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Layout Optimization for Blended Wing Body Aircraft Structure

Layout Optimization for Blended Wing Body Aircraft Structure Structural layout design of blended wing body (BWB) aircraft in the preliminary design phase is a challenging optimization problem due to large numbers of design variables and various constraints. A two-loop optimization strategy is proposed to solve the BWB aircraft structural layout design problem considering constraints of the displacement, stress, strain, and buckling. The two-loop optimization consists of an inner loop and an outer loop. The inner loop is to optimize each stiffened panel of the BWB aircraft structure, and outer loop is to find the best layout design. To improve computational efficiency, an equivalent finite element model is applied to BWB aircraft structure analysis, and an analytical method is used for buckling and static analysis of the stiffened panels. The proposed method can efficiently solve the structural layout optimization prob- lem of a notional BWB aircraft with acceptable computational burden. The result indicates the mass of main load-carrying structure of the BWB aircraft is reduced by 9.28% compared to that of the initial structural layout. Keywords Blended wing body · Structural layout · Optimization · Composite materials · Equivalent stiffness 1 Introduction a software tool to rapidly generate finite element model for structural optimization and mass prediction of BWB air- Over the past decades, there has been great interest in craft. The tool was written as a Matlab script that reads in improving the performance of transport aircraft for the user-provided data to generate a set of MSC Nastran input reductions in fuel burn, noise and NO emissions [1]. Non- files for analysis and optimization. Li and Kim [7 ] studied a conventional aircraft concepts, such as the BWB (blended detailed BWB structural finite element model that featured wing body) aircraft, have been proposed for revolutionary the aircraft’s fuselage skins, frames, ribs, spars, floors, mov - improvement for future air transportation while the current able control surfaces, high-lift devices, and bulkheads. The generation civil transports cannot fulfill those requirements total number of elements in the model was approximately [2]. The BWB aircraft is a tailless design concept that inte- 44,000, representing more than 142,000 degrees of freedom, grates wing and fuselage. The main aerodynamic advantage and a two-stage global–local optimization approach was of the BWB design is its lower wetted area to volume ratio implemented. Hansen and Horst [8] proposed a two-level and lower interference drag compared to the conventional optimization strategy for typical parts of the BWB aircraft aircraft, which may lead to large fuel savings and offer supe- fuselage structure. In their study, single skin, double skin rior operating economics [3–5]. and sandwich structural design optimization under multiple Since BWB is an unconventional configuration concept, loads and constraint conditions were investigated. there is a lack of experience and empirical data in the struc- The above studies for BWB aircraft structure mainly tural design of BWB aircraft. The BWB structural design focused on the dimension (size) optimization, but structural study is needed to explore its structural mass benefits or layout design for BWB aircraft was not investigated. Since penalties. Several studies on structural design optimization the structural layout has a large impact on the mass and stiff - of BWB aircraft have been conducted. Gern [6] developed ness of aircraft structure and, moreover, there is still lack of knowledge available on the optimal structural layout for BWB aircraft, layout optimization for BWB aircraft struc- * Xiongqing Yu ture design is needed to be investigated. Singh and Toropov yxq@nuaa.edu.cn [9] applied topology optimization to layout design of BWB aircraft, and the reasonable structural layout of the BWB College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China Vol.:(0123456789) 1 3 880 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 Table 1 Primary parameters of the BWB aircraft passenger aircraft was obtained. However, in their study the design constraints such as buckling were not included and Parameters Values structural materials were limited to metals. From views of Number of passengers 450 in aircraft structural design practice, inclusion of buckling con- 3-class straints in structural layout optimization is necessary. The cabin optimal structural layout design obtained by the method layout without buckling constraints might be very different with Maximum payload mass 55,000 kg the design from the method with buckling constraints. Fur- Fuel mass 150,000 kg thermore, use of composite materials in structure is essential Maximum takeoff mass 410,000 kg for advanced BWB concept. Our literature survey indicates Design range 14,000 km that there is little study on BWB aircraft structural layout Cruise Mach number 0.85 optimization that includes buckling constraints and deals Wing span 78 m with composite materials. Aspect ratio 5.49 In this paper, we attempt to propose an efficient method Centerbody length 40.5 m for structural layout optimization, which is expected to be Centerbody width 18.8 m used practically in preliminary structural design of BWB air- craft. In our method, structural constraints of stress, strain, deformation, and buckling are included and composite mate- leading edge sweep angles for the centerbody and the outer rial is considered. The remainder of the paper is organized wing are 57° and 36°, respectively. The average value of as follows. A notional BWB aircraft design concept and thickness to chord ratio of the centerbody is around 17% and structural optimization problem will be described in Sect. 2. the thickness to chord ratio distribution is averagely 9% on A layout optimization method solving the BWB aircraft the outer wing. The inboard wing blends the thick center- structural design problem will be presented in Sect. 3. The body with the thin outer wing with a large variation in its optimization results from the layout optimization method thickness. will be presented and discussed in Sect. 4, and followed by conclusions in Sect. 5. 2.2 Initial Structural Layout The initial structural layout of the BWB aircraft is illustrated 2 Description of Optimization Problem in Fig. 2. The centerbody of BWB aircraft has in general a large 2.1 Notional BWB Aircraft width considering the constraints of comfort and evacuation. The BWB centerbody is the most unique airframe since the A notional BWB passenger aircraft with 450 seats is used as airframe has the unusual loading pattern (i.e. fuselage-bending an example for structural layout optimization study in this loads, wing-bending loads and the cabin overpressurization), study. The configuration of the BWB aircraft is illustrated in which leads to high bending loads in the upper and lower Fig. 1 and the primary parameters for the BWB aircraft are skins. To eliminate high bending loads, the fuselage-stiff- presented in Table 1. As shown in Fig. 1, the BWB aircraft ened panels that are made up of skins, stringers and frames can be broken down into three main sections: a pressurized are designed as a bi-directionally stiffened panel, where the centerbody (fuselage), inboard wing and outer wing. The Outer wing Outer wing Frames Main frames Side wall of the centerbody Centerbody Centerbody (Fuselag (Fuselage) e) Ribs parallel to the flight path Short spar Front spar Middle spar Inboard wing Inboard wing Ribs perpendicular to the rear spar Rear spar Intermediate spar Pressure bulkheads Aft-body substructure Internal walls Fig. 1 BWB aircraft configuration Fig. 2 BWB aircraft structural layout 1 3 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 881 wing-bending loads are carried by the frame members and the aluminum materials [17]. The material properties used in this fuselage-bending loads are carried by the stringers [10]. The study are shown in Tables 2 and 3. resulting panel design is beneficial for reduction of the mass penalty. Large internal walls are used to divide the cabin bays 2.4 Loads and decrease the span distance. By decreasing the span dis- tance, this additional support decreases the bending moments The loads considered in this study include the aerodynamic induced from resisting the internal pressure [11]. Cabin floor load and inertia loads from mass distributions. The load case is positioned based on desired cabin height, and the rear spar is the 2.5-g flight maneuver with a safety factor 1.5. The aer - in centerbody is specified as bulkheads. The main frames are odynamic load is computed by the in-house code [18] which attached to multi-spars [12] and the pressure loads are carried is developed based on the potential flow. The masses that are by a bending-resistant structure (i.e. normal frames). The aft- considered in structure analysis include masses of payloads body section is not pressurized and consists of upper and lower and fuels, mass of the BWB aircraft structure, and masses of skin, and aft-body substructure. landing gears and engines. The payloads are located in the The inboard wing structure blends the centerbody with centerbody and fuel tanks are located in the inboard wing outer wing, and consists of multiple spars, ribs, and upper and and outer wing sections [19], as depicted in Fig. 3. lower stiffened panels. Front and rear spars provide continu- ous load paths from the outer wing to the centerbody cabin. 2.5 Formulation of Structural Layout Optimization Intermediate spars are inserted if the interval between the two middle spars is larger than some specified allowance. Middle The structural layout of the BWB aircraft is defined by a set spars connect the front spar of the outer wing to the side wall of parameters such as rib spacing, stringer spacing, inter- of the centerbody. All ribs in the inboard wing are oriented in val of frames and spar location, which will be illustrated the stream-wise direction. in detail in Sect. 3.1. Usually, change of structural layout The structure layout of the outer wing is similar to that of parameters results in change of the stiffened panel sizes and conventional aircraft wing, which consists of a front spar, a mass. For example, the ribs provide support for the stiffened rear spar, upper and lower stiffened wing panels, and evenly panels and rib spacing affects the global buckling of the spaced ribs. And the ribs are perpendicular to the rear spar, panels. If the rib spacing (a parameter of the structural lay- thus the rib length is shorter and its mass can be reduced [13]. out) is changed, the sizes of stiffened panels will be changed Basically, BWB aircraft structure consists of a large num- to satisfy requirement of the buckling load factor. Conse- ber of stiffened panels composed of skin and stringers. The quently, those changes lead to change of mass of entire BWB stringers in centerbody and inboard wing are oriented in the aircraft structure. The aim of structural layout optimization span-wise direction, and stringers in outer wing are parallel to is to find a set of structural layout parameters which lead to the outboard rear spar. Table 3 Isotropic material properties 2.3 Structural Materials Material E (MPa) G (MPa) ν ρ (kg/m ) Al 7075-T6 71,700 26,900 0.33 2800 The BWB aircraft is designed with advanced composite mate- Foam core 144.8 54.8 – 100 rials for both primary and secondary structures. The composite sandwich frame whose stacking sequence of face sheet is a symmetry orientation [± 45°, 0°, 90°] is built with composite fabric wrapped around the long foam core [14, 15]. The bulb- stiffened panel [16] using composite material is applied to the load-carrying structure and the stringers or stiffeners in bulb- stiffened panel consist of webs with a unidirectional carbon Passenger cabin fiber rod at the top of the web. All of structural components, such as skins, spars, ribs and stringers or stiffeners, are made of composite laminates with eight layers and a symmetry orienta- Locationoffueltanks tion [± 45°, 0°, 90°] . Floor structures are made of isotropic Table 2 Material properties of composite laminates E (MPa) E (MPa) G (MPa) ν ρ (kg/m ) 11 22 12 12 154,000 8500 4200 0.35 1600 Fig. 3 The location of passenger cabin and fuel tanks 1 3 Outer loop Inner loop 882 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 the minimum mass of the stiffened panels in BWB aircraft Start structural design. The initial structural layout (Fig. 2) might not be optimal Structural layout definition for BWB aircraft in terms of structural mass reduction. Optimization method will be applied to find a better structural layout for the BWB Parametric geometry model aircraft. The structural design problem of the BWB aircraft for structural layout can be formulated as follows in term of optimization. Structure analysis using FEM Objective: Minimize mass of t he BWB aircraft structure Design variable: There are two kinds of the design vari- In-plane load extraction ables: (1) design variables for structural layout, and (2) design variables for the Optimization for each stiffened stiffened panel sizes. The structural panel layout design variables include rib and stringer spacing, intervals of the frames Update static failure No Satisfied with deflection and locations of the spars, and will be coefficient and panel constraint? sizes defined in more detail in Sect.  3.1. The Yes design variables of the stiffened panel sizes include the thickness of skins and Optimization in outer loop stringer web, and height of stringers. Detailed geometry for the stie ff ned panel No will be presented in Sect. 3.3 Convergence? Constraints: The s tructure must be satisfied with Yes allowable stress and strain of materials, Optimal structural layout limitation of the structural deformation, and allowable buckling factor Fig. 4 The layout optimization procedure with two loops The above optimization problem has a large number of design variables including design variables for structural layout and design variables for stiffened panel sizes, and has optimization problem with a large number of variables is now transformed into the optimization in the inner loop and varieties of constraints. An initial attempt using conventional optimization method failed to solve the above optimization the optimization in the outer loop. In the inner loop, the optimization problem for each stiffened panel is very simple problem due to unacceptable computational burden. To solve this problem in more practical and efficient way, we propose and can be solved with small computation expense. The opti- mization in the outer loop can be completed in reasonable a layout optimization method that will be presented in next section. computing expense because of small computation expense in the inner loop. The procedure starts with BWB aircraft structural layout definition by a given values of layout design variables, and 3 Layout Optimization Method output of the procedure is optimal structural layout design. Each step of the procedure in Fig.  4 will be detailed as Theoretically, topological optimization methods can be applied to layout design [20]. But those methods have dif- follows. ficulties dealing with the buckling constraints and composite materials in layout optimization of BWB aircraft structure. 3.1 Definition for Structural Layout In this study, we propose a more straightforward strat- egy for layout optimization of BWB aircraft structure. The The structural layout is defined by a set of parameters, in which a subset of the parameters is used as the design vari- procedure of proposed method is shown in Fig. 4, which consists of an inner loop and an outer loop. The function of ables for structural layout optimization. Generally, the most efficient structure can be achieved the inner loop is to compute structural mass through panel optimization for a given layout design, and the function of by adjusting layout design variables (rib spacing, stringer spacing, interval of frames, and spar location) in preliminary the outer loop is to find best values of layout design variables with minimum structural mass. In this manner, the layout design phase. As illustrated in Fig. 5, the design variables 1 3 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 883 of structural layout optimization are rib spacing (b1 and torsional stiffness of the entire BWB aircraft are assumed to b2), upper and lower stringer spacing in wing section (L1 mainly depend on the main load-carrying structures. Thus, and L2), intervals of frames (F1 and F2), and locations of the leading and trailing edge are not considered in the layout front and rear spar (S1, S2, S3 and S4: the percentages of optimization. the local chord). The stringers run through the entire wing span, and each stiffened panel has the same rib spacing. The 3.2 Parametric Geometry Model of Structural spar location and intervals of internal walls in centerbody Layout section are not considered as the design variables because those parameters are set by cabin layout sized by the num- Since the structural layout will be updated in the outer loop, ber of passengers or amount of cargo. The bending and the the geometric model of the BWB aircraft structural layout needs to be generated automatically when the values of structural layout design variables are changed. The auto- matic generation of the structural layout geometric model is implemented in MSC Patran using PCL (Patran command language). An example of the structural layout geometric model generated in this manner is illustrated in Fig. 5. When A-A the values of structural layout design variables are changed, .. .. . the geometric model will be changed accordingly. Upper panel L1 F1 L2 3.3 Generating Finite Element Model Frames . .... Lower panel The structure defined by the above geometric model will be Wing panel analyzed by finite element method in structure analysis soft- S1 ware MSC Nastran. When the generation of the structural layout geometric model is completed, a finite element (FE) Front spar model can be generated automatically using the PCL [21]. F2 In the FE model, spar webs, rib webs, frame webs, floors and stiffened skin panels are mainly modeled by quadrilat- S2 b1 eral elements with shell properties, and triangular elements b2 are used in transition areas (green area in Fig. 6). Axial rod S3 elements are used to represent spar flanges, the caps of frames Rear spar and ribs. The direct modeling of stringer or stiffeners in the S4 structural FE model leads to complicacy, and automatic gen- eration of the structural FE model might be not robust. Thus, Fig. 5 Definition for design variables of structural layout the stringers of the stiffened panels are not directly modeled Fig. 6 BWB finite element model for layout optimization 1 3 884 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 load of the stiffened panel will be extracted as applied but rather their stiffness properties will be represented by an equivalent shell element [22]. Figure 6 shows the structural loads for the panel optimization. The aerodynamic loads usually generates bending and FEM model for the BWB aircraft structure. Simplifying the stiffened panel with equivalent panel can twist moments on the main load-carrying structures, and causes upper stiffened panels to bear in-plane compres- significantly decrease the scale of FE model. Without the complex shapes of stringers, equivalent panel can efficiently sion and shearing loads, and lower stiffened panels to bear tension and shearing loads. Based on this load case, the simulate global buckling modes. Figure 7 shows the detailed stiffened panel model and its equivalent panel model. stiffened panels carry combined in-plane loads including axial loads and shear loads. The stiffness of equivalent panel can be described as the superposition of skin’s stiffness and stiffeners’ stiffness. Thus, Generally, the in-plane axial load F (y) and shear load xi F (y) extracted from the FE model are not the uniform the equivalent matrix of the entire panel can be obtained by si assembling the stiffness matrixes of skins and stiffeners, which load as shown in Fig. 8 and the nonuniform load need to be unified using the following equation: can be calculated by F (y)= F (y)+ F (y) ∕2  +   +  x x1 x2 sk str sk str K = , (2) (1) eq F (y)= F (y)+ F (y) ∕2  +   +  s s1 s2 sk str sk str where A , B and D are in-plane, coupling and bending where F and F are the uniform load of the axial load and x s sk sk sk shear load. stiffness coefficient matrices of skin and A , B and D are str str str in-plane, coupling and bending stiffness coefficient matrices Moreover, the equivalent panel from the FE model is usually trapezoidal plate and needs to be transformed into of a stringer [23, 24]. a rectangular plate [22] for the reason that the theoretical analysis of the composite mechanics is based on a rectan- 3.4 In‑Plane Load Extraction gular plate, as shown in Fig. 8. Once the FE model of BWB aircraft is generated, the 3.5 Optimization for Each Stiffened Panel structural analysis can be carried out. Then, the in-plane After the FE model is generated and in-plane load is extracted, the sizes of each stiffened panel will be deter - Detailed stiffenedpanel mined by panel optimization. The panel optimization is for- mulated as follows. w w y ' y ' 1 2 1 sk Fy () Fy () F F x1 x2 x x x ' x ' s s Fy () Fy () s1 s2 Equivalentpanel with Stiffened panel with actual loads unified loads Equivalent panel eq BWBStructure Fig. 8 Panel and loads extracted from BWB aircraft Fig. 7 Detailed stiffened panel and equivalent panel model 1 3 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 885 Objective: Minimize the mass of each stiffened For a combined load case, the interaction curves can be panel obtained by substituting the global buckling, local buck- The design variables: The thickness of the skin, and the ling, and static failure loads into the following equation: thickness and height of the stringer of each stiffened panel N xy + = 1. (7) The constraints: The g lobal buckling factor, N N xcrit xycrit e ≥ 1.0, the local buckling factor, glo e ≥ 1.0, and the static failure fac- Interaction curves [25] provide a means for determin- loc tor, e ≥ 1.0 under the compres- ing: (a) if a stiffened panel fails under combined loads static sion and shear N and N ; (b) the maximum allowable in one direction x xy (compression or shear) given the applied load in the other. A sequential quadratic programming (SQP) is used to Load combinations inside the interaction curve imply that solve the above optimization problem. The key point in the the stiffened panel does not buckle. Load combinations optimization for each stiffened panel is computation of the corresponding to points outside the interaction curve cor- global buckling factor, e , local buckling factor, e , and respond to a stiffened panel that has buckled already. glo loc the static failure factor, e . To improve the efficiency of As shown in Figs. 9 and 10, points M and X represent static the stiffened panel optimization, an analytical method is the global and local buckling loads and the static failure used for computation of those factors [24]. load, respectively. Points N and Y denote the correspond- Edge boundary condition of the stiffened panel is ing applied loads. Thus, the global and local buckling fac- assumed to be simply supported boundary condition and tor can be calculated by e = e = OM∕ON, and the static glo loc carrying combined in-plane uniform loads including axial failure factor is e = OX∕OY. When all of e , e and static glo loc compressive N and shearing N . Thus, the buckling loads e are greater than 1.0, the stiffened panels will with- x xy static (N under compression and N under shear) are given stand the applied loads without buckling and static failure. xcrit xycrit by the following equations, respectively: 3.6 Deflection Constraint Consideration and Static 2 4 (AR) 2 2 N = D m + 2(D + 2D )(AR) + D , Failure Coefficient Updating xcrit 11 12 66 22 2 2 a m (3) Since the panel optimization does not consider the deforma- 4 2 4 tion constraint, the wingtip deflection of the BWB aircraft 9 b a a N =± D + 2(D + 2D ) + D , (4) xycrit 11 12 66 22 needs to be evaluated using the finite element analysis of the 3 2 4 32a b b entire structure after a panel optimization is completed. The where m represent the number of half wave and AR is the deformation constraint is that the wingtip deflection must be aspect ratio (AR = a/b) of the plate. The parameters a and b less than 5% of the span of the BWB aircraft. If the wingtip represent the length and width of the plate. D is the bend- ij ing stiffness of the stiffened panel and the ± sign indicates that buckling can be caused by either positive or negative Nxy/Nxycrit shear loads. Stringers are usually cemented or co-cured with skin in 1.0 composite-stiffened panels, and the skin among two adjacent stringers might be under a boundary case of simply support. So, local buckling of skin also can use formulas described above. The static allowable axial load N and allowable x-static M shear load N of the stiffened panel are: xy-static N =  A , x - static x - allow eq (5) N =  A , xy - static xy - allow 66 (6) 0(O) 1.0 where ε and ε represent the allowable strain under Nx/Nxcrit x-allow xy-allow the axial and shear loads, respectively. A is the equivalent eq axial tensile stiffness of the stiffened panel and A is the Fig. 9 Interaction curve for global buckling and local buckling under shear stiffness coefficient of the stiffened panel. combined compression and shear 1 3 886 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 to find the global optimum. The genetic algorithm uses Nxy/Nxystatic both crossover and mutation operators which make its 1.0 population more diverse and thus has the ability to avoid being trapped in a local optima. In theory, the diversity also helps the algorithm to be faster in reaching the global optima since it will allow the algorithm to explore the solu- tion space faster. 4 Optimization Results and Discussion According to the method of the layout optimization of the 0(O) 1.0 Nx/Nxstatic BWB aircraft structure presented in the above, a comput- ing framework is implemented in software iSIGHT-FD, as Fig. 10 Interaction curve for static failure under combined compres- shown in Fig. 11. The entire optimization process can be sion and shear executed automatically. The structural optimization of the BWB aircraft in the deflection is not satisfied with the constraint, the static fail- inner loop (Fig. 4) requires about 20 min on an Intel Xeon ure factor will be updated. E5-2630, (2.6 GHz, 32 GB RAM) for a given structural lay- Usually structural stiffness reaches higher levels under out. In the outer loop, 250 structural layouts are generated by more strict strength constraint, thus the increment of the the multi-island genetic algorithm. Total computation time stiffness can be achieved by updating the static strength fail- for the structural layout optimization of the BWB aircraft is ure factor by the violated percentage [26], which would be around 3 days. employed as new constraint criteria in the next inner loop. The iteration history corresponds to the outer loop in For example, if the wing tip deflection limit of the BWB the layout optimization which is illustrated in Fig. 12. Each aircraft is 3 m, while the predicted deflection is 3.6 m, then solid circle in the diagram represents one individual out of the limit is violated by 20%. Therefore, the current static the populations (25 individuals/generation) while red solid strength failure factor is multiplied by 1.2 and uses this triangles represent the best individual of each generation’s failure coefficient as new constraint in the next iteration. population (total ten generations). The red curve in Fig. 12 The inner loop is iterated until the deformation constraint shows the reduction of the structural mass over the number is satisfied. of generations. The structural mass decreases rapidly within seven generations, and then decreases slightly and has only small changes. 3.7 Optimization in Outer Loop The layout parameters resulting from the layout optimi- zation are given in Table 4. Comparison between the initial The different structural layout design results in different structural layout and optimal one is demonstrated in Fig. 13. structural mass computed by the inner loop. The task of the After optimization, we can see that the frames in center optimization in outer loop is to find the optimal structural areas of centerbody are more densely arranged to carry more layout design with minimal mass. The optimization in outer loads and resist buckling while the front areas have sparse loop can be formulated as follows: frames. The front spar is shifted rearward and the rear spar is shifted forward in the outer wing, which shows that the Objective: Minimize the structure mass sectional height needs to be increased to make structure The design variables: The structural layout design varia- more efficient in bending. The stringers along the upper bles (b1, b2, L1, L2, F1, F2, S1, S2, surface are more closely spaced than those on the lower S3 and S4, see Sect. 3.1 for detail surface in the outer wing for the reason that the wing-bend- definitions) ing loads which cause compression at the upper surface are higher than those causing compression at the lower surface. A multi-island genetic algorithm is used to search the Besides, using the bulb-stiffened panel, the local bending optimal structural layout design. Compared to traditional stiffness of the skin increases, the local stability of the skin optimization methods, the genetic algorithm is more likely is enhanced, the structure efficiency is improved, and then 1 3 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 887 Fig. 11 Computing framework of layout optimization for BWB aircraft 54000 initial layout, which implies that structural layout has a large 53000 impact on the mass BWB aircraft structure. Baseline layout 52000 The distributions of the thickness of the skins and the 51000 areas of stringers after the two-loop optimization are pre- 50000 sented in Fig. 14. The thickness of skins and the areas of stringers increase rapidly along the span-wise direction and 48000 up to the peak around the kink (the interface of inboard wing and outer wing). Then, they both decrease from the root of 46000 the outer wing to the wingtip. The static and buckling analysis results after the two- Optimal layout 44000 loop optimization are illustrated in Fig. 15. It could be seen 050 100 150 200 250 in Fig. 15 that the kink area carries relative heavy loads, Layout optimization iteration and thus the maximum strain and buckling deformation occur in this area. And Fig. 15 also shows that the results, Fig. 12 Iteration history in layout optimization in which maximum strain is 4360 με, wingtip displacement is 3890 mm, and first-order buckling factor is 1.03, meet the stringer spacing can increase. Moreover, the number of all of constraints including stress, strain, deformation, and ribs at the inboard wing and outer wing is reduced to reach buckling. higher structure efficiency. The structural mass after the lay - out optimization is reduced by 9.28% compared to that of the Table 4 Results from layout Parameters Initial layout Optimal layout optimization Number of ribs at inboard wing 5 3 Number of ribs at outer wing 34 26 Frame interval of front area F1 (mm) 609.6 577.64 Frame interval of back area F2 (mm) 406.4 456.78 Location of front spar at root chord of outer wing S1 (%) 15 18.4 Location of rear spar at root chord of outer wing S2 (%) 70 65.1 Location of front spar at tip chord of outer wing S3 (%) 15 15.4 Location of rear spar at tip chord of outer wing S4 (%) 70 67.8 Upper stringer spacing in wing section L1 (mm) 160 176.39 Lower stringer spacing in wing section L2 (mm) 180 190.95 Structural mass of main load-carrying structure (kg) 49,357.5 44,774.9 1 3 Stuctural mass of load-carrying structure/kg 888 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 Fig. 13 Comparison between the initial and optimal structural layout Fig. 14 Distributions of the thickness of the skins and the areas of stringers According to the two-loop optimization strategy, the 5 Conclusions FE model of BWB aircraft is utilized only for computa- tion of the in-plane loads of the stiffened panels in each To solve the challenging optimization problem of BWB outer loop and evaluation of the deflection of the BWB aircraft structural layout design, a two-loop optimiza- aircraft structure in the inner loop. Therefore, the struc- tion strategy (inner loop and outer loop) is proposed. The tural layout optimization using the proposed strategy does inner loop is to optimize the sizes of each stiffened panel not consume large computational resources. The results of BWB aircraft structure, and outer loop is to find best from the notional BWB aircraft structural layout optimi- values of layout design variables. To improve computa- zation indicate that the structural layout parameters have a tional efficiency, an equivalent panel model for the BWB large impact on the mass BWB aircraft structure, and the aircraft structure and an analytical method for the stiffened structural mass of main load-carrying structure is reduced panels are used. By use of the equivalent panel model, by 9.28% compared to that of the initial structural layout. the FE model of the BWB aircraft structure is simplified In future study, more load cases will be considered in significantly without modeling the stiffener. By use of the the BWB aircraft structural layout optimization, and the analytical method, the buckling factor and the static fail- method proposed in the paper will be applied to the struc- ure factor of the stiffened panels can be computed directly tural mass prediction in BWB aircraft preliminary design. without FE analysis. 1 3 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 889 Fig. 15 The strain, displace- ment distribution and buckling mode shapes after the two-loop optimization 1 3 890 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 Acknowledgements This study was supported by the Priority Aca- 13. Niu MCY (2006) Airframe structural design: practical design demic Program Development of Jiangsu Higher Education Institu- information and data on aircraft structures, 2nd edn. Conmilit tions and the National Natural Science Foundation of China (Grant Press, California, pp 251–256 No. 11602103) is gratefully acknowledged. 14. Mukhopadhyay V (2014) Hybrid-wing-body vehicle composite fuselage analysis and case study. AIAA Paper 2014-2427 15. Mukhopadhyay V (2012) Hybrid-wing-body pressurized fuselage Open Access This article is distributed under the terms of the Crea- modeling, analysis, and design for weight reduction. AIAA Paper tive Commons Attribution 4.0 International License (http://creat iveco 2012-1999 mmons.or g/licenses/b y/4.0/), which permits unrestricted use, distribu- 16. Niu MCY (2005) Composite airframe structures: practical design tion, and reproduction in any medium, provided you give appropriate information and data. Conmilit Press, Hong Kong, pp 434–438 credit to the original author(s) and the source, provide a link to the 17. Bonet JT, Schellenger HG, Rawdon BK et al (2011) Environmen- Creative Commons license, and indicate if changes were made. tally Responsible Aviation (ERA) Project—N + 2 advanced vehi- cle concepts study and conceptual design of subscale test vehicle (STV). 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Zhao Q, Ding YL, Jin HB (2011) A layout optimization method of structural design evaluation. Comput Struct 86(1):104–118 composite wing structures based on carrying efficiency criterion. 9. Singh G, Toropov V (2016) Topology optimization of a blended Chin J Aeronaut 24(4):425–431 wing body aircraft structure. AIAA Paper 2016-3364 25. Kassapoglou C (2010) Design and analysis of composite struc- 10. Jegley DC, Velicki A (2015) Development of the PRSEUS multi- tures: with applications to aerospace structures. Wiley, Chichester, bay pressure box for a hybrid wing body vehicle. AIAA Paper pp 121–138 2015-1871 26. Collier Research Corporation (2008) HyperSizer pro user manual- 11. Laughlin T, Corman J, Mavris D (2013) A parametric and physics- automated iteration with finite element analysis. Collier Research based approach to structural weight estimation of the hybrid wing Corporation, Newport News, pp 4–7 body aircraft. AIAA Paper 2013-1082 12. Hansen LU, Heinze W, Horst P (2006) Representation of struc- Publisher’s Note Springer Nature remains neutral with regard to tural solutions in blended wing body preliminary design. In: 25th jurisdictional claims in published maps and institutional affiliations. international congress on aeronautical sciences ICAS 1 3 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Aeronautical & Space Sciences Springer Journals

Layout Optimization for Blended Wing Body Aircraft Structure

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Springer Journals
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Copyright © 2019 by The Author(s)
Subject
Engineering; Aerospace Technology and Astronautics; Fluid- and Aerodynamics
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2093-274X
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2093-2480
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10.1007/s42405-019-00172-7
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Abstract

Structural layout design of blended wing body (BWB) aircraft in the preliminary design phase is a challenging optimization problem due to large numbers of design variables and various constraints. A two-loop optimization strategy is proposed to solve the BWB aircraft structural layout design problem considering constraints of the displacement, stress, strain, and buckling. The two-loop optimization consists of an inner loop and an outer loop. The inner loop is to optimize each stiffened panel of the BWB aircraft structure, and outer loop is to find the best layout design. To improve computational efficiency, an equivalent finite element model is applied to BWB aircraft structure analysis, and an analytical method is used for buckling and static analysis of the stiffened panels. The proposed method can efficiently solve the structural layout optimization prob- lem of a notional BWB aircraft with acceptable computational burden. The result indicates the mass of main load-carrying structure of the BWB aircraft is reduced by 9.28% compared to that of the initial structural layout. Keywords Blended wing body · Structural layout · Optimization · Composite materials · Equivalent stiffness 1 Introduction a software tool to rapidly generate finite element model for structural optimization and mass prediction of BWB air- Over the past decades, there has been great interest in craft. The tool was written as a Matlab script that reads in improving the performance of transport aircraft for the user-provided data to generate a set of MSC Nastran input reductions in fuel burn, noise and NO emissions [1]. Non- files for analysis and optimization. Li and Kim [7 ] studied a conventional aircraft concepts, such as the BWB (blended detailed BWB structural finite element model that featured wing body) aircraft, have been proposed for revolutionary the aircraft’s fuselage skins, frames, ribs, spars, floors, mov - improvement for future air transportation while the current able control surfaces, high-lift devices, and bulkheads. The generation civil transports cannot fulfill those requirements total number of elements in the model was approximately [2]. The BWB aircraft is a tailless design concept that inte- 44,000, representing more than 142,000 degrees of freedom, grates wing and fuselage. The main aerodynamic advantage and a two-stage global–local optimization approach was of the BWB design is its lower wetted area to volume ratio implemented. Hansen and Horst [8] proposed a two-level and lower interference drag compared to the conventional optimization strategy for typical parts of the BWB aircraft aircraft, which may lead to large fuel savings and offer supe- fuselage structure. In their study, single skin, double skin rior operating economics [3–5]. and sandwich structural design optimization under multiple Since BWB is an unconventional configuration concept, loads and constraint conditions were investigated. there is a lack of experience and empirical data in the struc- The above studies for BWB aircraft structure mainly tural design of BWB aircraft. The BWB structural design focused on the dimension (size) optimization, but structural study is needed to explore its structural mass benefits or layout design for BWB aircraft was not investigated. Since penalties. Several studies on structural design optimization the structural layout has a large impact on the mass and stiff - of BWB aircraft have been conducted. Gern [6] developed ness of aircraft structure and, moreover, there is still lack of knowledge available on the optimal structural layout for BWB aircraft, layout optimization for BWB aircraft struc- * Xiongqing Yu ture design is needed to be investigated. Singh and Toropov yxq@nuaa.edu.cn [9] applied topology optimization to layout design of BWB aircraft, and the reasonable structural layout of the BWB College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China Vol.:(0123456789) 1 3 880 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 Table 1 Primary parameters of the BWB aircraft passenger aircraft was obtained. However, in their study the design constraints such as buckling were not included and Parameters Values structural materials were limited to metals. From views of Number of passengers 450 in aircraft structural design practice, inclusion of buckling con- 3-class straints in structural layout optimization is necessary. The cabin optimal structural layout design obtained by the method layout without buckling constraints might be very different with Maximum payload mass 55,000 kg the design from the method with buckling constraints. Fur- Fuel mass 150,000 kg thermore, use of composite materials in structure is essential Maximum takeoff mass 410,000 kg for advanced BWB concept. Our literature survey indicates Design range 14,000 km that there is little study on BWB aircraft structural layout Cruise Mach number 0.85 optimization that includes buckling constraints and deals Wing span 78 m with composite materials. Aspect ratio 5.49 In this paper, we attempt to propose an efficient method Centerbody length 40.5 m for structural layout optimization, which is expected to be Centerbody width 18.8 m used practically in preliminary structural design of BWB air- craft. In our method, structural constraints of stress, strain, deformation, and buckling are included and composite mate- leading edge sweep angles for the centerbody and the outer rial is considered. The remainder of the paper is organized wing are 57° and 36°, respectively. The average value of as follows. A notional BWB aircraft design concept and thickness to chord ratio of the centerbody is around 17% and structural optimization problem will be described in Sect. 2. the thickness to chord ratio distribution is averagely 9% on A layout optimization method solving the BWB aircraft the outer wing. The inboard wing blends the thick center- structural design problem will be presented in Sect. 3. The body with the thin outer wing with a large variation in its optimization results from the layout optimization method thickness. will be presented and discussed in Sect. 4, and followed by conclusions in Sect. 5. 2.2 Initial Structural Layout The initial structural layout of the BWB aircraft is illustrated 2 Description of Optimization Problem in Fig. 2. The centerbody of BWB aircraft has in general a large 2.1 Notional BWB Aircraft width considering the constraints of comfort and evacuation. The BWB centerbody is the most unique airframe since the A notional BWB passenger aircraft with 450 seats is used as airframe has the unusual loading pattern (i.e. fuselage-bending an example for structural layout optimization study in this loads, wing-bending loads and the cabin overpressurization), study. The configuration of the BWB aircraft is illustrated in which leads to high bending loads in the upper and lower Fig. 1 and the primary parameters for the BWB aircraft are skins. To eliminate high bending loads, the fuselage-stiff- presented in Table 1. As shown in Fig. 1, the BWB aircraft ened panels that are made up of skins, stringers and frames can be broken down into three main sections: a pressurized are designed as a bi-directionally stiffened panel, where the centerbody (fuselage), inboard wing and outer wing. The Outer wing Outer wing Frames Main frames Side wall of the centerbody Centerbody Centerbody (Fuselag (Fuselage) e) Ribs parallel to the flight path Short spar Front spar Middle spar Inboard wing Inboard wing Ribs perpendicular to the rear spar Rear spar Intermediate spar Pressure bulkheads Aft-body substructure Internal walls Fig. 1 BWB aircraft configuration Fig. 2 BWB aircraft structural layout 1 3 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 881 wing-bending loads are carried by the frame members and the aluminum materials [17]. The material properties used in this fuselage-bending loads are carried by the stringers [10]. The study are shown in Tables 2 and 3. resulting panel design is beneficial for reduction of the mass penalty. Large internal walls are used to divide the cabin bays 2.4 Loads and decrease the span distance. By decreasing the span dis- tance, this additional support decreases the bending moments The loads considered in this study include the aerodynamic induced from resisting the internal pressure [11]. Cabin floor load and inertia loads from mass distributions. The load case is positioned based on desired cabin height, and the rear spar is the 2.5-g flight maneuver with a safety factor 1.5. The aer - in centerbody is specified as bulkheads. The main frames are odynamic load is computed by the in-house code [18] which attached to multi-spars [12] and the pressure loads are carried is developed based on the potential flow. The masses that are by a bending-resistant structure (i.e. normal frames). The aft- considered in structure analysis include masses of payloads body section is not pressurized and consists of upper and lower and fuels, mass of the BWB aircraft structure, and masses of skin, and aft-body substructure. landing gears and engines. The payloads are located in the The inboard wing structure blends the centerbody with centerbody and fuel tanks are located in the inboard wing outer wing, and consists of multiple spars, ribs, and upper and and outer wing sections [19], as depicted in Fig. 3. lower stiffened panels. Front and rear spars provide continu- ous load paths from the outer wing to the centerbody cabin. 2.5 Formulation of Structural Layout Optimization Intermediate spars are inserted if the interval between the two middle spars is larger than some specified allowance. Middle The structural layout of the BWB aircraft is defined by a set spars connect the front spar of the outer wing to the side wall of parameters such as rib spacing, stringer spacing, inter- of the centerbody. All ribs in the inboard wing are oriented in val of frames and spar location, which will be illustrated the stream-wise direction. in detail in Sect. 3.1. Usually, change of structural layout The structure layout of the outer wing is similar to that of parameters results in change of the stiffened panel sizes and conventional aircraft wing, which consists of a front spar, a mass. For example, the ribs provide support for the stiffened rear spar, upper and lower stiffened wing panels, and evenly panels and rib spacing affects the global buckling of the spaced ribs. And the ribs are perpendicular to the rear spar, panels. If the rib spacing (a parameter of the structural lay- thus the rib length is shorter and its mass can be reduced [13]. out) is changed, the sizes of stiffened panels will be changed Basically, BWB aircraft structure consists of a large num- to satisfy requirement of the buckling load factor. Conse- ber of stiffened panels composed of skin and stringers. The quently, those changes lead to change of mass of entire BWB stringers in centerbody and inboard wing are oriented in the aircraft structure. The aim of structural layout optimization span-wise direction, and stringers in outer wing are parallel to is to find a set of structural layout parameters which lead to the outboard rear spar. Table 3 Isotropic material properties 2.3 Structural Materials Material E (MPa) G (MPa) ν ρ (kg/m ) Al 7075-T6 71,700 26,900 0.33 2800 The BWB aircraft is designed with advanced composite mate- Foam core 144.8 54.8 – 100 rials for both primary and secondary structures. The composite sandwich frame whose stacking sequence of face sheet is a symmetry orientation [± 45°, 0°, 90°] is built with composite fabric wrapped around the long foam core [14, 15]. The bulb- stiffened panel [16] using composite material is applied to the load-carrying structure and the stringers or stiffeners in bulb- stiffened panel consist of webs with a unidirectional carbon Passenger cabin fiber rod at the top of the web. All of structural components, such as skins, spars, ribs and stringers or stiffeners, are made of composite laminates with eight layers and a symmetry orienta- Locationoffueltanks tion [± 45°, 0°, 90°] . Floor structures are made of isotropic Table 2 Material properties of composite laminates E (MPa) E (MPa) G (MPa) ν ρ (kg/m ) 11 22 12 12 154,000 8500 4200 0.35 1600 Fig. 3 The location of passenger cabin and fuel tanks 1 3 Outer loop Inner loop 882 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 the minimum mass of the stiffened panels in BWB aircraft Start structural design. The initial structural layout (Fig. 2) might not be optimal Structural layout definition for BWB aircraft in terms of structural mass reduction. Optimization method will be applied to find a better structural layout for the BWB Parametric geometry model aircraft. The structural design problem of the BWB aircraft for structural layout can be formulated as follows in term of optimization. Structure analysis using FEM Objective: Minimize mass of t he BWB aircraft structure Design variable: There are two kinds of the design vari- In-plane load extraction ables: (1) design variables for structural layout, and (2) design variables for the Optimization for each stiffened stiffened panel sizes. The structural panel layout design variables include rib and stringer spacing, intervals of the frames Update static failure No Satisfied with deflection and locations of the spars, and will be coefficient and panel constraint? sizes defined in more detail in Sect.  3.1. The Yes design variables of the stiffened panel sizes include the thickness of skins and Optimization in outer loop stringer web, and height of stringers. Detailed geometry for the stie ff ned panel No will be presented in Sect. 3.3 Convergence? Constraints: The s tructure must be satisfied with Yes allowable stress and strain of materials, Optimal structural layout limitation of the structural deformation, and allowable buckling factor Fig. 4 The layout optimization procedure with two loops The above optimization problem has a large number of design variables including design variables for structural layout and design variables for stiffened panel sizes, and has optimization problem with a large number of variables is now transformed into the optimization in the inner loop and varieties of constraints. An initial attempt using conventional optimization method failed to solve the above optimization the optimization in the outer loop. In the inner loop, the optimization problem for each stiffened panel is very simple problem due to unacceptable computational burden. To solve this problem in more practical and efficient way, we propose and can be solved with small computation expense. The opti- mization in the outer loop can be completed in reasonable a layout optimization method that will be presented in next section. computing expense because of small computation expense in the inner loop. The procedure starts with BWB aircraft structural layout definition by a given values of layout design variables, and 3 Layout Optimization Method output of the procedure is optimal structural layout design. Each step of the procedure in Fig.  4 will be detailed as Theoretically, topological optimization methods can be applied to layout design [20]. But those methods have dif- follows. ficulties dealing with the buckling constraints and composite materials in layout optimization of BWB aircraft structure. 3.1 Definition for Structural Layout In this study, we propose a more straightforward strat- egy for layout optimization of BWB aircraft structure. The The structural layout is defined by a set of parameters, in which a subset of the parameters is used as the design vari- procedure of proposed method is shown in Fig. 4, which consists of an inner loop and an outer loop. The function of ables for structural layout optimization. Generally, the most efficient structure can be achieved the inner loop is to compute structural mass through panel optimization for a given layout design, and the function of by adjusting layout design variables (rib spacing, stringer spacing, interval of frames, and spar location) in preliminary the outer loop is to find best values of layout design variables with minimum structural mass. In this manner, the layout design phase. As illustrated in Fig. 5, the design variables 1 3 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 883 of structural layout optimization are rib spacing (b1 and torsional stiffness of the entire BWB aircraft are assumed to b2), upper and lower stringer spacing in wing section (L1 mainly depend on the main load-carrying structures. Thus, and L2), intervals of frames (F1 and F2), and locations of the leading and trailing edge are not considered in the layout front and rear spar (S1, S2, S3 and S4: the percentages of optimization. the local chord). The stringers run through the entire wing span, and each stiffened panel has the same rib spacing. The 3.2 Parametric Geometry Model of Structural spar location and intervals of internal walls in centerbody Layout section are not considered as the design variables because those parameters are set by cabin layout sized by the num- Since the structural layout will be updated in the outer loop, ber of passengers or amount of cargo. The bending and the the geometric model of the BWB aircraft structural layout needs to be generated automatically when the values of structural layout design variables are changed. The auto- matic generation of the structural layout geometric model is implemented in MSC Patran using PCL (Patran command language). An example of the structural layout geometric model generated in this manner is illustrated in Fig. 5. When A-A the values of structural layout design variables are changed, .. .. . the geometric model will be changed accordingly. Upper panel L1 F1 L2 3.3 Generating Finite Element Model Frames . .... Lower panel The structure defined by the above geometric model will be Wing panel analyzed by finite element method in structure analysis soft- S1 ware MSC Nastran. When the generation of the structural layout geometric model is completed, a finite element (FE) Front spar model can be generated automatically using the PCL [21]. F2 In the FE model, spar webs, rib webs, frame webs, floors and stiffened skin panels are mainly modeled by quadrilat- S2 b1 eral elements with shell properties, and triangular elements b2 are used in transition areas (green area in Fig. 6). Axial rod S3 elements are used to represent spar flanges, the caps of frames Rear spar and ribs. The direct modeling of stringer or stiffeners in the S4 structural FE model leads to complicacy, and automatic gen- eration of the structural FE model might be not robust. Thus, Fig. 5 Definition for design variables of structural layout the stringers of the stiffened panels are not directly modeled Fig. 6 BWB finite element model for layout optimization 1 3 884 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 load of the stiffened panel will be extracted as applied but rather their stiffness properties will be represented by an equivalent shell element [22]. Figure 6 shows the structural loads for the panel optimization. The aerodynamic loads usually generates bending and FEM model for the BWB aircraft structure. Simplifying the stiffened panel with equivalent panel can twist moments on the main load-carrying structures, and causes upper stiffened panels to bear in-plane compres- significantly decrease the scale of FE model. Without the complex shapes of stringers, equivalent panel can efficiently sion and shearing loads, and lower stiffened panels to bear tension and shearing loads. Based on this load case, the simulate global buckling modes. Figure 7 shows the detailed stiffened panel model and its equivalent panel model. stiffened panels carry combined in-plane loads including axial loads and shear loads. The stiffness of equivalent panel can be described as the superposition of skin’s stiffness and stiffeners’ stiffness. Thus, Generally, the in-plane axial load F (y) and shear load xi F (y) extracted from the FE model are not the uniform the equivalent matrix of the entire panel can be obtained by si assembling the stiffness matrixes of skins and stiffeners, which load as shown in Fig. 8 and the nonuniform load need to be unified using the following equation: can be calculated by F (y)= F (y)+ F (y) ∕2  +   +  x x1 x2 sk str sk str K = , (2) (1) eq F (y)= F (y)+ F (y) ∕2  +   +  s s1 s2 sk str sk str where A , B and D are in-plane, coupling and bending where F and F are the uniform load of the axial load and x s sk sk sk shear load. stiffness coefficient matrices of skin and A , B and D are str str str in-plane, coupling and bending stiffness coefficient matrices Moreover, the equivalent panel from the FE model is usually trapezoidal plate and needs to be transformed into of a stringer [23, 24]. a rectangular plate [22] for the reason that the theoretical analysis of the composite mechanics is based on a rectan- 3.4 In‑Plane Load Extraction gular plate, as shown in Fig. 8. Once the FE model of BWB aircraft is generated, the 3.5 Optimization for Each Stiffened Panel structural analysis can be carried out. Then, the in-plane After the FE model is generated and in-plane load is extracted, the sizes of each stiffened panel will be deter - Detailed stiffenedpanel mined by panel optimization. The panel optimization is for- mulated as follows. w w y ' y ' 1 2 1 sk Fy () Fy () F F x1 x2 x x x ' x ' s s Fy () Fy () s1 s2 Equivalentpanel with Stiffened panel with actual loads unified loads Equivalent panel eq BWBStructure Fig. 8 Panel and loads extracted from BWB aircraft Fig. 7 Detailed stiffened panel and equivalent panel model 1 3 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 885 Objective: Minimize the mass of each stiffened For a combined load case, the interaction curves can be panel obtained by substituting the global buckling, local buck- The design variables: The thickness of the skin, and the ling, and static failure loads into the following equation: thickness and height of the stringer of each stiffened panel N xy + = 1. (7) The constraints: The g lobal buckling factor, N N xcrit xycrit e ≥ 1.0, the local buckling factor, glo e ≥ 1.0, and the static failure fac- Interaction curves [25] provide a means for determin- loc tor, e ≥ 1.0 under the compres- ing: (a) if a stiffened panel fails under combined loads static sion and shear N and N ; (b) the maximum allowable in one direction x xy (compression or shear) given the applied load in the other. A sequential quadratic programming (SQP) is used to Load combinations inside the interaction curve imply that solve the above optimization problem. The key point in the the stiffened panel does not buckle. Load combinations optimization for each stiffened panel is computation of the corresponding to points outside the interaction curve cor- global buckling factor, e , local buckling factor, e , and respond to a stiffened panel that has buckled already. glo loc the static failure factor, e . To improve the efficiency of As shown in Figs. 9 and 10, points M and X represent static the stiffened panel optimization, an analytical method is the global and local buckling loads and the static failure used for computation of those factors [24]. load, respectively. Points N and Y denote the correspond- Edge boundary condition of the stiffened panel is ing applied loads. Thus, the global and local buckling fac- assumed to be simply supported boundary condition and tor can be calculated by e = e = OM∕ON, and the static glo loc carrying combined in-plane uniform loads including axial failure factor is e = OX∕OY. When all of e , e and static glo loc compressive N and shearing N . Thus, the buckling loads e are greater than 1.0, the stiffened panels will with- x xy static (N under compression and N under shear) are given stand the applied loads without buckling and static failure. xcrit xycrit by the following equations, respectively: 3.6 Deflection Constraint Consideration and Static 2 4 (AR) 2 2 N = D m + 2(D + 2D )(AR) + D , Failure Coefficient Updating xcrit 11 12 66 22 2 2 a m (3) Since the panel optimization does not consider the deforma- 4 2 4 tion constraint, the wingtip deflection of the BWB aircraft 9 b a a N =± D + 2(D + 2D ) + D , (4) xycrit 11 12 66 22 needs to be evaluated using the finite element analysis of the 3 2 4 32a b b entire structure after a panel optimization is completed. The where m represent the number of half wave and AR is the deformation constraint is that the wingtip deflection must be aspect ratio (AR = a/b) of the plate. The parameters a and b less than 5% of the span of the BWB aircraft. If the wingtip represent the length and width of the plate. D is the bend- ij ing stiffness of the stiffened panel and the ± sign indicates that buckling can be caused by either positive or negative Nxy/Nxycrit shear loads. Stringers are usually cemented or co-cured with skin in 1.0 composite-stiffened panels, and the skin among two adjacent stringers might be under a boundary case of simply support. So, local buckling of skin also can use formulas described above. The static allowable axial load N and allowable x-static M shear load N of the stiffened panel are: xy-static N =  A , x - static x - allow eq (5) N =  A , xy - static xy - allow 66 (6) 0(O) 1.0 where ε and ε represent the allowable strain under Nx/Nxcrit x-allow xy-allow the axial and shear loads, respectively. A is the equivalent eq axial tensile stiffness of the stiffened panel and A is the Fig. 9 Interaction curve for global buckling and local buckling under shear stiffness coefficient of the stiffened panel. combined compression and shear 1 3 886 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 to find the global optimum. The genetic algorithm uses Nxy/Nxystatic both crossover and mutation operators which make its 1.0 population more diverse and thus has the ability to avoid being trapped in a local optima. In theory, the diversity also helps the algorithm to be faster in reaching the global optima since it will allow the algorithm to explore the solu- tion space faster. 4 Optimization Results and Discussion According to the method of the layout optimization of the 0(O) 1.0 Nx/Nxstatic BWB aircraft structure presented in the above, a comput- ing framework is implemented in software iSIGHT-FD, as Fig. 10 Interaction curve for static failure under combined compres- shown in Fig. 11. The entire optimization process can be sion and shear executed automatically. The structural optimization of the BWB aircraft in the deflection is not satisfied with the constraint, the static fail- inner loop (Fig. 4) requires about 20 min on an Intel Xeon ure factor will be updated. E5-2630, (2.6 GHz, 32 GB RAM) for a given structural lay- Usually structural stiffness reaches higher levels under out. In the outer loop, 250 structural layouts are generated by more strict strength constraint, thus the increment of the the multi-island genetic algorithm. Total computation time stiffness can be achieved by updating the static strength fail- for the structural layout optimization of the BWB aircraft is ure factor by the violated percentage [26], which would be around 3 days. employed as new constraint criteria in the next inner loop. The iteration history corresponds to the outer loop in For example, if the wing tip deflection limit of the BWB the layout optimization which is illustrated in Fig. 12. Each aircraft is 3 m, while the predicted deflection is 3.6 m, then solid circle in the diagram represents one individual out of the limit is violated by 20%. Therefore, the current static the populations (25 individuals/generation) while red solid strength failure factor is multiplied by 1.2 and uses this triangles represent the best individual of each generation’s failure coefficient as new constraint in the next iteration. population (total ten generations). The red curve in Fig. 12 The inner loop is iterated until the deformation constraint shows the reduction of the structural mass over the number is satisfied. of generations. The structural mass decreases rapidly within seven generations, and then decreases slightly and has only small changes. 3.7 Optimization in Outer Loop The layout parameters resulting from the layout optimi- zation are given in Table 4. Comparison between the initial The different structural layout design results in different structural layout and optimal one is demonstrated in Fig. 13. structural mass computed by the inner loop. The task of the After optimization, we can see that the frames in center optimization in outer loop is to find the optimal structural areas of centerbody are more densely arranged to carry more layout design with minimal mass. The optimization in outer loads and resist buckling while the front areas have sparse loop can be formulated as follows: frames. The front spar is shifted rearward and the rear spar is shifted forward in the outer wing, which shows that the Objective: Minimize the structure mass sectional height needs to be increased to make structure The design variables: The structural layout design varia- more efficient in bending. The stringers along the upper bles (b1, b2, L1, L2, F1, F2, S1, S2, surface are more closely spaced than those on the lower S3 and S4, see Sect. 3.1 for detail surface in the outer wing for the reason that the wing-bend- definitions) ing loads which cause compression at the upper surface are higher than those causing compression at the lower surface. A multi-island genetic algorithm is used to search the Besides, using the bulb-stiffened panel, the local bending optimal structural layout design. Compared to traditional stiffness of the skin increases, the local stability of the skin optimization methods, the genetic algorithm is more likely is enhanced, the structure efficiency is improved, and then 1 3 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 887 Fig. 11 Computing framework of layout optimization for BWB aircraft 54000 initial layout, which implies that structural layout has a large 53000 impact on the mass BWB aircraft structure. Baseline layout 52000 The distributions of the thickness of the skins and the 51000 areas of stringers after the two-loop optimization are pre- 50000 sented in Fig. 14. The thickness of skins and the areas of stringers increase rapidly along the span-wise direction and 48000 up to the peak around the kink (the interface of inboard wing and outer wing). Then, they both decrease from the root of 46000 the outer wing to the wingtip. The static and buckling analysis results after the two- Optimal layout 44000 loop optimization are illustrated in Fig. 15. It could be seen 050 100 150 200 250 in Fig. 15 that the kink area carries relative heavy loads, Layout optimization iteration and thus the maximum strain and buckling deformation occur in this area. And Fig. 15 also shows that the results, Fig. 12 Iteration history in layout optimization in which maximum strain is 4360 με, wingtip displacement is 3890 mm, and first-order buckling factor is 1.03, meet the stringer spacing can increase. Moreover, the number of all of constraints including stress, strain, deformation, and ribs at the inboard wing and outer wing is reduced to reach buckling. higher structure efficiency. The structural mass after the lay - out optimization is reduced by 9.28% compared to that of the Table 4 Results from layout Parameters Initial layout Optimal layout optimization Number of ribs at inboard wing 5 3 Number of ribs at outer wing 34 26 Frame interval of front area F1 (mm) 609.6 577.64 Frame interval of back area F2 (mm) 406.4 456.78 Location of front spar at root chord of outer wing S1 (%) 15 18.4 Location of rear spar at root chord of outer wing S2 (%) 70 65.1 Location of front spar at tip chord of outer wing S3 (%) 15 15.4 Location of rear spar at tip chord of outer wing S4 (%) 70 67.8 Upper stringer spacing in wing section L1 (mm) 160 176.39 Lower stringer spacing in wing section L2 (mm) 180 190.95 Structural mass of main load-carrying structure (kg) 49,357.5 44,774.9 1 3 Stuctural mass of load-carrying structure/kg 888 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 Fig. 13 Comparison between the initial and optimal structural layout Fig. 14 Distributions of the thickness of the skins and the areas of stringers According to the two-loop optimization strategy, the 5 Conclusions FE model of BWB aircraft is utilized only for computa- tion of the in-plane loads of the stiffened panels in each To solve the challenging optimization problem of BWB outer loop and evaluation of the deflection of the BWB aircraft structural layout design, a two-loop optimiza- aircraft structure in the inner loop. Therefore, the struc- tion strategy (inner loop and outer loop) is proposed. The tural layout optimization using the proposed strategy does inner loop is to optimize the sizes of each stiffened panel not consume large computational resources. The results of BWB aircraft structure, and outer loop is to find best from the notional BWB aircraft structural layout optimi- values of layout design variables. To improve computa- zation indicate that the structural layout parameters have a tional efficiency, an equivalent panel model for the BWB large impact on the mass BWB aircraft structure, and the aircraft structure and an analytical method for the stiffened structural mass of main load-carrying structure is reduced panels are used. By use of the equivalent panel model, by 9.28% compared to that of the initial structural layout. the FE model of the BWB aircraft structure is simplified In future study, more load cases will be considered in significantly without modeling the stiffener. By use of the the BWB aircraft structural layout optimization, and the analytical method, the buckling factor and the static fail- method proposed in the paper will be applied to the struc- ure factor of the stiffened panels can be computed directly tural mass prediction in BWB aircraft preliminary design. without FE analysis. 1 3 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 889 Fig. 15 The strain, displace- ment distribution and buckling mode shapes after the two-loop optimization 1 3 890 International Journal of Aeronautical and Space Sciences (2019) 20:879–890 Acknowledgements This study was supported by the Priority Aca- 13. Niu MCY (2006) Airframe structural design: practical design demic Program Development of Jiangsu Higher Education Institu- information and data on aircraft structures, 2nd edn. Conmilit tions and the National Natural Science Foundation of China (Grant Press, California, pp 251–256 No. 11602103) is gratefully acknowledged. 14. Mukhopadhyay V (2014) Hybrid-wing-body vehicle composite fuselage analysis and case study. AIAA Paper 2014-2427 15. Mukhopadhyay V (2012) Hybrid-wing-body pressurized fuselage Open Access This article is distributed under the terms of the Crea- modeling, analysis, and design for weight reduction. AIAA Paper tive Commons Attribution 4.0 International License (http://creat iveco 2012-1999 mmons.or g/licenses/b y/4.0/), which permits unrestricted use, distribu- 16. Niu MCY (2005) Composite airframe structures: practical design tion, and reproduction in any medium, provided you give appropriate information and data. Conmilit Press, Hong Kong, pp 434–438 credit to the original author(s) and the source, provide a link to the 17. Bonet JT, Schellenger HG, Rawdon BK et al (2011) Environmen- Creative Commons license, and indicate if changes were made. tally Responsible Aviation (ERA) Project—N + 2 advanced vehi- cle concepts study and conceptual design of subscale test vehicle (STV). 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Hansen LU, Heinze W, Horst P (2006) Representation of struc- Publisher’s Note Springer Nature remains neutral with regard to tural solutions in blended wing body preliminary design. In: 25th jurisdictional claims in published maps and institutional affiliations. international congress on aeronautical sciences ICAS 1 3

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Published: May 16, 2019

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