On design optimization for structural crashworthiness and its state of the art
Optimization for structural crashworthiness and energy absorption has become an important topic of research attributable to its proven benefits to public safety and social economy. This paper provides a comprehensive review of the important studies on design optimization for structural crashworthine...
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| Published in: | Structural and multidisciplinary optimization Vol. 55; no. 3; pp. 1091 - 1119 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.03.2017
Springer Nature B.V |
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| ISSN: | 1615-147X, 1615-1488 |
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| Abstract | Optimization for structural crashworthiness and energy absorption has become an important topic of research attributable to its proven benefits to public safety and social economy. This paper provides a comprehensive review of the important studies on design optimization for structural crashworthiness and energy absorption. First, the design criteria used in crashworthiness and energy absorption are reviewed and the surrogate modeling to evaluate these criteria is discussed. Second, multiobjective optimization, optimization under uncertainties and topology optimization are reviewed from concepts, algorithms to applications in relation to crashworthiness. Third, the crashworthy structures are summarized, from generically novel structural configurations to industrial applications. Finally, some conclusions and recommendations are provided to enable academia and industry to become more aware of the available capabilities and recent developments in design optimization for structural crashworthiness and energy absorption. |
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| AbstractList | Optimization for structural crashworthiness and energy absorption has become an important topic of research attributable to its proven benefits to public safety and social economy. This paper provides a comprehensive review of the important studies on design optimization for structural crashworthiness and energy absorption. First, the design criteria used in crashworthiness and energy absorption are reviewed and the surrogate modeling to evaluate these criteria is discussed. Second, multiobjective optimization, optimization under uncertainties and topology optimization are reviewed from concepts, algorithms to applications in relation to crashworthiness. Third, the crashworthy structures are summarized, from generically novel structural configurations to industrial applications. Finally, some conclusions and recommendations are provided to enable academia and industry to become more aware of the available capabilities and recent developments in design optimization for structural crashworthiness and energy absorption. |
| Author | Fang, Jianguang Li, Qing Sun, Guangyong Qiu, Na Kim, Nam H. |
| Author_xml | – sequence: 1 givenname: Jianguang surname: Fang fullname: Fang, Jianguang organization: School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney – sequence: 2 givenname: Guangyong surname: Sun fullname: Sun, Guangyong email: sgy800@126.com organization: School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney – sequence: 3 givenname: Na surname: Qiu fullname: Qiu, Na organization: Department of Mechanical & Aerospace Engineering, University of Florida – sequence: 4 givenname: Nam H. surname: Kim fullname: Kim, Nam H. organization: Department of Mechanical & Aerospace Engineering, University of Florida – sequence: 5 givenname: Qing surname: Li fullname: Li, Qing email: qing.li@sydney.edu.au organization: School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney |
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| Copyright | Springer-Verlag Berlin Heidelberg 2016 Copyright Springer Science & Business Media 2017 Structural and Multidisciplinary Optimization is a copyright of Springer, (2016). All Rights Reserved. |
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| Keywords | Uncertainty Surrogate model Multiobjective optimization Literature review Topology optimization Energy absorption Crashworthiness optimization |
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| References | WuJPNusholtzGSBilkhuSOptimization of vehicle crash pulses in relative displacement domainInt J Crashworth20027397413 LiaoXLiQYangXLiWZhangWA two-stage multi-objective optimisation of vehicle crashworthiness under frontal impactInt J Crashworth20081327928810.1080/13588260801933659 AcarEOptimizing the shape parameters of radial basis functions: an application to automobile crashworthinessProc Institution Mech Eng Part D-J Automobile Eng20102241541155310.1243/09544070JAUTO1560 PazJDíazJRomeraLCostasMCrushing analysis and multi-objective crashworthiness optimization of GFRP honeycomb-filled energy absorption devicesFinite Elem Anal Des201491303910.1016/j.finel.2014.07.006 Zhou Q, Wu X, Xia Y, Cai W (2014) Spot weld layout optimization of tube crash performance with manufacturing constraints. J Manufact Sci Eng-Trans Asme 136 KochPNSimpsonTWAllenJKMistreeFStatistical approximations for multidisciplinary design optimization: the problem of sizeJ Aircr19993627528610.2514/2.2435 SinhaKKrishnanRRaghavendraDMulti-objective robust optimisation for crashworthiness during side impactInt J Veh Des20074311613510.1504/IJVD.2007.012299 FangJGaoYSunGXuCLiQMultiobjective robust design optimization of fatigue life for a truck cabReliab Eng Syst Saf20151351810.1016/j.ress.2014.10.007 ShakeriMMirzaeifarRSalehghaffariSNew insights into the collapsing of cylindrical thin-walled tubes under axial impact loadProc Instit Mech Eng Part C-J Mech Eng Sci200722186988510.1243/09544062JMES562 SeitzbergerMRammerstorferFGDegischerHPGradingerRCrushing of axially compressed steel tubes filled with aluminium foamActa Mech1997125931051071.7468710.1007/BF01177301 YounBDChoiKKA new response surface methodology for reliability-based design optimizationComput Struct20048224125610.1016/j.compstruc.2003.09.002 ZhangZLiuSTangZDesign optimization of cross-sectional configuration of rib-reinforced thin-walled beamThin-Walled Struct20094786887810.1016/j.tws.2009.02.009 AlexanderJAn approximate analysis of the collapse of thin cylindrical shells under axial loadingQuarter J Mech Appl Math19601310151143920096.3950210.1093/qjmam/13.1.10 ZhuPPanFChenWVianaFACLightweight design of vehicle parameters under crashworthiness using conservative surrogatesComput Ind20136428028910.1016/j.compind.2012.11.004 MohammadihaOBeheshtiHOptimization of functionally graded foam-filled conical tubes under axial impact loadingJ Mech Sci Technol2014281741175210.1007/s12206-014-0320-2 HanJYamazakiKCrashworthiness optimization of S-shape square tubesInt J Veh Des200331728510.1504/IJVD.2003.002048 YinHWenGGanNCrashworthiness design for honeycomb structures under axial dynamic loadingInt J Comput Methods2011886387710.1142/S0219876211002885 ZerpaLEQueipoNVPintosSSalagerJ-LAn optimization methodology of alkaline–surfactant–polymer flooding processes using field scale numerical simulation and multiple surrogatesJ Pet Sci Eng20054719720810.1016/j.petrol.2005.03.002 ZhangXWenZZhangHAxial crushing and optimal design of square tubes with graded thicknessThin-Walled Struct20148426327410.1016/j.tws.2014.07.004 ChoiWParkGTransformation of dynamic loads into equivalent static loads based on modal analysisInt J Numer Methods Eng19994629430960.7402910.1002/(SICI)1097-0207(19990910)46:1<29::AID-NME661>3.0.CO;2-D KaushikARamaniATopology optimization for nonlinear dynamic problems: considerations for automotive crashworthinessEng Optim20144648750210.1080/0305215X.2013.776553 Park G (2011) Technical overview of the equivalent static loads method for non-linear static response structural optimization. Struct Multidisc Optim 43:319–337 HanssenAGLangsethMHopperstadOSOptimum design for energy absorption of square aluminium columns with aluminium foam fillerInt J Mech Sci2001431531760958.7452410.1016/S0020-7403(99)00108-3 ShiQHagiwaraIOptimal design method to automobile problems using holographic neural network’s approximationJpn J Ind Appl Math20001732133917941741306.6516210.1007/BF03167370 MilhoJFAmbrósioJACPereiraMFOSDesign of train crash experimental tests by optimization proceduresInt J Crashworth2004948349310.1533/ijcr.2004.0304 QuXHaftkaRReliability-based design optimization using probabilistic sufficiency factorStruct Multidisc Optim20042731432510.1007/s00158-004-0390-3 HanssenAGLangsethMHopperstadOSStatic and dynamic crushing of circular aluminium extrusions with aluminium foam fillerInt J Impact Eng2000244755070944.7450410.1016/S0734-743X(99)00170-0 Schonlau M (1998) Computer experiments and global optimization. University of Waterloo YinHWenGHouSChenKCrushing analysis and multiobjective crashworthiness optimization of honeycomb-filled single and bitubular polygonal tubesMater Des2011324449446010.1016/j.matdes.2011.03.060 Stander N An Adaptive Surrogate-Assisted Strategy for Multi-Objective Optimization. In: 10th World Congress on Structural and Multidisciplinary Optimization, Orlando, Florida, USA, 2013. ZhangSZhuPChenWArendtPConcurrent treatment of parametric uncertainty and metamodeling uncertainty in robust designStruct Multidisc Optim201347637630389281274.7430110.1007/s00158-012-0805-5 AhmetogluMABrouwersDShulkinLTaupinLKinzelGLAltanTDeep drawing of round cups from tailor-welded blanksJ Mater Process Technol19955368469410.1016/0924-0136(94)01767-U ShiYZhuPShenLLinZLightweight design of automotive front side rails with TWB conceptThin-Walled Struct20074581410.1016/j.tws.2007.01.013 ZhangYZhuPChenGLightweight design of automotive front side rail based on robust optimisationThin-Walled Struct20074567067610.1016/j.tws.2007.05.007 LeeS-JLeeH-AYiS-IKimD-SYangHWParkGDesign flow for the crash box in a vehicle to maximize energy absorptionProc Inst Mech Eng Part D-J Automobile Eng201322717920010.1177/0954407012451545 SinhaKReliability-based multiobjective optimization for automotive crashworthiness and occupant safetyStruct Multidisc Optim20073325526810.1007/s00158-006-0050-x SimpsonTWBookerAJGhoshDGiuntaAAKochPNYangRApproximation methods in multidisciplinary analysis and optimization: a panel discussionStruct Multidisc Optim20042730231310.1007/s00158-004-0389-9 Raquel C, Naval P (2005) An effective use of crowding distance in multiobjective particle swarm optimization. In: Proceedings of the 2005 conference on Genetic and evolutionary computation, Washington DC, USA. New York, NY, USA, pp 257-264 SimpsonTWPoplinskiJKochPNAllenJKMetamodels for computer-based engineering design: survey and recommendationsEng Comput2001171291500985.6859910.1007/PL00007198 TuJChoiKKParkYHA new study on reliability-based design optimizationJ Mech Des199912155756410.1115/1.2829499 MayerRRKikuchiNScottRAApplication of topological optimization techniques to structural crashworthinessInt J Numer Methods Eng199639138314030889.7305210.1002/(SICI)1097-0207(19960430)39:8<1383::AID-NME909>3.0.CO;2-3 SobesterALearySJKeaneAJA parallel updating scheme for approximating and optimizing high fidelity computer simulationsStruct Multidisc Optim20042737138310.1007/s00158-004-0397-9 Goel T, Stander N, Lin Y-Y (2010) Efficient resource allocation for genetic algorithm based multi-objective optimization with 1,000 simulations. Struct Multidisc Optim 41:421–432 Stander N (2012) An efficient new sequential strategy for multi-objective optimization using LS-OPT®. Paper presented at the 12th International LS-DYNA Users Conference, Dearborn, Michigan, USA LönnDBergmanGNilssonLSimonssonKExperimental and finite element robustness studies of a bumper system subjected to an offset impact loadingInt J Crashworth20111615516810.1080/13588265.2010.539339 TarlochanFSamerFHamoudaAMSRameshSKhalidKDesign of thin wall structures for energy absorption applications: Enhancement of crashworthiness due to axial and oblique impact forcesThin-Walled Struct20137171710.1016/j.tws.2013.04.003 DuanSTaoYHanXYangXHouSHuZInvestigation on structure optimization of crashworthiness of fiber reinforced polymers materialsComposit Part B-Eng20146047147810.1016/j.compositesb.2013.12.062 ChoY-BBaeC-HSuhM-WSinH-CA vehicle front frame crash design optimization using hole-type and dent-type crush initiatorThin-Walled Struct20064441542810.1016/j.tws.2006.03.011 KurtaranHEskandarianAMarzouguiDBedewiNECrashworthiness design optimization using successive response surface approximationsComput Mech2002294094211146.7434810.1007/s00466-002-0351-x Villa A, Strano M, Mussi V (2011) Optimization of Design and Manufacturing Process of Metal Foam Filled Anti-Intrusion Bars. 14th International Conference on Material Forming Esaform, 2011 Proceedings 1353:1656-1661 HuangXXieYMLuGTopology optimization of energy-absorbing structuresInt J Crashworth20071266367510.1080/13588260701497862 RedheMForsbergJJanssonTMarklundPONilssonLUsing the response surface methodology and the D-optimality criterion in crashworthiness related problemsStruct Multidisc Optim20022418519410.1007/s00158-002-0228-9 ZuradaJMIntroduction to artificial neural systems vol 81992St. PaulWest publishing company Friedman JH (1991) Multivariate adaptive regression splines. Ann Stat:1–67 GuJLiGYDongZHybrid and adaptive meta-model-based global optimizationEng Optim2012448710410.1080/0305215X.2011.564768 Acar E, Solanki K (2009b) System reliability based vehicle design for crashworthiness and effects of various uncertainty reduction measures. Struct Multidisc Optim 39:311–325 SeitzbergerMRammerstorferFGGradingerRDegischerHPBlaimscheinMWalchCExperimental studies on the quasi-static axial crushing of steel columns filled with aluminium foamInt J Solids Struct2000374125414710.1016/S0020-7683(99)00136-5 Chen Z, Qiu H, Gao L, Li X, Li P (2014) A local adaptive sampling method for reliability-based design optimization using Kriging model. Struct Multidisc Optim 49:401–416 Davis SC, Diegel SW, Boundy RG (2013) Transportation energy data book. 32 edn., Oak Ridge National Lab SacksJWelchWJMitchellTJWynnHPDesign and analysis of computer experimentsStat Sci1989440942310417650955.6261910.1214/ss/1177012413 ShinMKYiSIKwonOTParkGStructural optimization of the automobile frontal structure for pedestrian protection |
| References_xml | – reference: Messac A, Sundararaj GJ, Tappeta RV, Renaud JE (2000b) Ability of objective functions to generate points on nonconvex Pareto frontiers. AIAA J 38:1084–1091 – reference: PanFZhuPDesign optimisation of vehicle roof structures: benefits of using multiple surrogatesInt J Crashworth201116859510.1080/13588265.2010.514773 – reference: SunGLiGStoneMLiQA two-stage multi-fidelity optimization procedure for honeycomb-type cellular materialsComput Mater Sci20104950051110.1016/j.commatsci.2010.05.041 – reference: ZhangXChengGWangBZhangHOptimum design for energy absorption of bitubal hexagonal columns with honeycomb coreInt J Crashworth2008139910710.1080/13588260701731732 – reference: FangHRais-RohaniMLiuZHorstemeyerMFA comparative study of metamodeling methods for multiobjective crashworthiness optimizationComput Struct2005832121213610.1016/j.compstruc.2005.02.025 – reference: LönnDÖmanMNilssonLSimonssonKFinite element based robustness study of a truck cab subjected to impact loadingInt J Crashworth20091411112410.1080/13588260802412992 – reference: AbdullahKWildPJeswietJGhasempoorATensile testing for weld deformation properties in similar gage tailor welded blanks using the rule of mixturesJ Mater Process Technol2001112919710.1016/S0924-0136(01)00555-6 – reference: MayerRRKikuchiNScottRAApplication of topological optimization techniques to structural crashworthinessInt J Numer Methods Eng199639138314030889.7305210.1002/(SICI)1097-0207(19960430)39:8<1383::AID-NME909>3.0.CO;2-3 – reference: Forrester A, Sobester A, Keane A (2008) Engineering design via surrogate modelling: a practical guide. John Wiley & Sons – reference: ZhangSZhuPChenWCrashworthiness-based lightweight design problem via new robust design method considering two sources of uncertaintiesProc Instit Mech Eng Part C-J Mech Eng Sci20132271381139110.1177/0954406212460824 – reference: Sheldon A, Helwig E, Cho Y-B (2011) Investigation and application of multi-disciplinary optimization for automotive body-in-white development. In: 8th European LS-DYNA Users conference, Strasbourg, 23–24 – reference: ChoiWParkGTransformation of dynamic loads into equivalent static loads based on modal analysisInt J Numer Methods Eng19994629430960.7402910.1002/(SICI)1097-0207(19990910)46:1<29::AID-NME661>3.0.CO;2-D – reference: ZhangYSunGLiGLuoZLiQOptimization of foam-filled bitubal structures for crashworthiness criteriaMater Des2012389910910.1016/j.matdes.2012.01.028 – reference: HanssenAGLangsethMHopperstadOSOptimum design for energy absorption of square aluminium columns with aluminium foam fillerInt J Mech Sci2001431531760958.7452410.1016/S0020-7403(99)00108-3 – reference: KaushikARamaniATopology optimization for nonlinear dynamic problems: considerations for automotive crashworthinessEng Optim20144648750210.1080/0305215X.2013.776553 – reference: AvalleMChiandussiGOptimisation of a vehicle energy absorbing steel component with experimental validationInt J Impact Eng20073484385810.1016/j.ijimpeng.2006.02.001 – reference: SobesterALearySJKeaneAJA parallel updating scheme for approximating and optimizing high fidelity computer simulationsStruct Multidisc Optim20042737138310.1007/s00158-004-0397-9 – reference: QiCYangSDongFCrushing analysis and multiobjective crashworthiness optimization of tapered square tubes under oblique impact loadingThin-Walled Struct20125910311910.1016/j.tws.2012.05.008 – reference: Acar E, Rais-Rohani M (2009) Ensemble of metamodels with optimized weight factors. Struct Multidisc Optim 37:279–294 – reference: Lanzi L, Bisagni C, Ricci S (2004a) Crashworthiness optimization of helicopter subfloor based on decomposition and global approximation. Struct Multidisc Optim 27:401–410 – reference: YiSILeeJYParkGCrashworthiness design optimization using equivalent static loadsProc Instit Mech Eng Part D-J Automobile Eng2012226233810.1177/0954407011411638 – reference: MilhoJFAmbrósioJACPereiraMFOSDesign of train crash experimental tests by optimization proceduresInt J Crashworth2004948349310.1533/ijcr.2004.0304 – reference: GuoLTovarAPenningerCLRenaudJEStrain-based topology optimisation for crashworthiness using hybrid cellular automataInt J Crashworth20111623925210.1080/13588265.2010.544892 – reference: GuLYangRThoCHMakowskiMFaruqueOLiYOptimization and robustness for crashworthiness of side impactInt J Veh Des20012634836010.1504/IJVD.2001.005210 – reference: HanJYamazakiKCrashworthiness optimization of S-shape square tubesInt J Veh Des200331728510.1504/IJVD.2003.002048 – reference: GuJLiGYDongZHybrid and adaptive meta-model-based global optimizationEng Optim2012448710410.1080/0305215X.2011.564768 – reference: NguyenVSWenGYinHVanTPOptimisation design of reinforced S-shaped frame structure under axial dynamic loadingInt J Crashworth20141938539310.1080/13588265.2014.904598 – reference: SotoCAStructural topology optimization for crashworthinessInt J Crashworth2004927728310.1533/ijcr.2004.0288 – reference: YildizARSolankiKNMulti-objective optimization of vehicle crashworthiness using a new particle swarm based approachInt J Adv Manuf Technol20125936737610.1007/s00170-011-3496-y – reference: LanziLCastellettiLMLAnghileriMMulti-objective optimisation of composite absorber shape under crashworthiness requirementsCompos Struct20046543344110.1016/j.compstruct.2003.12.005 – reference: Stander N (2012) An efficient new sequential strategy for multi-objective optimization using LS-OPT®. Paper presented at the 12th International LS-DYNA Users Conference, Dearborn, Michigan, USA – reference: ChiandussiGAvalleMMaximisation of the crushing performance of a tubular device by shape optimisationComput Struct2002802425243210.1016/S0045-7949(02)00247-X – reference: XuHChuangCYangRA data mining-based strategy for direct multidisciplinary optimizationSAE Int J Mater Manufact20158357363 – reference: GhamarianAZareiHCrashworthiness investigation of conical and cylindrical end-capped tubes under quasi-static crash loadingInt J Crashworth201217192810.1080/13588265.2011.623025 – reference: ZhuPZhangYChenGMetamodeling development for reliability-based design optimization of automotive body structureComput Ind20116272974110.1016/j.compind.2011.05.008 – reference: KianiMMotoyamaKRais-RohaniMShiozakiHJoint stiffness analysis and optimization as a mechanism for improving the structural design and performance of a vehicleProc Instit Mech Eng Part D-J Automobile Eng201422868970010.1177/0954407013516107 – reference: SunGLiGHouSZhouSLiWLiQCrashworthiness design for functionally graded foam-filled thin-walled structuresMater Sci Eng A-Struct Mater Properties Microstruct Process20105271911191910.1016/j.msea.2009.11.022 – reference: YangRAkkermanAAndersonDFFaruqueOGuLRobustness optimization for vehicular crash simulationsComput Sci Eng2000281310.1109/5992.881701 – reference: YaoWChenXLuoWvan ToorenMGuoJReview of uncertainty-based multidisciplinary design optimization methods for aerospace vehiclesProg Aerosp Sci20114745047910.1016/j.paerosci.2011.05.001 – reference: Shariati M, Allahbakhsh HR, Saemi J, Sedighi M (2010) Optimization of foam filled spot-welded column for the crashworthiness design. Mechanika:10-16 – reference: AbramowiczWJonesNDynamic progressive buckling of circular and square tubesInt J Impact Eng1986424327010.1016/0734-743X(86)90017-5 – reference: AbramowiczWWierzbickiTAxial crushing of multicorner sheet metal columnsJ Appl Mech19895611312010.1115/1.3176030 – reference: Forsberg J, Nilsson L (2007) Topology optimization in crashworthiness design. Struct Multidisc Optim 33:1–12 – reference: RangavajhalaSMahadevanSDesign optimization for robustness in multiple performance functionsStruct Multidisc Optim20134752353830388931274.9053210.1007/s00158-012-0860-y – reference: ShinMKParkKJParkGOptimization of structures with nonlinear behavior using equivalent loadsComput Methods Appl Mech Eng2007196115411671120.7470710.1016/j.cma.2006.09.001 – reference: AcarEOptimizing the shape parameters of radial basis functions: an application to automobile crashworthinessProc Institution Mech Eng Part D-J Automobile Eng20102241541155310.1243/09544070JAUTO1560 – reference: AcarEGulerMAGercekerBCeritMEBayramBMulti-objective crashworthiness optimization of tapered thin-walled tubes with axisymmetric indentationsThin-Walled Struct2011499410510.1016/j.tws.2010.08.010 – reference: Chen Z, Qiu H, Gao L, Li X, Li P (2014) A local adaptive sampling method for reliability-based design optimization using Kriging model. Struct Multidisc Optim 49:401–416 – reference: ChoY-BBaeC-HSuhM-WSinH-CA vehicle front frame crash design optimization using hole-type and dent-type crush initiatorThin-Walled Struct20064441542810.1016/j.tws.2006.03.011 – reference: WangXShiLA new metamodel method using Gaussian process based bias function for vehicle crashworthiness designInt J Crashworth20141931132110.1080/13588265.2014.898932 – reference: AllahbakhshHRSaetniJDesign optimization of square and circular aluminium extrusion damage columns with crashworthiness criteriaIndian J Eng Mater Sci201118341350 – reference: Shimoyama K, Shinkyu J, Obayashi S (2013) Kriging-surrogate-based optimization considering expected hypervolume improvement in non-constrained many-objective test problems. In: Evolutionary Computation (CEC), 2013 I.E. Congress on, 658–665 – reference: AspenbergDJergeusJNilssonLRobust optimization of front members in a full frontal car impactEng Optim20124524526410.1080/0305215X.2012.669380 – reference: ZhangYZhuPChenGLinZQStudy on structural lightweight design of automotive front side rail based on response surface methodJ Mech Des200712955355710.1115/1.2712223 – reference: DuanSTaoYHanXYangXHouSHuZInvestigation on structure optimization of crashworthiness of fiber reinforced polymers materialsComposit Part B-Eng20146047147810.1016/j.compositesb.2013.12.062 – reference: FangJGaoYSunGXuCLiQMultiobjective robust design optimization of fatigue life for a truck cabReliab Eng Syst Saf20151351810.1016/j.ress.2014.10.007 – reference: Zhou XJ, Ma YZ, Li XF (2011) Ensemble of surrogates with recursive arithmetic average. Struct Multidisc Optim 44:651–671 – reference: Raquel C, Naval P (2005) An effective use of crowding distance in multiobjective particle swarm optimization. In: Proceedings of the 2005 conference on Genetic and evolutionary computation, Washington DC, USA. New York, NY, USA, pp 257-264 – reference: Avalle M, Chiandussi G, Belingardi G (2002) Design optimization by response surface methodology: application to crashworthiness design of vehicle structures. Struct Multidisc Optim 24:325–332 – reference: HouSLiQLongSYYangXJLiWMultiobjective optimization of multi-cell sections for the crashworthiness designInt J Impact Eng2008351355136710.1016/j.ijimpeng.2007.09.003 – reference: ZhengGWuSSunGLiGLiQCrushing analysis of foam-filled single and bitubal polygonal thin-walled tubesInt J Mech Sci20148722624010.1016/j.ijmecsci.2014.06.002 – reference: Witowski K, Erhart A, Schumacher P, Müllerschön H (2012) Topology optimization for crash – reference: PedersenCBWTopology optimization for crashworthiness of frame structuresInt J Crashworth20038293910.1533/ijcr.2003.0218 – reference: Jin R, Du X, Chen W (2003) The use of metamodeling techniques for optimization under uncertainty. Struct Multidisc Optim 25:99–116 – reference: ForresterAKeaneAJRecent advances in surrogate-based optimizationProg Aerosp Sci200945507910.1016/j.paerosci.2008.11.001 – reference: KhakhaliANariman-zadehNDarvizehAMasoumiANotghiBReliability-based robust multi-objective crashworthiness optimisation of S-shaped box beams with parametric uncertaintiesInt J Crashworth20101544345610.1080/13588261003696458 – reference: McKittrickJEnergy absorbent natural materials and bioinspired design strategies: A reviewMater Sci Eng C20103033134210.1016/j.msec.2010.01.011 – reference: LiuS-TTongZ-QTangZ-LZhangZ-HDesign optimization of the S-frame to improve crashworthinessActa Mech Sin20143058959910.1007/s10409-014-0032-y – reference: LiaoXLiQYangXLiWZhangWA two-stage multi-objective optimisation of vehicle crashworthiness under frontal impactInt J Crashworth20081327928810.1080/13588260801933659 – reference: Schonlau M (1998) Computer experiments and global optimization. University of Waterloo – reference: SacksJWelchWJMitchellTJWynnHPDesign and analysis of computer experimentsStat Sci1989440942310417650955.6261910.1214/ss/1177012413 – reference: ShiLYangRZhuPA method for selecting surrogate models in crashworthiness optimizationStruct Multidisc Optim20124615917010.1007/s00158-012-0760-1 – reference: YangRWangNThoCBobineauJWangBMetamodeling development for vehicle frontal impact simulationJ Mech Des20051271014102010.1115/1.1906264 – reference: Davis SC, Diegel SW, Boundy RG (2013) Transportation energy data book. 32 edn., Oak Ridge National Lab – reference: ParkGLeeT-HLeeKHHwangK-HRobust design: an overviewAIAA J20064418119110.2514/1.13639 – reference: RedheMGigerMNilssonLAn investigation of structural optimization in crashworthiness design using a stochastic approach - a comparison of stochastic optimization and the response surface methodologyStruct Multidisc Optim200427446459 – reference: HamzaKShalabyMA framework for parallelized efficient global optimization with application to vehicle crashworthiness optimizationEng Optim2014461200122110.1080/0305215X.2013.827672 – reference: HajelaPLeeETopological optimization of rotorcraft subfloor structures for crashworthiness considerationsComput Struct19976465760919.7310610.1016/S0045-7949(96)00143-5 – reference: YinHWenGHouSChenKCrushing analysis and multiobjective crashworthiness optimization of honeycomb-filled single and bitubular polygonal tubesMater Des2011324449446010.1016/j.matdes.2011.03.060 – reference: TangLWangHLiGXuFAdaptive heuristic search algorithm for discrete variables based multi-objective optimizationStruct Multidisc Optim201348821836310760610.1007/s00158-013-0932-7 – reference: LiuYCrashworthiness design of multi-corner thin-walled columnsThin-Walled Struct2008461329133710.1016/j.tws.2008.04.003 – reference: JeongSBYiSIKanCDNagabhushanaVParkGStructural optimization of an automobile roof structure using equivalent static loadsProc Institution Mech Eng Part D-J Automobile Eng20082221985199510.1243/09544070JAUTO855 – reference: MarklundPONilssonLOptimization of a car body component subjected to side impactStruct Multidisc Optim20012138339210.1007/s001580100117 – reference: LönnDFyllingenØNilssonaLAn approach to robust optimization of impact problems using random samples and meta-modellingInt J Impact Eng20103772373410.1016/j.ijimpeng.2009.07.002 – reference: Roux W (2011) Topology Design using LS-TaSC™ Version 2 and LS-DYNA® – reference: ZhangYZhuPChenGLinZStudy on structural lightweight design of automotive front side rail based on response surface methodJ Mech Des200712955355710.1115/1.2712223 – reference: Allahbakhsh HR, Saemi J, Hourali M (2011) Design optimization of square aluminium damage columns with crashworthiness criteria. Mechanika:187–192 – reference: SunGLiGZhouSLiHHouSLiQCrashworthiness design of vehicle by using multiobjective robust optimizationStruct Multidisc Optim2011449911010.1007/s00158-010-0601-z – reference: HardyRLMultiquadric equations of topography and other irregular surfacesJ Geophys Res1971761905191510.1029/JB076i008p01905 – reference: MontgomeryDCDesing and analysis of experiments1996New York, EUAWiley – reference: WangHLiELiGYProbability-based least square support vector regression metamodeling technique for crashworthiness optimization problemsComput Mech2011472512630587337010.1007/s00466-010-0532-y – reference: Patel NM, Kang B-S, Renaud JE, Tovar A (2009) Crashworthiness design using topology optimization. J Mech Design 131 – reference: KayaNOeztuerkFMulti-objective crashworthiness design optimisation of thin-walled tubesInt J Veh Des201052546310.1504/IJVD.2010.029635 – reference: Gu X, Sun G, Li G, Mao L, Li Q (2013) A Comparative study on multiobjective reliable and robust optimization for crashworthiness design of vehicle structure. Struct Multidisc Optim 48:669–684 – reference: LeeSHKimHYOhSICylindrical tube optimization using response surface method based on stochastic processJ Mater Process Technol200213049049610.1016/S0924-0136(02)00794-X – reference: AntonyJDesign for six sigma: a breakthrough business improvement strategy for achieving competitive advantageWork Stud2002516810.1108/00438020210415460 – reference: BiJFangHWangQRenXModeling and optimization of foam-filled thin-walled columns for crashworthiness designsFinite Elem Anal Des20104669870910.1016/j.finel.2010.03.008 – reference: Friedman JH (1991) Multivariate adaptive regression splines. Ann Stat:1–67 – reference: PedersenCBWCrashworthiness design of transient frame structures using topology optimizationComput Methods Appl Mech Eng20041936536781060.7458410.1016/j.cma.2003.11.001 – reference: SuRGuiLFanZMulti-objective optimization for bus body with strength and rollover safety constraints based on surrogate modelsStruct Multidisc Optim20114443144128353801274.7429410.1007/s00158-011-0627-x – reference: Vining GG, Myers RH (1990) Combining Taguchi and response surface philosophies: a dual response approach. J Qual Technol 22 – reference: YinHWenGFangHQingQKongXXiaoJLiuZMultiobjective crashworthiness optimization design of functionally graded foam-filled tapered tube based on dynamic ensemble metamodelMater Des20145574775710.1016/j.matdes.2013.10.054 – reference: WuJPNusholtzGSBilkhuSOptimization of vehicle crash pulses in relative displacement domainInt J Crashworth20027397413 – reference: JiangZGuMOptimization of a fender structure for the crashworthiness designMater Des2010311085109510.1016/j.matdes.2009.09.047 – reference: RedheMNilssonLOptimization of the new Saab 9-3 exposed to impact load using a space mapping techniqueStruct Multidisc Optim200427411420 – reference: KimHSNew extruded multi-cell aluminum profile for maximum crash energy absorption and weight efficiencyThin-Walled Struct20024031132710.1016/S0263-8231(01)00069-6 – reference: WangHLiGYLiETime-based metamodeling technique for vehicle crashworthiness optimizationComput Methods Appl Mech Eng2010199249725091231.7435610.1016/j.cma.2010.04.002 – reference: Acar E (2010b) Various approaches for constructing an ensemble of metamodels using local measures. Struct Multidisc Optim 42:879–896 – reference: KimS-HKimHKimNJBrittle intermetallic compound makes ultrastrong low-density steel with large ductilityNature2015518777910.1038/nature14144 – reference: TarlochanFSamerFHamoudaAMSRameshSKhalidKDesign of thin wall structures for energy absorption applications: Enhancement of crashworthiness due to axial and oblique impact forcesThin-Walled Struct20137171710.1016/j.tws.2013.04.003 – reference: ChristensenJBastienCBlundellMVEffects of roof crush loading scenario upon body in white using topology optimisationInt J Crashworth201217293810.1080/13588265.2011.625640 – reference: WangGGShanSReview of metamodeling techniques in support of engineering design optimizationJ Mech Des200712937038010.1115/1.2429697 – reference: HeltonJCJohnsonJDSallaberryCJStorlieCBSurvey of sampling-based methods for uncertainty and sensitivity analysisReliability Eng Syst Saf2006911175120910.1016/j.ress.2005.11.017 – reference: YinHWenGHouSQingQMultiobjective crashworthiness optimization of functionally lateral graded foam-filled tubesMater Des20134441442810.1016/j.matdes.2012.08.033 – reference: Abbasi M, Ghafari-Nazari A, Reddy S, Fard M (2014) A new approach for optimizing automotive crashworthiness: concurrent usage of ANFIS and Taguchi method. Struct Multidisc Optim 49:485–499 – reference: Chuang C, Yang R, Li G, Mallela K, Pothuraju P (2008) Multidisciplinary design optimization on vehicle tailor rolled blank design. Struct Multidisc Optim 35:551–560 – reference: DebKPratapAAgarwalSMeyarivanTA fast and elitist multiobjective genetic algorithm: NSGA-IIEvol Comput, IEEE Trans2002618219710.1109/4235.996017 – reference: XiangYJWangQFanZJFangHBOptimal crashworthiness design of a spot-welded thin-walled hat sectionFinite Elem Anal Des20064284685510.1016/j.finel.2006.01.001 – reference: Fang J, Gao Y, Sun G, Zhang Y, Li Q (2014a) Crashworthiness design of foam-filled bitubal Structures with uncertainty. Int J Non-Linear Mech – reference: KianiMGandikotaIParrishAMotoyamaKRais-RohaniMSurrogate-based optimisation of automotive structures under multiple crash and vibration design criteriaInt J Crashworth20131847348210.1080/13588265.2013.805294 – reference: ZareiHRKrogerMMultiobjective crashworthiness optimization of circular aluminum tubesThin-Walled Struct20064430130810.1016/j.tws.2006.03.010 – reference: HongUPParkGDetermination of the crash pulse and optimization of the crash components using the response surface approximate optimizationProc Institution Mech Eng Part D-J Automobile Eng200321720321310.1243/09544070360550408 – reference: Duddeck F (2008) Multidisciplinary optimization of car bodies. Struct Multidisc Optim 35:375–389 – reference: ZhuPPanFChenWVianaFACLightweight design of vehicle parameters under crashworthiness using conservative surrogatesComput Ind20136428028910.1016/j.compind.2012.11.004 – reference: KochPNYangRGuLDesign for six sigma through robust optimizationStruct Multidisc Optim20042623524810.1007/s00158-003-0337-0 – reference: SimpsonTWPoplinskiJKochPNAllenJKMetamodels for computer-based engineering design: survey and recommendationsEng Comput2001171291500985.6859910.1007/PL00007198 – reference: QiCYangSCrashworthiness and lightweight optimisation of thin-walled conical tubes subjected to an oblique impactInt J Crashworth20141933435110.1080/13588265.2014.893788 – reference: PanFZhuPZhangYMetamodel-based lightweight design of B-pillar with TWB structure via support vector regressionComput Struct201088364410.1016/j.compstruc.2009.07.008 – reference: BelingardiGBeyeneATKorichoEGGeometrical optimization of bumper beam profile made of pultruded composite by numerical simulationCompos Struct201310221722510.1016/j.compstruct.2013.02.013 – reference: ReidSRReddyTYStatic and dynamic crushing of tapered sheet metal tubes of rectangular cross-sectionInt J Mech Sci19862862363710.1016/0020-7403(86)90077-9 – reference: ZhuPZhangYChenGMetamodel-based lightweight design of an automotive front-body structure using robust optimizationProc Instit Mech Eng Part D-J Automobile Eng20092231133114710.1243/09544070JAUTO1045 – reference: Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodelling techniques under multiple modelling criteria. Struct Multidisc Optim 23:1–13 – reference: ShakeriMMirzaeifarRSalehghaffariSNew insights into the collapsing of cylindrical thin-walled tubes under axial impact loadProc Instit Mech Eng Part C-J Mech Eng Sci200722186988510.1243/09544062JMES562 – reference: ZhangYZhuPChenGLightweight design of automotive front side rail based on robust optimisationThin-Walled Struct20074567067610.1016/j.tws.2007.05.007 – reference: Lee Y, Ahn J-S, Park G Crash optimization of automobile frontal and side structures using equivalent static loads.In: 11th World Congress on Structural and Multidisciplinary Optimization, Sydney, NSW, Australia, 2015 – reference: PanFZhuPLightweight design of vehicle front-end structure: contributions of multiple surrogatesInt J Veh Des20115712414710.1504/IJVD.2011.044718 – reference: ZabarasNGanapathysubramanianSLiQA continuum sensitivity method for the design of multi-stage metal forming processesInt J Mech Sci2003453253581116.7440510.1016/S0020-7403(03)00048-1 – reference: ZhangBYangJZhongZOptimisation of vehicle side interior panels for occupant safety in side impactInt J Crashworth20101561762310.1080/13588265.2010.484193 – reference: FarkasLMoensDDondersSVandepitteDOptimisation study of a vehicle bumper subsystem with fuzzy parametersMech Syst Signal Process201232596810.1016/j.ymssp.2011.11.014 – reference: ReyesAHopperstadOHanssenALangsethMModeling of material failure in foam-based componentsInt J Impact Eng20043080583410.1016/j.ijimpeng.2004.03.008 – reference: ChristensenJBastienCBlundellMVBattPABuckling considerations and cross-sectional geometry development for topology optimised body in whiteInt J Crashworth20131831933010.1080/13588265.2013.792442 – reference: CouckuytIDeschrijverDDhaeneTFast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimizationJ Glob Optim20146057559432652461303.9009310.1007/s10898-013-0118-2 – reference: ChenWAllenJKTsuiK-LMistreeFA procedure for robust design: minimizing variations caused by noise factors and control factorsJ Mech Des199611847848510.1115/1.2826915 – reference: SmolaASchölkopfBA tutorial on support vector regressionStat Comput200414199222208639810.1023/B:STCO.0000035301.49549.88 – reference: RedheMForsbergJJanssonTMarklundPONilssonLUsing the response surface methodology and the D-optimality criterion in crashworthiness related problemsStruct Multidisc Optim20022418519410.1007/s00158-002-0228-9 – reference: FuYSahinKHBetter Optimization of Nonlinear Uncertain Systems (BONUS) for vehicle structural designAnn Oper Res200413269841090.9017910.1023/B:ANOR.0000045277.22566.5f – reference: Goel T, Haftka R, Shyy W, Queipo NV (2007) Ensemble of surrogates. Struct Multidisc Optim 33:199–216 – reference: Jansson T, Nilsson L, Redhe M (2003) Using surrogate models and response surfaces in structural optimization – with application to crashworthiness design and sheet metal forming. Struct Multidisc Optim 25:129–140 – reference: JacobGCFellersJFSimunovicSStarbuckJMEnergy absorption in polymer composites for automotive crashworthinessJ Compos Mater20023681385010.1177/0021998302036007164 – reference: CristelloNKimIYMultidisciplinary design optimization of a zero-emission vehicle chassis considering crashworthiness and hydroformabilityProc Instit Mech Eng Part D-J Automobile Eng200722151152610.1243/09544070JAUTO440 – reference: QuXHaftkaRReliability-based design optimization using probabilistic sufficiency factorStruct Multidisc Optim20042731432510.1007/s00158-004-0390-3 – reference: Hunkeler S, Duddeck F, Rayamajhi M, Zimmer H (2013) Shape optimisation for crashworthiness followed by a robustness analysis with respect to shape variables. Struct Multidisc Optim 48:367–378 – reference: ZareiHRKrogerMCrashworthiness optimization of empty and filled aluminum crash boxesInt J Crashworth20071225526410.1080/13588260701441159 – reference: MohammadihaOBeheshtiHOptimization of functionally graded foam-filled conical tubes under axial impact loadingJ Mech Sci Technol2014281741175210.1007/s12206-014-0320-2 – reference: RedheMNilssonLA multipoint version of space mapping optimization applied to vehicle crashworthiness designStruct Multidisc Optim20063113414610.1007/s00158-005-0544-y – reference: ParkinsonASorensenCPourhassanNA general approach for robust optimal designJ Mech Des1993115748010.1115/1.2919328 – reference: VianaFAHaftkaRSteffenVJrMultiple surrogates: how cross-validation errors can help us to obtain the best predictorStruct Multidisc Optim20093943945710.1007/s00158-008-0338-0 – reference: Hamza K, Saitou K (2012) A co-evolutionary approach for design optimization via ensembles of surrogates with application to vehicle crashworthiness. J Mech Design 134 – reference: ChoY-BBaeC-HSuhM-WSinH-CMaximisation of crash energy absorption by crash trigger for vehicle front frame using the homogenisation methodInt J Veh Des200846235010.1504/IJVD.2008.017068 – reference: Haftka R, Villanueva D, Chaudhuri A (2016) Parallel surrogate-assisted global optimization with expensive functions–a survey. Struct Multidisc Optim 54:3–13 – reference: GuptaNKVelmuruganRAxial compression of empty and foam filled composite conical shellsJ Compos Mater19993356759110.1177/002199839903300604 – reference: VianaFCHaftkaRWatsonLEfficient global optimization algorithm assisted by multiple surrogate techniquesJ Glob Optim2013566696891275.9007210.1007/s10898-012-9892-5 – reference: RakhejaSBalikeMHoaSVStudy of an energy dissipative under-ride guard for enhancement of crashworthiness in a car-truck collisionInt J Veh Des199922295310.1504/IJVD.1999.001858 – reference: Chuang C, Yang R (2012) Benchmark of topology optimization methods for crashworthiness design. In: 12th International LS-DYNA Users Conference, Dearborn, Michigan, USA – reference: Zhu P, Pan F, Chen W, Zhang S (2012) Use of support vector regression in structural optimization: application to vehicle crashworthiness design. Math Comput Simul 86:21–31 – reference: Rzesnitzek T, Müllerschön H, Günther FC, Wozniak M (2002) Two-Stage stochastic and deterministic optimization. In: 1st DYNAMORE Users’ Forum, Bad Mergentheim, German – reference: CraigKJStanderNDoogeDAVaradappaSAutomotive crashworthiness design using response surface-based variable screening and optimizationEng Comput20052238611191.7404110.1108/02644400510572406 – reference: Liao X, Li Q, Yang X, Zhang W, Li W (2008b) Multiobjective optimization for crash safety design of vehicles using stepwise regression model. Struct Multidisc Optim 35:561–569 – reference: OrtmannCSchumacherAGraph and heuristic based topology optimization of crash loaded structuresStruct Multidisc Optim2013478398541274.7437410.1007/s00158-012-0872-7 – reference: ZuradaJMIntroduction to artificial neural systems vol 81992St. PaulWest publishing company – reference: YamazakiKHanJMaximization of the crushing energy absorption of tubesStruct Optim199816374610.1007/BF01213998 – reference: Zhou Q, Wu X, Xia Y, Cai W (2014) Spot weld layout optimization of tube crash performance with manufacturing constraints. J Manufact Sci Eng-Trans Asme 136 – reference: AcarESolankiKImproving the accuracy of vehicle crashworthiness response predictions using an ensemble of metamodelsInt J Crashworth200914496110.1080/13588260802462419 – reference: BojanowskiCKulakRFMulti-objective optimisation and sensitivity analysis of a paratransit bus structure for rollover and side impact testsInt J Crashworth20111666567610.1080/13588265.2011.616118 – reference: ForsbergJNilssonLEvaluation of response surface methodologies used in crashworthiness optimizationInt J Impact Eng20063275977710.1016/j.ijimpeng.2005.01.007 – reference: BandiPSchmiedelerJPTovarADesign of crashworthy structures with controlled energy absorption in the hybrid cellular automaton frameworkJ Mech Des201313509100210.1115/1.4024722 – reference: LiangC-CLeG-NBus rollover crashworthiness under European standard: an optimal analysis of superstructure strength using successive response surface methodInt J Crashworth20091462363910.1080/13588260902920670 – reference: HanssenAGLangsethMHopperstadOSStatic and dynamic crushing of circular aluminium extrusions with aluminium foam fillerInt J Impact Eng2000244755070944.7450410.1016/S0734-743X(99)00170-0 – reference: SunGXuFLiGLiQCrashing analysis and multiobjective optimization for thin-walled structures with functionally graded thicknessInt J Impact Eng201464627410.1016/j.ijimpeng.2013.10.004 – reference: AlexanderJAn approximate analysis of the collapse of thin cylindrical shells under axial loadingQuarter J Mech Appl Math19601310151143920096.3950210.1093/qjmam/13.1.10 – reference: NaceurHGuoYQBen-ElechiSResponse surface methodology for design of sheet forming parameters to control springback effectsComput Struct2006841651166310.1016/j.compstruc.2006.04.005 – reference: ZhangXWenZZhangHAxial crushing and optimal design of square tubes with graded thicknessThin-Walled Struct20148426327410.1016/j.tws.2014.07.004 – reference: YangSQiCMultiobjective optimization for empty and foam-filled square columns under oblique impact loadingInt J Impact Eng20135417719110.1016/j.ijimpeng.2012.11.009 – reference: BeyerH-GSendhoffBRobust optimization–a comprehensive surveyComput Methods Appl Mech Eng20071963190321823307741173.7437610.1016/j.cma.2007.03.003 – reference: BisagniCLanziLRicciSOptimization of helicopter subfloor components under crashworthiness requirements using neural networksJ Aircr20023929630410.2514/2.2927 – reference: BlumhardtRFEM - crash simulation and optimizationInt J Veh Des20012633134710.1504/IJVD.2001.005209 – reference: DasIDennisJEA closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problemsStruct Optimization199714636910.1007/BF01197559 – reference: HouSLiQLongSYangXLiWDesign optimization of regular hexagonal thin-walled columns with crashworthiness criteriaFinite Elem Anal Des20074355556510.1016/j.finel.2006.12.008 – reference: Villa A, Strano M, Mussi V (2011) Optimization of Design and Manufacturing Process of Metal Foam Filled Anti-Intrusion Bars. 14th International Conference on Material Forming Esaform, 2011 Proceedings 1353:1656-1661 – reference: Breyfogle III FW (2003) Implementing six sigma: smarter solutions using statistical methods. John Wiley & Sons – reference: AstoriPImpariFCrash response optimisation of helicopter seat and subfloorInt J Crashworth20131857057810.1080/13588265.2013.815602 – reference: Du Bois P et al. (2004) Vehicle crashworthiness and occupant protection – reference: JeongSBYoonSXuSParkGNon-linear dynamic response structural optimization of an automobile frontal structure using equivalent static loadsProc Institution Mech Eng Part D-J Automobile Eng201022448950110.1243/09544070JAUTO1262 – reference: ZhuPShiYLZhangKZLinZQOptimum design of an automotive inner door panel with a tailor-welded blank structureProc Instit Mech Eng Part D-J Automobile Eng20082221337134810.1243/09544070JAUTO763 – reference: GedikliHCrashworthiness optimization of foam-filled tailor-welded tube using coupled finite element and smooth particle hydrodynamics methodThin-Walled Struct201367344810.1016/j.tws.2013.01.020 – reference: ShinMKYiSIKwonOTParkGStructural optimization of the automobile frontal structure for pedestrian protection and the low-speed impact testProc Instit Mech Eng Part D-J Automobile Eng20082222373238710.1243/09544070JAUTO788 – reference: Draper NR, Smith H (1981) Applied regression analysis 2nd ed – reference: SimpsonTWBookerAJGhoshDGiuntaAAKochPNYangRApproximation methods in multidisciplinary analysis and optimization: a panel discussionStruct Multidisc Optim20042730231310.1007/s00158-004-0389-9 – reference: YounBDChoiKKSelecting probabilistic approaches for reliability-based design optimizationAIAA J20044212413110.2514/1.9036 – reference: AhmetogluMABrouwersDShulkinLTaupinLKinzelGLAltanTDeep drawing of round cups from tailor-welded blanksJ Mater Process Technol19955368469410.1016/0924-0136(94)01767-U – reference: HorstemeyerMFRenXCFangHAcarEWangPTA comparative study of design optimisation methodologies for side-impact crashworthiness, using injury-based versus energy-based criterionInt J Crashworth20091412513810.1080/13588260802539489 – reference: Rais-RohaniMSolankiKNAcarEEamonCDShape and sizing optimisation of automotive structures with deterministic and probabilistic design constraintsInt J Veh Des20105430933810.1504/IJVD.2010.036839 – reference: ZareiHKrogerMOptimum honeycomb filled crash absorber designMater Des20082919320410.1016/j.matdes.2006.10.013 – reference: HanssenAGStobenerKRauschGLangsethMKellerHOptimisation of energy absorption of an A-pillar by metal foam insertInt J Crashworth20061123124110.1533/ijcr.2005.0396 – reference: ChenWGOptimisation for minimum weight of foam-filled tubes under large twisting rotationInt J Crashworth2001622324110.1533/cras.2001.0174 – reference: KinseyBLiuZCaoJA novel forming technology for tailor-welded blanksJ Mater Process Technol20009914515310.1016/S0924-0136(99)00412-4 – reference: HuangXXieYMLuGTopology optimization of energy-absorbing structuresInt J Crashworth20071266367510.1080/13588260701497862 – reference: WangGGAdaptive response surface method using inherited latin hypercube design pointsJ Mech Des200312521022010.1115/1.1561044 – reference: Park G (2011) Technical overview of the equivalent static loads method for non-linear static response structural optimization. Struct Multidisc Optim 43:319–337 – reference: BorvikTHopperstadOSReyesALangsethMSolomosGDyngelandTEmpty and foam-filled circular aluminium tubes subjected to axial and oblique quasi-static loadingInt J Crashworth2003848149410.1533/ijcr.2003.0254 – reference: KeaneAJStatistical improvement criteria for use in multiobjective design optimizationAIAA J20064487989110.2514/1.16875 – reference: ZareiHRKrogerMBending behavior of empty and foam-filled beams: structural optimizationInt J Impact Eng20083552152910.1016/j.ijimpeng.2007.05.003 – reference: RamakrishnaSMicrostructural design of composite materials for crashworthy structural applicationsMater Des19971816717310.1016/S0261-3069(97)00098-8 – reference: VianaFASimpsonTWBalabanovVToropovVMetamodeling in multidisciplinary design optimization: how far have we really come?AIAA J20145267069010.2514/1.J052375 – reference: ShiYZhuPShenLLinZLightweight design of automotive front side rails with TWB conceptThin-Walled Struct20074581410.1016/j.tws.2007.01.013 – reference: YounBDChoiKKA new response surface methodology for reliability-based design optimizationComput Struct20048224125610.1016/j.compstruc.2003.09.002 – reference: Stander N An Adaptive Surrogate-Assisted Strategy for Multi-Objective Optimization. In: 10th World Congress on Structural and Multidisciplinary Optimization, Orlando, Florida, USA, 2013. – reference: Acar E, Solanki K (2009b) System reliability based vehicle design for crashworthiness and effects of various uncertainty reduction measures. Struct Multidisc Optim 39:311–325 – reference: SeitzbergerMRammerstorferFGGradingerRDegischerHPBlaimscheinMWalchCExperimental studies on the quasi-static axial crushing of steel columns filled with aluminium foamInt J Solids Struct2000374125414710.1016/S0020-7683(99)00136-5 – reference: KochPNSimpsonTWAllenJKMistreeFStatistical approximations for multidisciplinary design optimization: the problem of sizeJ Aircr19993627528610.2514/2.2435 – reference: LeeIChoiKKNohYZhaoLGorsichDSampling-based stochastic sensitivity analysis using score functions for RBDO problems with correlated random variablesJ Mech Des201113302100310.1115/1.4003186 – reference: ShiLZhuPYangR-JLinS-PAdaptive sampling-based RBDO method for vehicle crashworthiness design using Bayesian metric and stochastic sensitivity analysis with independent random variablesInt J Crashworth20131833134210.1080/13588265.2013.793262 – reference: YangRTsengLNagyLChengJFeasibility study of crash optimizationASME19942549556 – reference: ZerpaLEQueipoNVPintosSSalagerJ-LAn optimization methodology of alkaline–surfactant–polymer flooding processes using field scale numerical simulation and multiple surrogatesJ Pet Sci Eng20054719720810.1016/j.petrol.2005.03.002 – reference: O’NeillBPreventing passenger vehicle occupant injuries by vehicle design—a historical perspective from IIHSTraffic Injury Prevent20091011312610.1080/15389580802486225 – reference: FangJGaoYAnXSunGChenJLiQDesign of transversely-graded foam and wall thickness structures for crashworthiness criteriaCompos Part B20169233834910.1016/j.compositesb.2016.02.006 – reference: BaeGHHuhHComparison of the optimum designs of center pillar assembly of an auto-body between conventional steel and ahss with a simplified side impact analysisInt J Automot Technol20121320521310.1007/s12239-012-0017-4 – reference: ShiQHagiwaraIOptimal design method to automobile problems using holographic neural network’s approximationJpn J Ind Appl Math20001732133917941741306.6516210.1007/BF03167370 – reference: ZhangYSunGXuXLiGLiQMultiobjective crashworthiness optimization of hollow and conical tubes for multiple load casesThin-Walled Struct20148233134210.1016/j.tws.2014.05.006 – reference: HouSLiQLongSYangXLiWCrashworthiness design for foam filled thin-wall structuresMater Des2009302024203210.1016/j.matdes.2008.08.044 – reference: BarilCYacoutSClementBDesign for six sigma through collaborative multiobjective optimizationComput Ind Eng201160435510.1016/j.cie.2010.09.015 – reference: SinhaKKrishnanRRaghavendraDMulti-objective robust optimisation for crashworthiness during side impactInt J Veh Des20074311613510.1504/IJVD.2007.012299 – reference: SeitzbergerMRammerstorferFGDegischerHPGradingerRCrushing of axially compressed steel tubes filled with aluminium foamActa Mech1997125931051071.7468710.1007/BF01177301 – reference: LiuYOptimum design of straight thin-walled box section beams for crashworthiness analysisFinite Elem Anal Des20084413914710.1016/j.finel.2007.11.003 – reference: Goel T, Stander N, Lin Y-Y (2010) Efficient resource allocation for genetic algorithm based multi-objective optimization with 1,000 simulations. Struct Multidisc Optim 41:421–432 – reference: LiuYCrashworthiness design of thin-walled curved beams with box and channel cross sectionsInt J Crashworth20101541342310.1080/13588261003647410 – reference: FangJGaoYSunGZhengGLiQDynamic crashing behavior of new extrudable multi-cell tubes with a functionally graded thicknessInt J Mech Sci2015103637310.1016/j.ijmecsci.2015.08.029 – reference: HouSHanXSunGLongSLiWYangXLiQMultiobjective optimization for tapered circular tubesThin-Walled Struct20114985586310.1016/j.tws.2011.02.010 – reference: YinHWenGLiuZQingQCrashworthiness optimization design for foam-filled multi-cell thin-walled structuresThin-Walled Struct20147581710.1016/j.tws.2013.10.022 – reference: Ramu P, Kim NH, Haftka R (2007) Error amplification in failure probability estimates of small errors in surrogates. In: SAE 2007 World Congress. Detroit, Michigan, USA – reference: HouSZhangZYangXYinHLiQCrashworthiness optimization of new thin-walled cellular configurationsEng Comput20143144 – reference: PazJDíazJRomeraLCostasMCrushing analysis and multi-objective crashworthiness optimization of GFRP honeycomb-filled energy absorption devicesFinite Elem Anal Des201491303910.1016/j.finel.2014.07.006 – reference: EsfahlaniSSShirvaniHShirvaniANwaubaniSMebrahtuHChirwaCHexagonal honeycomb cell optimisation by way of meta-model techniquesInt J Crashworth20131826427510.1080/13588265.2013.776337 – reference: KimHSAnalysis of crash response of aluminium foam-filled front side rail of a passenger carInt J Crashworth2001618920710.1533/cras.2001.0172 – reference: Hou S, Dong D, Ren L, Han X (2012) Multivariable crashworthiness optimization of vehicle body by unreplicated saturated factorial design. Struct Multidisc Optim 46:891–905 – reference: YinHWenGGanNCrashworthiness design for honeycomb structures under axial dynamic loadingInt J Comput Methods2011886387710.1142/S0219876211002885 – reference: LönnDBergmanGNilssonLSimonssonKExperimental and finite element robustness studies of a bumper system subjected to an offset impact loadingInt J Crashworth20111615516810.1080/13588265.2010.539339 – reference: WierzbickiTAbramowiczWOn the crushing mechanics of thin-walled structuresJ Appl Mech-T Asme1983507277340528.7304510.1115/1.3167137 – reference: NajafiARais-RohaniMSequential coupled process-performance simulation and multi-objective optimization of thin-walled tubesMater Des201241899810.1016/j.matdes.2012.03.057 – reference: XuFSunGLiGLiQCrashworthiness design of multi-component tailor-welded blank (TWB) structuresStruct Multidisc Optim20134865366710.1007/s00158-013-0916-7 – reference: HohenbichlerMRackwitzRFirst-order concepts in system reliabilityStruct Saf1982117718810.1016/0167-4730(82)90024-8 – reference: HouSTanWZhengYHanXLiQOptimization design of corrugated beam guardrail based on RBF-MQ surrogate model and collision safety considerationAdv Eng Softw201478284010.1016/j.advengsoft.2014.08.002 – reference: SongXSunGLiGGaoWLiQCrashworthiness optimization of foam-filled tapered thin-walled structure using multiple surrogate modelsStruct Multidisc Optim20134722123130389161274.7429310.1007/s00158-012-0820-6 – reference: OmanMNilssonLStructural optimization of product families subjected to multiple crash load casesStruct Multidisc Optim20104179781510.1007/s00158-009-0471-4 – reference: LeeS-JLeeH-AYiS-IKimD-SYangHWParkGDesign flow for the crash box in a vehicle to maximize energy absorptionProc Inst Mech Eng Part D-J Automobile Eng201322717920010.1177/0954407012451545 – reference: TranTHouSHanXTanWNguyenNTheoretical prediction and crashworthiness optimization of multi-cell triangular tubesThin-Walled Struct20148218319510.1016/j.tws.2014.03.019 – reference: TovarAPatelNMKaushikAKRenaudJEOptimality conditions of the hybrid cellular automata for structural optimizationAIAA J20074567368310.2514/1.20184 – reference: YounBDChoiKKYangRGuLReliability-based design optimization for crashworthiness of vehicle side impactStruct Multidisc Optim20042627228310.1007/s00158-003-0345-0 – reference: KimHSChenWWierzbickiTWeight and crash optimization of foam-filled three-dimensional “S” frameComput Mech2002284174241002.7457110.1007/s00466-002-0306-2 – reference: AbramowiczWJonesNDynamic axial crushing of square tubesInt J Impact Eng1984217920810.1016/0734-743X(84)90005-8 – reference: ShiLYangRZhuPAn adaptive response surface method for crashworthiness optimizationEng Optim2013451365137710.1080/0305215X.2012.734815 – reference: MessacAPuemi-SukamCMelachrinoudisEAggregate objective functions and Pareto frontiers: required relationships and practical implicationsOptim Eng2000117118819199160992.9006210.1023/A:1010035730904 – reference: NajafiAAcarERais-RohaniMMulti-objective robust design of energy-absorbing components using coupled process–performance simulationsEng Optim20144614616410.1080/0305215X.2012.753437 – reference: IngrassiaTNigrelliVButtittaRA comparison of simplex and simulated annealing for optimization of a new rear underrun protective deviceEng Comput20132934535810.1007/s00366-012-0270-1 – reference: Viana FAC, Haftka R, Steffen V (2009b) Multiple surrogates: how cross-validation errors can help us to obtain the best predictor. Struct Multidisc Optim 39:439–457 – reference: ZareiHKrögerMAlbertsenHAn experimental and numerical crashworthiness investigation of thermoplastic composite crash boxesCompos Struct20088524525710.1016/j.compstruct.2007.10.028 – reference: ParrishARais-RohaniMNajafiACrashworthiness optimisation of vehicle structures with magnesium alloy partsInt J Crashworth20121725928110.1080/13588265.2011.648518 – reference: SantosaSPWierzbickiTHanssenAGLangsethMExperimental and numerical studies of foam-filled sectionsInt J Impact Eng20002450953410.1016/S0734-743X(99)00036-6 – reference: Bishop CM (1995) Neural networks for pattern recognition. Oxford university press – reference: SinhaKReliability-based multiobjective optimization for automotive crashworthiness and occupant safetyStruct Multidisc Optim20073325526810.1007/s00158-006-0050-x – reference: LiuYDesign optimisation of tapered thin-walled square tubesInt J Crashworth20081354355010.1080/13588260802222102 – reference: KurtaranHEskandarianAMarzouguiDBedewiNECrashworthiness design optimization using successive response surface approximationsComput Mech2002294094211146.7434810.1007/s00466-002-0351-x – reference: SunGSongXBaekSLiQRobust optimization of foam-filled thin-walled structure based on sequential Kriging metamodelStruct Multidisc Optim20144989791310.1007/s00158-013-1017-3 – reference: PedersenCBWTopology optimization design of crushed 2D-frames for desired energy absorption historyStruct Multidisc Optim20032536838210.1007/s00158-003-0282-y – reference: TuJChoiKKParkYHA new study on reliability-based design optimizationJ Mech Des199912155756410.1115/1.2829499 – reference: Xu H, Majcher MT, Chuang C, Fu Y, Yang R (2014) Comparative benchmark studies of response surface model-based optimization and direct multidisciplinary design optimization. SAE Technical Paper – reference: MarzbanradJEbrahimiMRMulti-objective optimization of aluminum hollow tubes for vehicle crash energy absorption using a genetic algorithm and neural networksThin-Walled Struct2011491605161510.1016/j.tws.2011.08.009 – reference: Hou S, Liu T, Dong D, Han X (2014a) Factor screening and multivariable crashworthiness optimization for vehicle side impact by factorial design. Struct Multidisc Optim 49:147–167 – reference: ZareiHRKrogerMOptimization of the foam-filled aluminum tubes for crush box applicationThin-Walled Struct20084621422110.1016/j.tws.2007.07.016 – reference: ToksoyAKGüdenMThe optimisation of the energy absorption of partially Al foam-filled commercial 1050H14 and 6061T4 Al crash boxesInt J Crashworth2011169710910.1080/13588265.2010.514774 – reference: KangBChoiWParkGStructural optimization under equivalent static loads transformed from dynamic loads based on displacementComput Struct20017914515410.1016/S0045-7949(00)00127-9 – reference: MarsolekJReimerdesHGEnergy absorption of metallic cylindrical shells with induced non-axisymmetric folding patternsInt J Impact Eng2004301209122310.1016/j.ijimpeng.2004.06.006 – reference: Zhu F, Jiang B, Chou CC (2016) On the development of a new design methodology for vehicle crashworthiness based on data mining theory. SAE Technical Paper – reference: HouSLiQLongSYangaXLiWMultiobjective optimization of multi-cell sections for the crashworthiness designInt J Impact Eng2008351355136710.1016/j.ijimpeng.2007.09.003 – reference: CoelloCACPulidoGTLechugaMSHandling multiple objectives with particle swarm optimizationEvol Comput, IEEE Trans2004825627910.1109/TEVC.2004.826067 – reference: CostasMDíazJRomeraLHernándezSA multi-objective surrogate-based optimization of the crashworthiness of a hybrid impact absorberInt J Mech Sci201488465410.1016/j.ijmecsci.2014.07.002 – reference: FangJGaoYSunGZhangYLiQParametric analysis and multiobjective optimization for functionally graded foam-filled thin-wall tube under lateral impactComput Mater Sci20149026527510.1016/j.commatsci.2014.03.044 – reference: ZhangZLiuSTangZDesign optimization of cross-sectional configuration of rib-reinforced thin-walled beamThin-Walled Struct20094786887810.1016/j.tws.2009.02.009 – reference: LiuYThin-walled curved hexagonal beams in crashes - FEA and designInt J Crashworth20101515115910.1080/13588260903094400 – reference: Wang H, Shan S, Wang GG, Li G (2011b) Integrating least square support vector regression and mode pursuing sampling optimization for crashworthiness design. J Mech Des 133 – reference: ZhangSZhuPChenWArendtPConcurrent treatment of parametric uncertainty and metamodeling uncertainty in robust designStruct Multidisc Optim201347637630389281274.7430110.1007/s00158-012-0805-5 |
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| SubjectTerms | Algorithms Computational Mathematics and Numerical Analysis Crashworthiness Design criteria Design optimization Energy absorption Engineering Engineering Design Impact strength Industrial applications Multiple objective analysis Public safety Review Article Theoretical and Applied Mechanics Topology optimization |
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