AIAA-2001-1273 MULTIDISCIPLINARY DESIGN OPTIMIZATION OF A FULL VEHit2LE WITH HIGH PERFORMANCE COMPUTING I R. J. Yang, L. Gu, C. H. Tho Ford Motor Company 2101 Village Road, MD2115-SRL, Dearborn, MI 48124 Phone: (313) 845-5916 Email: Jaroslaw Sobieszczanski-Sobieski NASA Langley Research Center MS 139, Hampton, VA 23681 Phone: (757) 864-2799 Email: j.sobieski@larc.nasa.gov evolution and development of theoretically sound, ABSTRACT robust and efficient FEMs for the simulation of Multidisciplinary design optimization (ME)O) of a nonlinear structural dynamics have advanced computer full vehicle under the constraints of crashworthiness, aided vehicle design to the point where the results are NVH (Noise, Vibration and Harshness), durabil;ty, and trusted with a high degree of confidence. other performance attributes is one of the imperative The resulting surge in super computing is goals for automotive industry. However, it is often revolutionizing the way vehicles are designed. The infeasible due to the lack of computational resources, application of crashworthiness optimization to vehicle robust simulation capabilities, and efficient design has drawn significant attention and interest in optimization methodologies. This paper intends to automotive industry over the past few years [1-6]. move closer towards that goal by using parallel Recently, Yang et al. [5] developed a nonlinear computers for the intensive computation and combining response surface based safety optimization and different approximations for dissimilar analyses in the robustness process, which has been successfully applied MDO process. The MDO process presented in this to the vehicle safety design. They investigated four paper is an extension of the previous work reported by + nonlinear response surface methods for different crash Sobieski et aL In addition to the roof crush, two full modes of large-scale systems as well as occupant vehicle crash modes are added: full frontal impact and restraint system. Sobieski et al. [7] investigated the 50% frontal offset crash. Instead of using an adaptive multidisciplinary design optimization for a car body polynomial response surface method, this paper structure under constraints of VH and roof crush. This employs a DOE/RSM method for exploring the design study extends the previous work to include two more space and constructing highly nonlinear crash functions. crash modes: full frontal impact and 50% frontal offset Two MDO strategies are used and results are compared. crash. A 512-cpu SGI Origin 2000 computer is used for This paper demonstrates that with high performance computation as opposed to a 256-cpu one as in [7]. In computing, a conventionally intractable real world full addition, an alternative optimization strategy is vehicle multidisciplinary optimization problem investigated to compare the results. considering all performance attributes with large All the crash simulations are performed on NASA number of design variables become feasible. AMES SGI Origin 2000 machines: LOMAX (512 processors, 300 MHZ) and STEGER (256 processors, INTRODUCTION 250 MHZ). The nonlinear explicit finite element commercial software, RADIOSS, is used for crash Continuous demands on efficient design of vehicle simulations while MSC/NASTRAN is used to perform safety, NVH, durability, and other attribute performance NVH analyses. The conservative Taylor Series have increasingly emphasized on the analysis of the approximation [8] is used to approximate the NVH vehicle structural designs as well as occupant restraint performance functions. systems. Numerical computation methods have been widely employed for this purpose. The most popular VEHI(_LE MODELS AND, DESIGN TARGETS; and flexible computation method for vehicle design is the finite element methods (FEM). Over the past ten Vehicle safety design is one of the major attributes years, tremendous increase in computer speed and rapid in car product development. The vehicle structure must Copyright © 2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 1 American Institute of Aeronautics and Astronautics be designed to absorb enough crash energy through during impact structural deformation and attenuate the impact force to (t:-tJ is within 36ms a tolerable level when crash events occur. In the real world, all crash modes need to be considered If the occupant P,o,_ is equal to or less than 10%, it simultaneously for crash analysis and optimization. In is graded as 5-star, which is the highest rating in this paper however, only full front crash impact, 50% NCAP star-rating, with 50% confidence interval frontal offset impact, and roof crush are considered, as calculated from student t-distribution, as shown in the main scope of this research is to demonstrate the Figure 2. The finite element model is shown in Figure state-of-the-art MDO methodologies with high 3. performance computing. In addition to the safety Roof Crush Model attributes, the vehicle NVH performance measures are also included in this study. Vehicle roof crush is a federal mandatory requirement intended to enhance passenger protection Full Frontal Crash Model during a rollover event. The test procedure is defined in The full front car crash finite element model used FMVSS 216. The finite element roof crush model for in this study contains about 100,000 elements. It this study is converted from a NVH model, as shown crashes into a rigid 90 degree fixed barrier with the in Figure 4. speed of 35 MPH. The key safety performance measures The explicit finite element dynamic software in the full frontal crash include occupant Head Injury RADIOSS is used for crush simulation. Unnecessary Criteria (HIC) and Chest G, which are calculated from parts in the NVH model are deleted and some missing the MADYMO analysis with importing the crash pulse parts are added in the roof crush model, e.g., very from RADIOSS crash analysis. The MADYMO is a detailed side doors were added and the glasses are commercial multi-body occupant simulation product refined. The total number of elements for roof crush is from TNO. The process is shown in Figure 1. about 120,000. A 72 inches by 30 inches rectangular The full frontal crash is commonly used to design ram is added to perform the' roof crush as specified by and validate the vehicle front structures. Federal Motor the FMVSS 216. The longitudinal axis of the ram (see Vehicle Safety Standards 208 (FMVSS) specifies the Figure 4) is at a forward angle (side view) of 5 degrees safety regulations and test configuration. The regulation below the horizontal, and is parallel to the vertical states that the HIC and Chest G injury numbers have to plane through the vehicle's longitudinal centerline. The be within 1000 and 60g, respectively. The explicit lateral axis is at a lateral outboard angle, in the front finite element dynamic software RADIOSS is used to view projection, of 25 degrees below the horizontal. perform crash simulations throughout this study. The The lower surface is tangential to the surface of the design targets for the full frontal impact in this study vehicle and initial contact point is on the longitudinal are to satisfy both FMVSS 208 regulation and centerline of the lower surface of the ram and 10 inches corporate guidelines with occupant HIC and Chest G from the forward most point of the centerline. In roof targeted within 450 and 45g, respectively. Note that the crush simulation, the ram normal speed is set to be 7.5 numbers may not be realistic, as they are solely used MPH. for proving this methodology. Another design As described in the FMVSS 216, the force requirement is the New Car Assessment Program generated by vehicle resistance must be greater than (NCAP) star-rating criterion, proposed by the National 5,000 Ibs (22,240 N) or 1.5 times the vehicle weight, Highway Traffic Safety Administration (NHTSA) in w_r is less, through 5 inches of ram 1994. The NCAP star-rating criterion is derived from displacement. In this study, the roof crush resistant the total injury probability criteria combining the force is set to be larger than 6,000 lbs (-- 27kN). The occupant HIC and Chest G numbers. The total occupant door thickness and material yield stresses are chosen as probability of severe injury is given by: the design variables. 50% Frontal Offset Crash Model p,o,., = I- (1- PhylaJ,1- _h,,, ) where In addition to full frontal crash and roof crush, a 1 50% offset frontal impact mode is also considered in Phead = l+e" ............. ' the optimization process. The vehicle finite element model is exactly same as the front crash model. The 1 only difference isthe barrier. In this model, the vehicle l+e" ................. ' crashes into a 90 degree fixed rigid wall with 50% -- 2.5 offset (Figure 5). The impact velocity is 40 mph. The HIC = 1 " adt (t: - tI)_ RADIOSS is used for the simulation. The key output from the frontal offset impact is the toeboard intrusion. The design target for toeboard intrusion is set to be less where a is a multiple of G's than 10 inches. The design variables used for 50% tt, t2is expressed in second and measured 2 American Institute of Aeronautics and Astronautics frontal offset crash is same as those used for full front Db = displacement at local point = 0.9mm crash. Roof Crush Constraints: NVH Model Crush distance (D) < 5" In car product development process, different NVH Critical peak load (P,.r) > 27kN (=60001b) models are used for different purposes so that the quality of the NVH is high and the cost is at Full Frontal Impact Constraints: minimum. A car body called Body-In-Prime (BIP) is Head injury criteria < 450 used for this study. The BIP is a trimmed body Chest G < 45g without all the closures (door, hood, deck lid) and other Plo_a_< 10 % (i.e. 5-star NCAP rating) sub-systems (steering column, fuel tank, and seats) and where P,o_l= Total probability of severe injury trim items (carpeting, battery, etc.). A trimmed body structure may be thought of as a vehicle without the 50% Frontal Offset Crash Constraints: suspension and powertrain sub-systems. The BIP can Toe board intrusion < 10" also be thought as the "Body-In-White" with glass. The BIP plays an important role in determining the In the multidisciplinary design optimization dynamic characteristics of the vehicle. problem, there are 10 global (system) thickness design The BIP normal modes, static bending and static variables including windshield, roof panel, roof rail, torsion analyses were conducted using the roof cross members and pillars. The total number of MSC/NASTRAN. The full scale NVH finite element design variables for the NVH model is 19, including I0 model is shown in Figure 6. The total number of shell for backlite glasses and sheet metal thickness, 9 for the elements is close to 68,000. The total number of nodes stiffness of connection between the backlite glass and is about 69,000. The normal modes were calculated structures. The thickness design variables contain floor under the free-free condition. The static bending panels, jacking/towing on quarter panel, backlite glass, analysis was conduced with front (yz and z) and rear (xz shotgun and radiator support. There are 5 subsystem and xyz) shock towers constrained while for the static thickness design variables for full frontal and 50% torsion rear shock tower supports (xz and xyz) and a frontal offset crash models, namely rails and subframe. mid point of the lower radiator support (z) were As for the roof crush, 3 thickness and 7 material yield constrained. The bending stiffness calculated using a stress local design variables are taken into account for load applied at the front rocker locations was 4,551 consideration. N/mm while the torsion stiffness calculated using a torque applied at the front shock tower locations was M-DO PROCEDURE 8726 N-m/Deg. The free-free normal mode analysis showed that the overall torsion at 26.5Hz and overall The multidisciplinary .... design optimization_ bending at 38.9 Hz. procedure is based on the previous work by Sobieski et _ _ The torsion frequency for the BIP free-free normal -'al' [7], as shown in Figure 7. The difference in this "_ mode is set to increase by 5% from 26.5 to 27.8 Hz. paper is that instead of using an adaptive polynonial The upper bounds for static torsion and static bending response surface approximation, a DOE/RSM (Design displacements are chosen as 3.4 mm and 0.9 mm, of Experiments/Response Surface Method) method is _ respectively, i.e., 10% improvement from the initial employed to construct the approximation models for :" design. crash performance functions. Among the various methods for DOE and RSM, the optimal Latin _ MDO PROBLEM Hypercube Sampling method is employed to explore the design space uniformly to capture the nonlinear The multidisciplinary design optimization problem behavior of crash functions, while the stepwise is to minimize the total vehicle weight subjected to regression method is used to construct the nonlinear design constraints of NVH and 3 safety crash modes: response surfaces based on the computer experimental roof crush, full frontal impact, and 50% frontal offset points. The NVH responses are approximated by the crash. The problem is formulated as following: conservative Taylor Series Approximation (TSA) as in [7]. Minimize: Vehicle weight Two optimization strategies are employed to Subject to: perform the inner loop within the MDO process. The VII Constraints: first takes advantage of the design senitivity analysis 2"I.SHz< J3 <-29.3Hz capability in MSC/NASTTRAN [7] and the second Static torsion " Dt takes advantage of both the sensitivity and the Static bending -- Db optimization capabilities. where fi = 3'_frequency In the first strategy, the NVH sensitivities are Dt = displacement at local point = 3.4mm extracted from the MSC/NASTRAN output and 3 American Institute of Aeronautics and Astronautics approximations are constructed using TSA. In addition one predictor, which provides the best fit. The second to the three crash mode responses approximated by the independent predictor to be added to the regression quadratic order of stepwise regression, the MDO model is the one that provides the best fit in problem is solved by an SQP optimizer. As the NVH conjunction with the first predictor. Given the other model is less expensive to run in this case, the NVH predictors already in the model, further optimum • design variables are updated and the analysis is repeated predictors are then added at each step in a recursive in MCS/NASTRAN for several times (3 in this study) fashion. Alternatively, backward elimination can be while keeping the crash approximation models used. Atter certain predictors have been added in the unchanged. After three NVH inner loops, all design model, the predictors are dropped one at a time_ The variables are updated and reflected on the NVH and predictor that has the least effect on the fit of the model crash models. Simulations are then performed to. is dropped at the stage. The stepwise regression model conform the results from the first MDO cycle. The is built by combining the techniques of forward crash approximation models are updated and then selection with backward elimination. continue to perform the next MDO cycle if necessary. In this paper, the second order polynomial for the" The move limits of the design variables for VII regression is employed to construct the nonlinear approximation using the TSA are selected to be 20%. response surfaces for all crash modes (full frontal, 50% The second strategy for the inner loop optimization frontal offset, and roof crush) except the vehicle weight, " is to take advantage of the design optimization where a linear basis function is selected. • capabilities in MSC/NASTRAN. Instead of exporting the NVH sensitivities and performing inner HIGH PERFORMANCE COMPUTING optimization loop manually for three iterations, the The primary computational cost is in performing optimization process for each MDO cycle is completed the RADIOSS finite element analysis for the sample set entirely in the MSC/NASTRAN by imposing the crash performance constraints using the DEQATN and of design points corresponding to each of the 3 crash modes in section 2. The optimal Latin Hypercube DRESP2 cards for the explicit crash equations provided from the stepwise regression approximations._ The sampling method that is used in generating an initial advantage of this strategy is that the inner loop can be set of design points for frontal and offset frontal crash and the multilevel orthogonal arrays are for roof crush completed without any human intervention. However, the approximated crash functions needs to be inputed as in reference [7]. The computational details of the number of sample points and the elapsed computational explicitly. times are provided in Table 1. It is important to note i Optimal Latin Hypereube Sampling (LHS) that the RADIOSS analysis for the baseline and Sample--_ In this research, the optimal Latin Hypercube set (3*N) designs can be performed concurrently on a 7_ multiprocessor machine thereby reducing the elapsed Sampling method [9] is employed to explore the design space for constructing the response surfaces for crash time. The two confo.__ation analyses correspond to the models. The LHS is chosen due to the absence of a verification analyses on the optimal designs obtained prior knowledge of the parametric form of the model. Most RADIOSS crash simulations were performed The experimental design is directed to minimize the on NASA Ames LOMAX machine (SGI Origin 2000, bias part of the Mean Square Error (MSE) by 512 processors, 300 MHZ). Each simulation used 4 _! distributing the sample points uniformly over the entire processors. Based on numerical experience, running the design region. The number of runs in LHS is crash simulation with 4 processors using RADIOSS determined by the total number of factors including code can achieve an approximate speedup of 3, :t control variables and noisy variables. The minimum- compared to a simulation with a single processor. Ond number of runs is selected to be 3N in this paper, where _ cycle of the MDO process can be completed in 70 hours N is the total number of design variables. or approximately 3 days with the 512-cpu LOMAX computer running simultaneously. It may require 938 :a Stepwise Regression (SR) days to complete if it were executed on a single Among the various response surface methods processor. The 938 days estimate is based on the (RSM), the stepwise regression method is used to following formula: (46*60+46*65+25*70)*3 = 22,500 construct the response surface functions for its hours = 937.5 days (details see Table 1). In other simplicity and accuracy for structural crash problems words, a total speedup of 321 (22,500 hrs/70 hrs) can [5]. The regression analysis techniques have widely be achieved. Note that the two conformation runs are been used and a detailed description of stepwise not counted, as they can only be executed after the regression procedures can be found in [10]. In general, previous MDO cycle. In Reference [7], a similar MDO the stepwise regression model is constructed recursively problem, involving NVH and roof crush, was able to be by adding or deleting the independent predictions one completed in one day while it required 257 days of at a time. When the model is built up, the procedure is elapsed computing time for a complete solution on a known as forward selection. The first step is to choose single processor of an Origin 2000 server. Reference 4 American Institute of Aeronautics and Astronautics [6] reportedanevenbetterspeeduupsinga more t ! advancecdomputearnda MessagPeassingInterface A(_KNOWLEDGMENT_ [_1C5_ c, : (MPI)basevdersionofRADIOSS. The study was performed by collaboration of the/, _" Computational AeroSciences Team of the High This study shows that with high performance Performance Computing and Communication Program computing, conventional intractable vehicle design and Ford Research Laboratory. The authors problems now become feasible. acknowledge Mr. J. Chang of NASA Ames NAS Computing facility for his assistance. The authors would like to express their appreciation to D. Johnson NUMERICAl,, RESULTS and F. Maillet of RADIOSS Consulting Corporation The initial design is started from an infeasible for providing RADIOSS software license for crash region, as shown in Table 2. The constraints of the simulation. The authors also acknowledge Drs. T. Tyan third mode frequency, torsion and bending and M. Jayasuriya of Ford Motor Company for displacements, HIC and toe-board intrusion are all" providing the crash and NVH models and consultation. violated. The design variables, their lower bounds and upper bounds are in Table 3. REFERENCES After two MDO cycles, all constraints are satisfied 1. R. J. Yang, L. Tseng, L. Nagy and J. Cheng, and it is shown that the two MDO strategies yield "Feasibility Study of Crash Optimization", ASME, comparable results. The total vehicle weight is reduced Vol. 69-2, pp. 549-556, 1994. by 14.8kg and 15.6kg, _respectively. The objective and 2. M. Chargin, H. Miura, Computer Aided the maximum constraint histories are shown in Figure Engineering for Improved Vehicle Crashworthiness, 8. The design histories for the two strategies are Poster paper at Optimization in Industry-II, Banff, summarized in Tables 2. The design variables for both Canada, 1999. cases are in Tables 3. The DOE results for frontal crash 3. N. Stander, Crashworthiness Technology Using (P,o,a_vs. weight) and offset crash (maximum intrusion Response Surface Methodology and Massively vs. weight) are shown in Figures 9 and 10, Parallel Programming, Poster paper at respectively. It is observed that significant design Optimization in Industry-II, Banff, Canada, 1999. improvements for both strategies are achieved, after two 4. U. Schramm, D. Schneider and H. Thomas, complete cycles. In frontal crash, the Ptotal (total "Structural Optimization in Occupant Safety and probability of severe injury) is improved from 10% to Crash Analysis", Proceedings of Conference 8.0% and 7.5%, respectively. While in the offset crash, Opticon '99: Optimization Sofware, Methods and the maximum toe-board intrusion is successfully Applications, Newport Beach, California, October controlled within 10 inches, while reducing vehicle _. 14-15, 1999. weight. The roof crush performance constraint is 5. R. J. Yang, L. Gu, L. Liaw, C. Gearhart, C.H. Tho, insignificant as all designs are feasible before and after X. Liu, and B. P. Wang, "Approximations for the optimization process. All NVH targets are also met, Safety Optimization of Large Systems," i.e. improving the torsion and bending stiffness by Proceedings of ASME Design Engineering 10% and increasing the third mode frequency by 5%. Technical Conferences, September, Baltimore, CONCLUSIONS Maryland, 2000. 6. S. Kodiyalam, R. J. Yang, L. Gu, C. H. Tho, This research has successfully demonstrated the "Large-Scale, Multidisciplinary Optimization of a feasibility and benefits of the multidisciplinary design Car Body in a Scalable, High Performance optimization methodology with high performance Computing Environment", Submitted to ASME computing. The results showed that the MDO/HPC _ 2001 International Design Engineering Technical methodology could substantially reduce the design Conferences and the Computers and Information in cycle time and vehicle weight in the development and Engineering Conference, Pittsburgh, Pennsylvania, certification of new vehicle designs while satisfying the September 9-12, 2001. functionality requirements. 7. J. S. Sobieski, S. Kodiyalam, and R. J. Yang, Two optimization strategies were employed to "Optimization of Car Body under Constraints of perform the MDO process and they produced Noise, Vibration, and Harshness (NVH) and Crash", comparable results. Optimal designs were achieved with AIAA, 2000-1521, April, Atlanta, GA, 2000. significant reduction of vehicle weight in both 8. J. H. Starnes, R. T. Hattka, Preliminary Design of strategies. Apparently, more performance attributes Composite Wings for Buckling, Strength and (such as durability) and safety crash modes (such as Displacement Constraints, Journal of Aircraft, Vol. side impact, rear impact etc.) with a larger number of 16, pp. 560-570, 1979. design variables need to be incorporated into this -: 9. C. Currin, T. Mitchell, M. Morris,and D. process in the future to solve a real world problem. Ylvisaker, "Bayesian Prediction of Deterministic Function, with Applications to the Design and 5 American Institute of Aeronautics and Astronautics Analysisof Computer Experiments," Journal of the 10. P.R. Krishnaiah, "Selection of Variables American Statistical Association, Vol 86, pp. 953- under Univariate Regression Models," Handbook of 963. Statistics, Vol. 2, 1982. 6 American Institute of Aeronautics and Astronautics Extract crash Injury numbers • HIC I • Chest G I Figure 1. CAE Process for Frontal Crash Problem 1400 J 1200 1000 800 G00 400 20O 20 30 40 50 GO 70 Chest G Figure 2. NCAP Star-Rating Curve Figure 4. Roof Crush FE Model Figure 3. Frontal Crash FE Model 7 American Institute of Aeronautics and Astronautics Figure 5. 50% Frontal Offset Crash Model Figure 6. NVH FE Model _" System+Analysis (NVH, Crash)] Concurrent Processing using I C51ra2shproRcSessoCronstrSuGctIionO/Uringdinates2000 ] _-( NVH Analysis & Smsitivities ] Multidisciplinary Optimizati_on _ NVH SensitivityMbnadesledApproximation J j, Crash Response SMuorfdaecle Approximation ] ,nnevLoon( Update Variables (NVH, Crash) ] Outer Loon ] Figure 7. MDO/HPC Flow Chart 1745 0.15 Original (v_ight) [ N._ - - IF - Alternative (weight)l 0.10 1740 t,x _ -- A-- -Original (Gmax) [ 0.05 1735 o 0.00 1730 -0.05 ¢g 1725 -0.10 1720 -0.15 Initial 1 2 Number of Cycles Figure 8. MDO Design History 8 American Institute of Aeronautics and Astronautics 20 _ I Unfav°rable regi°n 4- 151t i / I I . I ii Baseline / ' _1°}1:y .....,._..... ,.,. ,.,.., ." ". I Favorablereg'on Ii 0 i c i 1720 1730 1740 1750 1760 Weight (Kg) Figure 9. DOE Matrix for Frontal Crash (P,ot,Z vs Weight) i Unfavorable region _" 1146t ....... _:- i .........t....... 12 ri 4'_ 9 • **_' t • • -3" r....... _-* ......... * ..........._'""'_ ....................o...._..................... ,_ L> , '_' ' II _,vorab,oreI g,on 81 , ,. , 1720 1730 1740 1750 1760 Weight (Kg) Figure 10. DOE Matrix for Offset Crash (Maximum Intrusion vs Weight) 9 American Institute of Aeronautics and Astronautics Table 1.Computational Requirements for Safety Disciplines Crash Modes Number of Design Number of RADIOSS Total Elapsed Time Variables (N) simulations (using 4 CPU/simulation) on Origin 2000 machine Frontal Crash 10 (system) + 3*N + 1(baseline) + 60 * 48 = 2,880 hrs 5(local) 2 (conformation) = 48 Offset Crash 10 (system) + _3*N+ 1(baseline) + 65 * 48 = 3,120 hrs 5(local) 2 (conformation) = 48 Roof Crush 10 (system)'+ L24 + 1(baseline) + 70 * 27 = 1,890 hrs I0 (local) 2 (conformation) = 27 Total 7,890 hrs Table 2. MDO Design History Attribute Performance Baseline Target Original* Alternative** .... Cycle 1 Cycle 2 Cycle 1 Cycle 2 3_ frequency (Hz) 26.5 27.8 < fi < 29.3 29.3 29.3 27.8 27.8 NVH Forsion disp. 1(mm) 3.8 < 3.4 3.4 3.4 3.4 3.4 I'orsion disp. 2 (mm) -3.8 > -3.4 -3.4 -3.4 -3.4 -3.4 Bending disp. (ram) -0.97 > -0.9 -0.9 -0.87 -0.9 -0.9 [-IIC 500 _<450 356 411 411 357 Frontal 2hest G 42 < 45 38 39 42 39 Ptot,t(%) 10 < 10 7.3 8.0 9,2 7.5 Roof Resistance force (kN) 34.7 _>27 30.5 31.2 31.4 31.3 Intrusion 1(in.) 11.2 < 10 9.7 9.9 10 9.9 Intrusion 2 (in.) 10.8 < 10 9.4 10 9.7 9.8 Offset intrusion 3 (in.) 10.9 < 10 9.4 10 10 9.8 Intrusion 4 (in.) 10.1 < 10 8.9 9.4 9.5 9.4 Intrusion 5 (in.) 10.5 < 10 9.3 9.8 9.9 9.6 Weight'(Kg) _.i_::_ 1740.5 M,n,_iz_"_ ._1726.6. _1725.7 1727.2_L172.4_, * 3 iterations for NVH loop ** 5 iterations for NVH loop in NASTRAN 10 American Institute of Aeronautics and Astronautics

NASA Technical Reports Server (NTRS) 20010098606: Multidisciplinary Design Optimization of a Full Vehicle with High Performance Computing

Similar NASA Technical Reports Server (NTRS) 20010098606: Multidisciplinary Design Optimization of a Full Vehicle with High Performance Computing