value of 662 MPa. Computation 2020, 8, x FOR PEER REVIEW 9 of 14 Bolt Load Shear Stress = Allowabe shear o f bolt (11) πd2 The bolt diameter is calculated according /to4 the≤ inequality of Equation (11). For the present wing design, titanium bolts are selected with an allowable shear strength value of 662 MPa. In Equation (11), the Bolt Load for a double row of bolts is calculated with the use of Equation (12). = ≤ (11) Bolt Load = 2 d q (12) × × In Εquation (11), the Bolt Load for a double row of bolts is calculated with the use of Εquation (12).In Equation (12), q are the extracted spar web shear flow values, as calculated from the FE model solution. = 2 × × (12) 3.3.3. BearingIn Equation Bypass (12), Loading are the extracted spar web shear flow values, as calculated from the FE model solution. For a joint configuration with specific bolt diameter, bolt pitch and spar flange thickness, the respective3.3.3. Bearing bearing Bypass and bypass Loading loads can be calculated as follows:

For a joint configuration withBearing specific Load bolt= Bolt diam Loadeter,= bolt2 pitchq d and spar flange thickness, the (13) respective bearing and bypass loads can be calculated as follows:× × = Flange = Axial2 × × Load Bypass Load = (13) (14) 12d = (14) In Equation (14), the values for Flange Axial Load12parameter are extracted from the FE model solution by considering the section bounded by the upper and lower flanges, which lies between two sequentialInribs. Equation (14), the values for parameter are extracted from the FE model solution by considering the section bounded by the upper and lower flanges, which lies between two 3.3.4.sequential Failure Envelope ribs. 3.3.4.Failure Failure envelopes Envelope covering all possible failure modes of a bolted joint, i.e., tension, cleavage, shear andFailure bearing envelopes have thecovering typical all formpossible of failure Figure modes7. Such of a failure bolted envelopesjoint, i.e., tension, are constructed cleavage, by experimentallyshear and bearing testing have diff erentthe typical geometrical form of configurationsFigure 7. Such failure of bolted envelopes joints withare constructed different materialby typesexperimentally and lay-ups. Thetesting bearing different bypass geometrical failure configurations envelope, which of bolted corresponds joints with to the different geometry, material material systemtypes and and lamination lay-ups. The of bearing the joint bypass as defined failure inenve eachlope, iteration, which corresponds is examined to the in ordergeometry, to examine material if the appliedsystem bearing and lamination bypass load of the combination joint as defined (indicated in each by iteration, the red is dot examined plotted in in order Figure to examine7) falls within if the the respectiveapplied failure bearing envelope. bypass load Apparently, combination when (indicated the bearing by the red bypass dot plotted load combination in Figure 7) falls falls within inside the envelope,the respective no joint failure failure envelope. is expected, Apparently, while when when the thedot bearing lies outsidebypass load the failurecombination envelope falls inside a failure is the envelope, no joint failure is expected, while when the dot lies outside the failure envelope a failure predicted, thus another re-sizing iteration should be performed. is predicted, thus another re-sizing iteration should be performed.

FigureFigure 7. 7.Bearing Bearing bypass failure failure envelope. envelope.

Computation 2020, 8, 24 10 of 14

TheComputation sizing 2020 of, spar8, x FOR flanges PEER REVIEW additionally requires that the values of flange thickness t10f l andof 14 bolt diameter d, satisfy the condition of Equation (15), in order to avoid bolt intrusion to the laminated flange. The sizing of spar flanges additionally requires that the values of flange thickness and bolt diameter , satisfy the conditionBearing of Load Equation (15), in order to avoid bolt intrusion to the laminated Bearing Strength o f Laminate (15) flange. t f l d ≤ × ≤ ℎ (15) The entire bearing bypass sizing× procedure described above is programmed in Visual Basic for Applications (VBA) of Excel and hence the procedure can be repeated iteratively until a safe design is The entire bearing bypass sizing procedure described above is programmed in Visual Basic for obtained for each joint area. Applications (VBA) of Excel and hence the procedure can be repeated iteratively until a safe design 4. Comparisonis obtained betweenfor each joint 2- and area. 4-Spar Configurations A4. postComparison processing between code 2- has and been 4-Spar developed Configurations as an ANSYS macro-routine in order to perform an automatedA allowablepost processing check code of has all thebeen components developed as ofan theANSYS wing macro-routine model. The inmacro-routine order to perform extracts an geometricautomated data andallowable strain check/stress of results, all the derivescomponents magnitudes of the wing of interestmodel. The out macro-routine of them using extracts analytical functionsgeometric and comparesdata and strain/stress them with results, the pre-set derives limits, magnitudes i.e., maximum of interest allowable out of them strain using levels,analytical critical bucklingfunctions loads, and bearing compares bypass them limits, with the etc. pre-set Several limits, iterations i.e., maximum are required allowable until strain all levels, design critical rules are satisfiedbuckling and the loads, final bearing sizing bypass that eventually limits, etc. provides Several iterations the lightest are structure required ofuntil each all configurationdesign rules are arises. Twosatisfied different and the variations final sizing of thethat optimization eventually prov processides the have lightest been structure trailed in of the each present configuration study; both arises. variations consist of the same four steps, specifically: (a) sizing of the entire wing, such that all its Two different variations of the optimization process have been trailed in the present study; both components satisfy the pre-set strain levels; (b) sizing of the upper skin panels, such that compression variations consist of the same four steps, specifically: (a) sizing of the entire wing, such that all its bucklingcomponents constraints satisfy are the satisfied; pre-set (c)strain sizing levels; of the(b) sizi websng accordingof the upper to skin shear panels, and bendingsuch that bucklingcompression criteria, and (d)buckling bearing constraints bypass analysisare satisfied; for the(c) sizing bolted of joint the webs areas. according In the first to shear variation and bending of the optimizationbuckling procedurecriteria, (referred and (d) hereafterbearing bypass as OP-1), analysis at each for optimizationthe bolted joint step, areas. the In structural the first variation members of are the sized accordingoptimization to one constraintprocedure and(referred consequently hereafter allas otherOP-1), structuralat each optimization members are step, resized the structural with respect to allmembers other constraints. are sized according In the second to one variation constraint of and the consequently optimization all procedure other structural (referred members hereafter are as OP-2),resized no resizing with respect of already to all sizedother membersconstraints. is In performed, the second whenvariation other of the members optimization are checked procedure for the additional(referred constraints. hereafter as OP-2), no resizing of already sized members is performed, when other members are checked for the additional constraints. The flow chart of Figure8 illustrates the details of the di fferent stages of the optimization process The flow chart of Figure 8 illustrates the details of the different stages of the optimization process followed, highlighting the differences between the two iterative schemes. followed, highlighting the differences between the two iterative schemes.

FigureFigure 8. Detailed 8. Detailed ﬂow chartflow ofchart the of two the variations two variations of the optimizationof the optimization process process applied applied to both to composite both wing conﬁgurations.composite wing configurations.

Computation 2020, 8, 24 11 of 14

5. Results and Discussions A comparison between 2- and 4-spar wing designs is performed. In Table1, a detailed mass breakdown in (kg) for both conﬁgurations is presented. Comparing the results of Table1, the 4-spar arrangement appears to be relatively lighter compared to the conventional 2-spar design.

Table 1. Detailed ﬁnal mass breakdown of the 2-spar and the 4-spar composite wing structural conﬁgurations.

Optimization Procedure 1 Optimization Procedure 2 2-Spar 4-Spar 2-Spar 4-Spar Wing Component Arrangement Arrangement Arrangement Arrangement Upper Skin 1405 956 1474 993 Lower Skin 776 656 862 749 Front Spar Web 154 123 156 119 Front Spar Flange 84 55 175 92 2nd Spar Web - 158 - 160 2nd Spar Flange - 213 - 160 3rd Spar Web - 133 - 132 3rd Spar Flange - 166 - 152 Rear Spar Web 99 75 99 78 Rear Spar Flange 106 53 131 71 Ribs 213 210 241 233 Total Wing Weight (kg) 2837 2798 3138 2939

It can also be observed from Table1 that the 4-spar arrangement appears to be lighter than the 2-spar by approximately 1.3% (38 kg) and 6.3% (198 kg), when OP-1 and OP-2 are applied, respectively. Another important remark refers to the lateral wing tip displacement (Uz), which has been calculated to be about 3.3 m for both models, indicating that the entire wing stiffness remains almost constant in both configurations. This can be initially explained by considering that both configurations are sized based on the same allowable strain values. This important remark is better understood if a wing cross-section is considered; it is evident that when the number of spars increases, the design optimization requires a mass movement from the skin towards the spar flanges, with a tendency to keep the overall second moment of inertia almost constant. This observation indicates that no significant mass savings can be achieved, if the sizing is based exclusively on strain allowable. As previously mentioned, compression buckling is the driving design factor for the upper skin panels for both wing arrangements (2- and 4-spar). The fulfillment of compression buckling constraints can give advantage to a multispar configuration, due to a positive change of the panel aspect ratios, resulting to higher critical buckling loads (Equation (1)). It is found that for the case considered, the weight penalty due to buckling reaches to approximately 30% of the upper skin mass, i.e., between 500 kg and 600 kg for the conventional arrangement. On the other hand, the weight penalty required to fulfill upper cover buckling constraints of the 4-spar arrangement is only 10% of the upper skin mass. Therefore, the margin for a potential weight saving relevant to panel compression buckling is quite essential. Nevertheless, the total mass of the spars in the 4-spar arrangement is higher compared to those in the conventional configuration. The reduction of the skin mass in the 4-spar arrangement is relatively higher to the mass penalty caused by the addition of intermediate spars in the multispar configuration, which results to an overall advantage of the multispar arrangement. The material system has not been considered as an optimization parameter in the present study. However, an important remark with respect to the selection material system for a multispar configuration is that a material system with significantly higher elastic modulus (E11) in the principal material direction is required for the spars. It is believed that a lamination enhanced in the spanwise wing direction will withstand higher axial loads, which will result a more beneficial multispar configuration. It is worth mentioning at this point that this parametric study is carried out in the frames of the preliminary structural design phase and its aim is to explore whether a multispar configuration has Computation 2020, 8, 24 12 of 14 potential advantages for further analysis. The impact of a multispar configuration to the aircraft’s performance has not been considered at this stage. However, it is expected, in the multispar configuration, to have a reduced space in the wings for fuels, compared to a conventional spar arrangement that will probably result to reduced overall flight range and endurance if no further actions or considerations are taken. In the multispar configuration, the fuel space issues that will arise due to the additional spars in the wingbox, can be overcome by adopting the fuel tank scheme that is used in fighter aircrafts with multispar wing layouts. Moreover, an extended center fuel tank in the fuselage can be also foreseen to meet the flight range and endurance requirements of the aircraft.

6. Conclusions An effective method for sizing large scale composite components, such as aircraft wings, is developed and presented in the current paper. The method is demonstrated in the preliminary design of a multispar composite wing configuration and it has been proven that the actual member sizing (spar, skin, etc.) can be obtained in a relative small time frame, even though iterations are required. Analytical closed form solutions for predicting the critical buckling load of stiffened panels are developed with the use of a smearing approach so that the buckling solution equations can be programmed easily, within ANSYS (ANSYS Parametric Design Language) APDL, and provide instant results during an iteration loop. Moreover, empirical bolting rules for joining the skin to the spar flanges are applied and in conjunction with the derived bolted-joint failure envelopes, the sizing of all joint areas is obtained. By utilizing the bolted-joint failure envelopes the determination of the sizing of the bolts can be completed without running any joint FE analyses that will increase the computational cost and time of each iteration. Additionally, two optimization procedures (OP) are followed to obtain the final sizing solutions. OP-2 does not allow resizing of all wing members between consequent iterations of the optimization results to more conservative designs and hence has less mass saving. Moreover, for the OP-2 the required time and number of iterations, to obtain a converged solution regarding the member sizing, is less than the time required for OP-1. However, both optimization procedures require less than two hours in a standard computer (8GB RAM) to converge to the final member sizing (regardless the configuration). The final comparison between the two optimized configurations showed that the 4-spar arrangement appears to be lighter than the conventional 2-spar wing by 1.3% (38 kg) or 6.3% (198 kg) depending on the optimization procedure followed. The lateral displacement of the wing tip is found to be approximately the same for both configurations indicating that the total stiffness of the two wing configurations remains almost constant. Compression buckling is the driving constraint for the upper skin; its fulfillment provides advantage to the multispar configuration, due to positively changing of the wing panel aspect ratios which result to higher critical buckling loads. It is believed that a more efficient multispar arrangement may be achieved by employing a material system of higher modulus of elasticity in the spar direction. Finally, apart from the reduction of wing mass, a multispar wing solution can have advantages from a manufacturing point of view if modular manufacturing techniques are considered.

Author Contributions: The conceptualization of this research was conceived by D.S. and G.L. the methodology was developed by D.S. and G.L. The numerical analyses (programming) as well as the validation of the FE models was performed by D.S. The original draft of this manuscript was prepared by D.S. and reviewed and edited by G.L. G.L. supervised the documented research and he was responsible for the project administration on behalf of the University of Patras. Finally, the authors have read and agreed to the published version of the manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the EU research project Advanced Low Cost Aircraft Structure “ALCAS”, grant number 516092. Acknowledgments: The authors wish to acknowledge AIRBUS-UK for the support of this research. Conﬂicts of Interest: The authors declare no conﬂict of interest. Computation 2020, 8, 24 13 of 14

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