Conceptual Design of a Bendable UAV Wing Considering Aerodynamic and Structural Performance

Transcription

1 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<br>17th 4-7 May 2009, Palm Springs, California AIAA Conceptual Design of a Bendable UAV Wing Considering Aerodynamic and Structural Performance Vijay Jagdale 1, Abhishek Patil 2, Bret Stanford 3, and Peter Ifju 4, University of Florida, Gainesville, FL, A bendable UAV wing, developed at University of Florida, shows the ability to load stiffen in positive flight load direction, still remaining compliant in the opposite direction. Such a wing enables UAV storage inside smaller packing volumes. The present paper discusses utilization of a multidisciplinary design approach for conceptual design of a bendable wing having 24 inch span and 7 inch root chord. The wing shape definition parameters and the layup scheme used to manufacture wing, are treated as design variables. Aerodynamic performance of the wing is studied using an extended vortex lattice method based Athena Vortex Lattice (AVL) software. An arc length method based nonlinear FEA routine in ABAQUS is used to evaluate the structural performance of the wing and to determine maximum flying velocity that the wing can withstand without buckling or failing under flight loads. An analytical approach is used to study the stresses developed in the composite wing during storage and Tsai-Wu criterion is used to check failure of the wing due to the rolling stresses to determine minimum storage diameter. Multidisciplinary shape and layup optimization is performed using an elitist non-dominated sorting genetic algorithm: NSGA-II. The design points on the Pareto optimal front thus achieved are compared with a baseline design to observe some designs with improved performance. Important design variables are identified for further investigation. Nomenclature α = angle of attack α twist = wing twist angle, measure positive up Λ = wing sweep angle, measure positive backwards θ 1, θ 2, θ 3 = layup angles of composite layers ρ = air density at normal pressure and temperature λ = wing taper ratio AVL = Athena Vortex Lattice C D0 = zero lift drag coefficient ΔC p = differential pressure coefficient C L = coefficient of lift C D = coefficient of drag D_min = minimum storage diameter f, g = generic functions F e = force on the finite element K n = static stability margin LE = Leading Edge LF λ = Load proportionality factor L/D = lift-to-drag ratio MAV = Micro Air Vehicle 1 Research Assistant, Department of Mechanical and Aerospace Engineering: vjagdale@ufl.edu 2 Research Assistant, Department of Mechanical and Aerospace Engineering: ajpatil@ufl.edu 3 Research Assistant, Department of Mechanical and Aerospace Engineering: bstan@ufl.edu 4 Professor, Department of Mechanical and Aerospace Engineering: ifju@ufl.edu 1 Copyright 2009 by Vijay Jagdale. Published by the, Inc., with permission.

2 S S e TE UAV W X ac X cg x 1 x 2 z 1 z 2 = wing planform area = area of the finite element = Trailing Edge = Unmanned Air Vehicle = weight of the air vehicle = aerodynamic center of the wing = center of gravity of air vehicle = chord normalized maximum camber location = chord normalized maximum reflex location = chord normalized maximum camber = chord normalized maximum reflex I. Introduction A unique bendable UAV wing, developed at University of Florida, shows the ability to load stiffen in positive flight load direction, still remaining compliant in the opposite direction. Such wings are constructed from bidirectional plain weave graphite/epoxy composite shells, and can be rolled around the fuselage of the vehicle, as seen in Figure 1. This enables storage of UAVs at reduced packing volumes. This bendable wing concept has been demonstrated on vehicles that range in size from 6 to 36 inch wingspans and are capable of being packed within volumes of cubic inch 1,2. Such a configuration is desirable for a number of potential applications. These vehicles can be stored in a canister within the platform of a manned vehicle or a larger UAV. Vehicles have also been constructed with a bendable wing in order to fit into the cargo pocket of a soldier s battle dress uniform, providing reduced storage space and easy access to over-the-hill surveillance capabilities. The conceptual design of such a bendable UAV wing must incorporate several disparate factors, necessitating a multi-disciplinary, multi-objective optimization procedure 3. As discussed in the previous work of the authors 4, from a structural standpoint, the composite wing must be able to withstand being bent into the desired storage radius 5, example as seen in Figure 1, without failing (fiber delamination, matrix cracking, etc. 6 ). Conversely, the wing must be strong enough to handle a positive aerodynamic flight load without buckling. Higher wing loading is expected during some of the UAV flight regimes, for example, during pullover maneuvers and the wing should not buckle under such aggressive loads, causing the vehicle to become uncontrollable; possibly leading to a crash. While these may seem two conflicting design requirements, the camber built into the wing provides a dissimilar stiffness in these two directions. When a positive (flight) load is applied to the wing, the leading edge of the wing root actually deflects downward, increasing the wing s moment of inertia at the root and the centerline camber. This results in a stable wing structure which may become stiffer as the positive load is increased. Such an airfoil geometry is not thought to significantly remove the wing s ability to roll into a canister, though does induce chord-wise strains in the wing as the camber flattens out 7. Addition of quarter chord aft sweep is also found to help in increasing wings load carrying capacity, as demonstrated in previous work by Jagdale et al. 8 Figure 1. Bendable UAV wing concept: flight-ready wing (left) and folded for storage (right). From aerodynamic considerations, the wing must be able to produce enough lift to balance the weight of the UAV, and the tailless vehicle (flying wing) configuration must be able to achieve longitudinal static stability in forward flight. Wing sweep may reduce aerodynamic efficiency of the wing 9, and may increase the final packing volume of the aircraft. The various balancing acts that will govern the conceptual design of a bendable UAV wing then become evident: compliant wings are preferred in order to fold the wing into a canister (whose diameter is geometrically limited by the wing span and fuselage size), but stiff wings are needed to withstand aggressive flight loads. The wing sweep helps in the latter performance metric, though it will increase drag and decrease the aerodynamic efficiency through glide performance, fuel consumption, etc. 2

3 The literature pertaining to multidisciplinary design and optimization of micro and small unmanned air vehicles is fairly diverse and is discussed in the previous work by the authors 4. In the present work, the airfoil shape, wing taper ratio, wing twist, and wing sweep will be considered as design variables, as well as the lay-up scheme of the composite bendable wing. An aerodynamic analysis will compute the pressure distribution over the wing, as well as the concomitant lift, lift-to-drag ratio, and the static stability margin. A nonlinear finite element module will calculate the forward flight velocity at which snap through buckling will occur, while an analytical stress/strain analysis is used to monitor the failure of the laminate as the wing is bent into the desired storage diameter. A multi-objective analysis will be used to optimize the lift-to-drag ratio and the flight velocity at which wing buckles due to aggressive flight loads, with various constraints upon static stability margin, cruise speed, and laminate failure due to folding. Design points on the Pareto optimal front are compared with a baseline design to highlight improvements expected in the wing performance. II. Wing Modeling While both aerodynamic and structural metrics are included in the wing design, the analyses are not explicitly coupled in an aeroelastic sense 17,20 : stable deflections of the wing due to air loads are thought to be small, excess of which will lead to buckling failure. A. Aerodynamic Analysis For aerodynamic analysis, Athena Vortex Lattice (AVL) software developed by Harold Youngren and Mark Drela 21 is used. AVL employs an inviscid, extended vortex lattice model for the lifting surfaces and is useful for the aerodynamic and flight-dynamic analysis of rigid aircraft of arbitrary configuration. In vortex lattice methods, as that of AVL, the continuous distribution of bound vorticity is approximated by discretizing the wing into a paneled grid, and placing a horseshoe vortex upon each panel. Each horseshoe vortex is comprised of a bound vortex (which coincides with the quarter-chord line of each panel), and two trailing vortices extending downstream. Each vortex filament creates a velocity whose magnitude is assumed to be governed by the Biot-Savart law. Furthermore, a control point is placed at the three-quarter-chord point of each panel. The tangency condition is applied (i.e., the wing becomes a streamline of the flow) by stipulating that the induced flow (from the horseshoe vortices) along the outward normal at each control point exactly cancels with that caused by the free-stream velocity. Further details are given by Bertin and Smith 22, among many others. In present study AVL is used to compute the aerodynamic pressure distribution over the wing. AVL is run within the MATLAB environment using a code developed in-house to automate the AVL input file generation for various optimization trials. Drag computations present a problem for such inviscid modeling techniques, which can only provide induced drag due to lift (the downwash of the finite span deflects the local velocity vector at each wing section downward, tilting the lift vector slightly backward to provide a small drag force): drag due to flow separation and viscous shear is unaccounted for. The latter terms are included by augmenting the drag with a non-zero C Do, estimated from experimental data 18 to be The viscous drag terms are not truly constant (flow separation generally increases with angle of attack, for example), and so the vortex lattice method is expected to under-predict the overall drag. While these issues will become more problematic as the Reynolds number decreases (as is the case for small UAVs), successful MAV analysis studies with vortex lattice methods are evidenced in the work of Stanford and Ifju 20 and Abdulrahim and Lind 23. Based on the geometry variables (discussed in detail below) a structured wing grid is built, an example of which can be seen in Figure 2. The coordinates of the wing mesh, as well as the angle of attack variable are fed into AVL program. This program then returns the differential pressure coefficient of each panel ΔC p, the coefficient of lift C L, the coefficient of drag C D, and the aerodynamic center of the wing X ac. Figure 2. AVL grid on semi wing (left), FEA model with boundary conditions and sample loading (right). The cruising speed of the vehicle can then be computed: 3

4 0.5 VC 2.W/{ S.C L}..(1) Where, W is the weight of the vehicle, ρ is the air density, and S is the planform area. Furthermore, the static stability margin of the wing can be computed by 14 : Kn Xac X cg /Xcg..(2) Where, X cg is estimated from the wing geometry and mass properties, as well as a pre-determined payload distribution throughout the airframe. B. Structural Analysis As discussed above, the structural portions of the wing design must incorporate two disparate analyses: the first is finding out maximum aerodynamic load and thus maximum flight velocity that wing can sustain without in-flight buckling and the second is to find the safe rolling diameter at which the wing can be bent and stored inside canister without composite material failure due to the stresses induced during the rolling process (Figure 1). For the former, a nonlinear snap through buckling analysis is conducted within the ABAQUS family of finite element software. For the current work, snap through buckling of the wing is the state, where the root airfoil of the wing flattens out and the wing loses its load carrying capacity. The modified Riks analysis procedure, a nonlinear arc length method, is implemented in ABAQUS 24. The analysis assumes aerodynamic loading to be proportional; all load magnitudes vary with a single scalar parameter. In addition, it is also assumed that the load wing deformation response is reasonably smooth and no sudden bifurcations occur. These assumptions are found to be valid on simulating and testing some trial wings in ABAQUS. Half of the wing is analyzed in ABAQUS using Y-symmetry boundary conditions and appropriate support conditions as are used on actual air vehicle (Figure 2). Geometrical nonlinearity is considered and the loads are made to follow nodes during analysis. The ΔC p distribution computed from AVL is used to compute normal flight aerodynamic loading on elements, given by : 2 Fe Se Cp,e 0.5 (V cruise).. (3) where S e is the area of the finite element. The value of V cruise is used from Eq. 1. This loading is then interpolated onto the finite element mesh, giving nodal forces. The analysis procedure then travels along the load-wing deformation arc, in effect, increasing the wing loading from the normal flight load to a reference load (20 times normal flight load), in return, finding out the load proportionality factor, LF λ at which wing buckles. The buckling flight velocity then can be shown to be related to load proportionality factor and V cruise by : V 0.5 buckle LF.20.V cruise.. (4) The snap through buckling velocity is found by plotting V buckle versus camber at the root airfoil to find a point where the V buckle starts reducing in magnitude (wing 1 in Figure 3) or a point when graph reaches a minimum camber point (wing 2 in Figure 3); whichever occurs first. If the wing continues to load stiffen (wing 3 in Figure 3), the flight velocity corresponding to 20 times the normal flight load will be returned to calculate the buckling velocity. The stresses induced in the wing are also monitored throughout the buckling analysis process, with the highest stresses expected to occur at the root. Wing material failure along the root due to excessive loading is predicted using the Tsai-Wu composite failure criterion 25 with a factor of safety of 1.5. Flight velocity at which the first ply failure is encountered is returned as material failure velocity. Buckling velocity for the wing is then, the minimum of the snap through buckling velocity or the material failure velocity. Optimization will try to maximize thus found buckling velocity. Figure 3. Completely buckled shape of the baseline wing (left), buckling analysis possible plots (right). 4

5 In order to simulate the wing rolling/storage, a simpler analytical method is thought to suffice. As a downward force is placed at the wing tips to begin the rolling process, the root of the wing will experience snap-through buckling, in the opposite direction of that shown in Figure 3 (left) and the airfoil will flatten out. This happens very quickly, long before the wings are actually folded into the final shape. As such, the chord-wise strains induced by this airfoil-flattening are assumed to be constant during the further rolling process. The curvatures along the root airfoil are known (discussed below), and so the strains, and stresses can be computed at each point along the root airfoil. These stresses act in conjunction with a span-wise curvature, computed from the rolling diameter. The stresses in each ply, at every location along the root airfoil are continually monitored and assessed with the Tsai-Wu composite failure criteria 25, with a factor of safety of 1.5. If the rolling diameter that initiates the first ply failure is larger than the desired diameter of the packed volume (4.5 inches), the design is unacceptable. For the T300/934 bidirectional prepreg carbon composite used for wing manufacturing, following material properties are considered during the ABAQUS and the analytical analysis procedures: Elastic properties, E 1 = E 2 = 34.8 GPa, μ 12 = 0.05, G 12 = 2.34 GPa and failure strengths 26, F 1t = 648 MPa, F 1c = 675 MPa, F 2t = 627 MPa, F 2c = 641 MPa, F 6 = 82 MPa. III. Optimization Framework Ten design variables are utilized for this design study. The airfoil at the root of the wing is completely defined by four variables (the camber towards the leading edge z 1, the chord-wise position of this control point x 1, and similar information for the camber towards the trailing edge, z 2 and x 2 ). A combination of 3 curves is used to define the airfoil shape. A quadratic curve from the leading edge to the maximum camber point (curve 1 in Figure 4), a 5 th order polynomial in the middle (curve 2) and another quadratic curve from reflex point to the trailing edge (curve 3), can completely and uniquely define root airfoil shape. Curvature continuity is ensured between these 3 curves. Such a definition avoids any secondary reflection points as that was observed in previous study 4 on some of the wing designs. Such a formulation allows for a reflex in the airfoil towards the trailing edge. The negative aerodynamic forces in this region can help offset the nose-down forces of the remainder of the wing, and provide a certain measure of static stability for this tailless flying wing. Figure 4. Wing root airfoil control variables. Wing chord and span are fixed for the current work, and thus three variables control the remainder of the wing shape: taper ratio λ, wing twist α twist, and the wing sweep Λ. All the metrics are cubically interpolated between the root and the tip to get kink free wing shape, as graphically seen in Figure 5. The remaining variables constitute the layup schedule of the graphite/epoxy wing. Between one and three layers of bi-directional plain weave laminates are permissible, with fiber orientations θ 1 to θ 3. In the case of a single layer laminate, for example, θ 2 to θ 3 can be set to null values. Such an action is easily accommodated by the genetic algorithm, described below. Each layer extends uniformly throughout the semi-wing. Due to manufacturing constraints and to ensure symmetric deformation of the two wing halves under aerodynamic loading, only ±45 or 0/90 layup orientations are allowed. The numerical analysis given here will study only one semi-wing as discussed above, with the appropriate symmetric boundary conditions at the root. The design variables can then be summarized as X = (z 1, x 1, z 2, x 2, λ, α twist, Λ, θ 1, θ 2, θ 3 ), and the design optimization problem is formally given as: maximize f(x) = L/D and maximize g(x) = V buckle such that: cruising speed V cruise 20 m/s C L > 0 K n 10% rolled diameter at first ply failure < desired diameter of packing volume L X U 5

6 Figure 5. Wing shape control variables. Since we are simultaneously trying to optimize two objectives: maximize the lift-to-drag ratio and maximize the buckling velocity, it is not expected that a single design will simultaneously perform best in both aerodynamic and structural metrics, and so a trade-off curve (Pareto optimal front) between the two metrics is required. The first constraint reflects the fact that cruising speeds larger than 20 m/s are unreasonable for such a vehicle, while the second constraint is added because the airfoil formulation seen in Figure 4, can easily provide a wing with negative lift at the candidate angles of attack of 6. The third constraint ensures the static stability of the wing, while the fourth allows the wing to roll into the desired packing diameter without laminate failure. The side constraints are given in Table 1. Table 1. Side constraints for design parameters. z 1 x 1 z 2 x 2 λ α twist Λ θ 1 θ 2 θ 3 Lower 1 % 15% -10% 65% Bound Upper 10% 35% 0 % 85% Bound The above optimization problem will be solved with an elitist non-dominated sorting genetic algorithm: NSGA- II 4, 27. As such, the design variable X given above is now considered a chromosome. Each of the continuous design variables given above is discretized into a finite number of intervals (typically 10) between the lower and upper bounds, except layup angles. Genetic algorithms are particularly well-suited to laminate design 28 : each laminate orientation of interest (either 45 or 90, to avoid ply orientations not amenable to manufacturing) is converted into an integer of either 1 or 2. Due to the bi-directional nature of the laminate, orientations of 0 are the same as 90, and need not be included. Integers of 0 are also permissible, which would indicate that the laminate does not exist. A laminate variable string of 102 would imply 2 layer layup of 45 and 90 orientation, for example. NSGA-II ranks designs, not based explicitly upon aerodynamic or structural performance (f(x) and g(x) stated above) but by non-domination. If for example, design A has a L/D of 5.5 and a maximum V buckle of 40 m/s, design B has a L/D of 6.5 and a buckling velocity of 60 m/s, and design C has a L/D of 5.8 and a buckling velocity of 70 m/s, then A is dominated by both B and C (and thus undesirable), but B and C are non-dominated with respect to one another (and thus Pareto optimal). The proposed design problem is not expected to have a globally dominating design, as discussed above. For a given set of designs, the Pareto front is rank 1, the next layer is rank 2, etc. Low-rank designs are given the greatest probability of being selected to reproduce, and crossover and mutation functions can then be used to create the child population. The child and parent populations are combined, and elitism (selection of the lowestranking designs) and niching (a parameter based upon crowding distance, where designs which provide the greatest spread along the Pareto front are favored) techniques create the next generation. Constraints can be handled with constraint-domination ideas. If two designs are both feasible, the standard non-domination techniques given above apply. If one design is feasible and the other is not, the former is obviously favored. If both designs are infeasible, the design with a smaller overall constraint violation is favored 27. 6

7 IV. Results and discussion To gain confidence in the buckling velocity prediction methodology used in the present paper, two wings analyzed in the previous study 8 are tested inside wind tunnel to observe their buckling behavior. Both swept (15º aft sweep) and straight wings (zero sweep) have 24 inch wing span and 7 inch root chord. Both the wings have same chord-wise shape (baseline airfoil detailed in Table 3) at different span stations, only difference is sweep angle. Both the wings are fixed at relatively high angle of attack (16º) to ensure buckling occurs at relatively low air speeds, from wind tunnel working limit point of view and air speed is increased from zero to a velocity at which the wings buckled. The maximum camber of the root airfoil is monitored during the wind tunnel test with a digital image correlation technique 29. The predictions about the buckling velocity are also made using the ABAQUS procedure outlined earlier in this paper to find good agreement of results. As can be seen in Figure 6, straight wing results lay on top of each other, whereas for swept wing, the velocity at which wing buckles, is predicted very well. Figure 6. Buckling test Comparison of wind tunnel test data and the results from buckling velocity predictor used in the present paper Figure 7 shows the Pareto optimal front obtained from the optimization work. A population of 30 design points at each generation is considered and such 70 generations are required to get all non-dominated designs. Figure 7. Pareto optimal front. 7

8 Table 2 details objective functions and constraint values for design points A, B, C, D and E (collectively called pareto designs, henceforth), as well as a baseline wing design (a wing currently used on some of the UAVs at University of Florida) as noted in Figure 7. The buckling velocity indicates, the pareto designs are continually load stiffening wings (wing 3, in Figure 3), whereas the baseline wing was found to load stiffen initially, which further buckles on encountering aggressive loads (wing 1, in Figure 3). As can be seen in Table 2, design E has higher buckling velocity but lower L/D ratio, whereas design A has lower buckling velocity but also has higher L/D ratio. Other designs considered for discussion, points B, C and D, are non-dominated with respect to each other as well and thus fall on the Pareto optimal front. The designs A, B, C have better performance than the baseline design, for both the objectives, whereas baseline design has better L/D ratio than the designs D and E. All the designs on the Pareto optimal front that have L/D ratio greater than 6.39 are expected to dominate the baseline design. Table 2. Objective function and constraint values for designs. Design point L/D ratio V buckle V cruise C L K n D_min f(x) g(x) (m/s) (m/s) (inch) E D C B A Baseline wing Table 3 gives corresponding design variable values and Figure 8 shows respective root airfoils, curvatures along root airfoils and the semi-wing planform geometries. All the designs have aggressive curvatures than the baseline design which results in baseline design requiring lowest storage diameter (D_min in Table 2), whereas design B has the most aggressive curvatures among all the designs considered here, also requiring highest minimum storage diameter. Static stability margin is seen to be greatly influenced by the sweep back angle, as expected. Pareto designs, which use higher sweep back angles, have higher K n than the baseline design. Since V cruise is related to C L, wing designs A, B, C which have higher C L than baseline design require lower V cruise to carry same payload. The baseline design has lower maximum camber as well as lower sweep back. This has resulted in baseline design buckling at lower speeds than the pareto designs. Table 3. Variables for designs. Design point z 1 x 1 z 2 x 2 λ α twist Λ θ 1 θ 2 θ 3 E 7 % 20 % -0.5 % 80 % º 30º 45 º 45 º 0 D 7 % 20 % -1 % 65 % º 30 º 45 º 45 º 0 C 7 % 20 % -0.5 % 65 % º 28 º 45 º 45 º 0 B 8.5 % 35 % 0 % 70 % º 30 º 45 º 45 º 0 A 10 % 35 % 0 % 85 % º 30 º 45 º 45 º 0 Baseline wing 6 % 25 % -1 % 75 % º 15 º 45 º 45 º 0 Effect of sweep back angle on optimization work is of great interest. From aerodynamic point of view, for wings with similar root airfoil, taper and twist, increase in sweep back angle is expected to reduce the L/D ratio, which has been clearly observed from AVL experimentation and also can be observed by noting marginal differences in designs D and C. From structural point of view, sweep back helps in increasing the wing stiffness and the load stiffening ability 8, requiring higher buckling velocities, which is also demonstrated by comparing results for designs D and C. In the present work increased sweep back was found to benefit more to the structural stiffness of the wing while minimally penalizing the L/D ratio. This has resulted in most of the designs on the Pareto optimal front using sweep back angle of 30º (maximum allowed in the study) or close. All the designs on the Pareto optimal front use a taper ratio of 0.5 (also minimum allowed in the study) and 2 layers of 45 /45 carbon/epoxy composite laminate for manufacturing. 0 /90 layup is practically found to be too difficult to roll and store inside canister of diameter 4.5 8

9 inches 7, without failure, also accurately predicted by the analytical method used for storage analysis in the current work. By observing Table 3, and all the designs on the Pareto optimal front, the spread across the Pareto optimal front is looked to be influenced by the root airfoil design parameters (z 1, x 1, z 2 and x 2 ) and the twist angle (α twist ) more. Further investigation is warranted in this regard. Figure 8. Designs on Pareto optimal front : Root airfoil (top) and curvatures (left) and planforms of semiwings (right). Considering all the designs on the Pareto optimal front, following averages are found, Cruise velocity : minimum = m/s, maximum = m/s, Minimum storage diameter : minimum = 4.15 inch, maximum = inch. V. Conclusion Conceptual design of a bendable wing involves aerodynamic as well as structural performance evaluations, thus requiring a multidisciplinary approach. Air vehicle wing aerodynamics, wing structural performance under aggressive flight loads and stresses developed in the wing during rolling process are observed using appropriate numerical and analytical tools. Aerodynamics is studied using AVL software, an inviscid, extended vortex lattice model based program, while, nonlinear snap through buckling is studied using a modified Riks analysis based FEA routine in ABAQUS. Maximum velocity, at which air vehicle can fly, without wing structural failure or material failure, is calculated. Analytical approach is used to study stresses developed in composite wing during the rolling process and Tsai-Wu failure criterion with appropriate safety factor is used to predict failure of the composite laminate wing during the rolling process. Conceptual design of a 24 inch span and 7 inch root chord bendable wing is performed using an elitist non-dominated sorting genetic algorithm: NSGA-II. Wing is designed to maximize L/D ratio, an aerodynamic performance metric and to maximize buckling velocity, a structural performance metric. The designs on the Pareto optimal front are compared with a baseline design. Designs on the Pareto optimal front having 9

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