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 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.

[1]  J. M. Alexander AN APPROXIMATE ANALYSIS OF THE COLLAPSE OF THIN CYLINDRICAL SHELLS UNDER AXIAL LOADING , 1960 .

[2]  R. L. Hardy Multiquadric equations of topography and other irregular surfaces , 1971 .

[3]  Norman R. Draper,et al.  Applied regression analysis (2. ed.) , 1981, Wiley series in probability and mathematical statistics.

[4]  R. Rackwitz,et al.  First-order concepts in system reliability , 1982 .

[5]  T. Wierzbicki,et al.  On the Crushing Mechanics of Thin-Walled Structures , 1983 .

[6]  W. Abramowicz,et al.  Dynamic axial crushing of square tubes , 1984 .

[7]  S. Reid,et al.  Static and dynamic crushing of tapered sheet metal tubes of rectangular cross-section , 1986 .

[8]  Norman Jones,et al.  Dynamic progressive buckling of circular and square tubes , 1986 .

[9]  T. Wierzbicki,et al.  Axial Crushing of Multicorner Sheet Metal Columns , 1989 .

[10]  G. Geoffrey Vining,et al.  Combining Taguchi and Response Surface Philosophies: A Dual Response Approach , 1990 .

[11]  J. Friedman Multivariate adaptive regression splines , 1990 .

[12]  Carl D. Sorensen,et al.  A general approach for robust optimal design , 1993 .

[13]  Taylan Altan,et al.  Deep drawing of round cups from tailor-welded blanks , 1995 .

[14]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[15]  Noboru Kikuchi,et al.  APPLICATION OF TOPOLOGICAL OPTIMIZATION TECHNIQUES TO STRUCTURAL CRASHWORTHINESS , 1996 .

[16]  J. Dennis,et al.  A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems , 1997 .

[17]  Farrokh Mistree,et al.  A procedure for robust design: Minimizing variations caused by noise factors and control factors , 1996 .

[18]  Prabhat Hajela,et al.  Topological optimization of rotorcraft subfloor structures for crashworthiness considerations , 1997 .

[19]  S. Ramakrishna MICROSTRUCTURAL DESIGN OF COMPOSITE MATERIALS FOR CRASHWORTHY STRUCTURAL APPLICATIONS , 1997 .

[20]  William J. Welch,et al.  Computer experiments and global optimization , 1997 .

[21]  F. Rammerstorfer,et al.  Crushing of axially compressed steel tubes filled with aluminium foam , 1997 .

[22]  Koetsu Yamazaki,et al.  Maximization of the crushing energy absorption of tubes , 1998 .

[23]  Gyung-Jin Park,et al.  Transformation of dynamic loads into equivalent static loads based on modal analysis , 1999 .

[24]  Forrest W. Iii Breyfogle Implementing Six Sigma: Smarter Solutions Using Statistical Methods , 1999 .

[25]  Subhash Rakheja,et al.  Study of an energy dissipative under-ride guard for enhancement of crashworthiness in a car-truck collision , 1999 .

[26]  N. Gupta,et al.  Axial Compression of Empty and Foam Filled Composite Conical Shells , 1999 .

[27]  Kyung K. Choi,et al.  A NEW STUDY ON RELIABILITY-BASED DESIGN OPTIMIZATION , 1999 .

[28]  Farrokh Mistree,et al.  Statistical Approximations for Multidisciplinary Design Optimization: The Problem of Size , 1999 .

[29]  Glynn J. Sundararaj,et al.  Ability of Objective Functions to Generate Points on Nonconvex Pareto Frontiers , 2000 .

[30]  Jian Cao,et al.  A novel forming technology for tailor-welded blanks , 2000 .

[31]  A. Messac,et al.  Aggregate Objective Functions and Pareto Frontiers: Required Relationships and Practical Implications , 2000 .

[32]  T. Wierzbicki,et al.  Experimental and numerical studies of foam-filled sections , 2000 .

[33]  Ren-Jye Yang,et al.  Robustness optimization for vehicular crash simulations , 2000, Comput. Sci. Eng..

[34]  M. Avalle,et al.  Maximisation of the crushing performance of a tubular device by shape optimisation , 2000 .

[35]  F. Rammerstorfer,et al.  Experimental studies on the quasi-static axial crushing of steel columns filled with aluminium foam , 2000 .

[36]  O. Hopperstad,et al.  Static and dynamic crushing of square aluminium extrusions with aluminium foam filler , 2000 .

[37]  Ichiro Hagiwara,et al.  Optimal design method to automobile problems using holographic neural network’s approximation , 2000 .

[38]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[39]  Ren-Jye Yang,et al.  Metamodeling development for vehicle frontal impact simulation , 2001, DAC 2001.

[40]  Gyung-Jin Park,et al.  Structural optimization under equivalent static loads transformed from dynamic loads based on displacement , 2001 .

[41]  Hyoung-Soo Kim Analysis of crash response of aluminium foam-filled front side rail of a passenger car , 2001 .

[42]  O. Hopperstad,et al.  Optimum design for energy absorption of square aluminium columns with aluminium foam filler , 2001 .

[43]  Larsgunnar Nilsson,et al.  Optimization of a car body component subjected to side impact , 2001 .

[44]  R Blumhardt FEM - crash simulation and optimization , 2001 .

[45]  Weigang Chen,et al.  Optimisation for minimum weight of foam-filled tubes under large twisting rotation , 2001 .

[46]  Xiaoping Du,et al.  The use of metamodeling techniques for optimization under uncertainty , 2001 .

[47]  Yun Li,et al.  Optimization and robustness for crashworthiness of side impact , 2001 .

[48]  J. Jeswiet,et al.  Tensile testing for weld deformation properties in similar gage tailor welded blanks using the rule of mixtures , 2001 .

[49]  T. Simpson,et al.  Comparative studies of metamodelling techniques under multiple modelling criteria , 2001 .

[50]  Sergio Ricci,et al.  Optimization of Helicopter Subfloor Components Under Crashworthiness Requirements Using Neural Networks , 2002 .

[51]  Hasan Kurtaran,et al.  Crashworthiness design optimization using successive response surface approximations , 2002 .

[52]  Jiju Antony,et al.  Design for six sigma: a breakthrough business improvement strategy for achieving competitive advantage , 2002 .

[53]  J. M. Starbuck,et al.  Energy Absorption in Polymer Composites for Automotive Crashworthiness , 2002 .

[54]  Massimiliano Avalle,et al.  Design optimization by response surface methodology: application to crashworthiness design of vehicle structures , 2002 .

[55]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[56]  Guy S. Nusholtz,et al.  Optimization of Vehicle Crash Pulses in Relative Displacement Domain , 2002 .

[57]  Soo-Ik Oh,et al.  Cylindrical tube optimization using response surface method based on stochastic process , 2002 .

[58]  Tomasz Wierzbicki,et al.  Weight and crash optimization of foam-filled three-dimensional “S” frame , 2002 .

[59]  Tomas Jansson,et al.  Using the response surface methodology and the D-optimality criterion in crashworthiness related problems , 2002 .

[60]  Heung-Soo Kim,et al.  New extruded multi-cell aluminum profile for maximum crash energy absorption and weight efficiency , 2002 .

[61]  J. Han,et al.  Crashworthiness optimization of S-shape square tubes , 2003 .

[62]  G. Park,et al.  Determination of the crash pulse and optimization of the crash components using the response surface approximate optimization , 2003 .

[63]  Claus B. W. Pedersen,et al.  Topology optimization design of crushed 2D-frames for desired energy absorption history , 2003 .

[64]  C B W Pedersen Topology optimization for crashworthiness of frame structures , 2003 .

[65]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[66]  N. Zabaras,et al.  A continuum sensitivity method for the design of multi-stage metal forming processes , 2003 .

[67]  Tomas Jansson,et al.  Using surrogate models and response surfaces in structural optimization – with application to crashworthiness design and sheet metal forming , 2003 .

[68]  G. G. Wang,et al.  Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points , 2003 .

[69]  G. Solomos,et al.  Empty and foam-filled circular aluminium tubes subjected to axial and oblique quasistatic loading , 2003 .

[70]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[71]  Kyung K. Choi,et al.  Reliability-based design optimization for crashworthiness of vehicle side impact , 2004 .

[72]  Jorge Ambrósio,et al.  Design of train crash experimental tests by optimization procedures , 2004 .

[73]  Ren-Jye Yang,et al.  Design for six sigma through robust optimization , 2004 .

[74]  Marcus Redhe,et al.  Optimization of the new Saab 9-3 exposed to impact load using a space mapping technique , 2004 .

[75]  Sergio Ricci,et al.  Crashworthiness optimization of helicopter subfloor based on decomposition and global approximation , 2004 .

[76]  Claus B. W. Pedersen,et al.  Crashworthiness design of transient frame structures using topology optimization , 2004 .

[77]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[78]  Ciro A. Soto,et al.  Structural topology optimization for crashworthiness , 2004 .

[79]  Stephen J. Leary,et al.  A parallel updating scheme for approximating and optimizing high fidelity computer simulations , 2004 .

[80]  R. Haftka,et al.  Reliability-based design optimization using probabilistic sufficiency factor , 2004 .

[81]  O. Hopperstad,et al.  Modeling of material failure in foam-based components , 2004 .

[82]  Marcus Redhe,et al.  An investigation of structural optimization in crashworthiness design using a stochastic approach , 2004 .

[83]  Marco Anghileri,et al.  Multi-objective optimisation of composite absorber shape under crashworthiness requirements , 2004 .

[84]  J. Marsolek,et al.  Energy absorption of metallic cylindrical shells with induced non-axisymmetric folding patterns , 2004 .

[85]  Ren-Jye Yang,et al.  Approximation methods in multidisciplinary analysis and optimization: a panel discussion , 2004 .

[86]  Yan Fu,et al.  Better Optimization of Nonlinear Uncertain Systems (BONUS) for Vehicle Structural Design , 2004, Ann. Oper. Res..

[87]  Kyung K. Choi,et al.  A new response surface methodology for reliability-based design optimization , 2004 .

[88]  Kyung K. Choi,et al.  Selecting probabilistic approaches for reliability-based design optimization , 2004 .

[89]  Salvador Pintos,et al.  An Optimization Methodology of Alkaline-Surfactant-Polymer Flooding Processes Using Field Scale Numerical Simulation and Multiple Surrogates , 2005 .

[90]  Prospero C. Naval,et al.  An effective use of crowding distance in multiobjective particle swarm optimization , 2005, GECCO '05.

[91]  Masoud Rais-Rohani,et al.  A comparative study of metamodeling methods for multiobjective crashworthiness optimization , 2005 .

[92]  Ken J. Craig,et al.  Automotive crashworthiness design using response surface‐based variable screening and optimization , 2005 .

[93]  Andy J. Keane,et al.  Statistical Improvement Criteria for Use in Multiobjective Design Optimization , 2006 .

[94]  Marcus Redhe,et al.  A multipoint version of space mapping optimization applied to vehicle crashworthiness design , 2006 .

[95]  Tae Hee Lee,et al.  Robust Design: An Overview , 2006 .

[96]  Larsgunnar Nilsson,et al.  Evaluation of response surface methodologies used in crashworthiness optimization , 2006 .

[97]  Yujiang Xiang,et al.  Optimal crashworthiness design of a spot-welded thin-walled hat section , 2006 .

[98]  Y. Guo,et al.  Response surface methodology for design of sheet forming parameters to control springback effects , 2006 .

[99]  L. Nilsson,et al.  Topology optimization in crashworthiness design , 2006 .

[100]  Jon C. Helton,et al.  Survey of sampling-based methods for uncertainty and sensitivity analysis , 2006, Reliab. Eng. Syst. Saf..

[101]  A G Hanssen,et al.  Optimisation of energy absorption of an A-pillar by metal foam insert , 2006 .

[102]  H. R. Zarei,et al.  Multiobjective crashworthiness optimization of circular aluminum tubes , 2006 .

[103]  H. Sin,et al.  A vehicle front frame crash design optimization using hole-type and dent-type crush initiator , 2006 .

[104]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007 .

[105]  Qing Li,et al.  Design optimization of regular hexagonal thin-walled columns with crashworthiness criteria , 2007 .

[106]  Ping Zhu,et al.  Lightweight Design of Automotive Front Side Rail Based on Robust Optimisation , 2007 .

[107]  Massimiliano Avalle,et al.  Optimisation of a vehicle energy absorbing steel component with experimental validation , 2007 .

[108]  Kaushik Sinha,et al.  Reliability-based multiobjective optimization for automotive crashworthiness and occupant safety , 2007 .

[109]  Bernhard Sendhoff,et al.  Robust Optimization - A Comprehensive Survey , 2007 .

[110]  J. Renaud,et al.  Optimality Conditions of the Hybrid Cellular Automata for Structural Optimization , 2007 .

[111]  Ping Zhu,et al.  Study on Structural Lightweight Design of Automotive Front Side Rail Based on Response Surface Method , 2007 .

[112]  Il Yong Kim,et al.  Multidisciplinary design optimization of a zero-emission vehicle chassis considering crashworthiness and hydroformability , 2007 .

[113]  H. Zarei,et al.  Crashworthiness optimization of empty and filled aluminum crash boxes , 2007 .

[114]  Kaushik Sinha,et al.  Multi-objective robust optimisation for crashworthiness during side impact , 2007 .

[115]  R. Haftka,et al.  Error Amplification in Failure Probability Estimates of Small Errors in Surrogates , 2007 .

[116]  G. Park,et al.  Optimization of structures with nonlinear behavior using equivalent loads , 2007 .

[117]  Yi Min Xie,et al.  Topology optimization of energy-absorbing structures , 2007 .

[118]  R. Haftka,et al.  Ensemble of surrogates , 2007 .

[119]  Ping Zhu,et al.  Lightweight design of automotive front side rails with TWB concept , 2007 .

[120]  R. Haftka,et al.  Error Amplification in Failure Probability Estimates of Small Errors in Response Surface Approximations , 2007 .

[121]  Mahmoud Shakeri,et al.  New insights into the collapsing of cylindrical thin-walled tubes under axial impact load , 2007 .

[122]  Yunbo Liu Design optimisation of tapered thin-walled square tubes , 2008 .

[123]  P. Pothuraju,et al.  Multidisciplinary design optimization on vehicle tailor rolled blank design , 2008 .

[124]  Fabian Duddeck,et al.  Multidisciplinary optimization of car bodies , 2008 .

[125]  H. R. Zarei,et al.  Optimization of the foam-filled aluminum tubes for crush box application , 2008 .

[126]  Yucheng Liu,et al.  Crashworthiness design of multi-corner thin-walled columns , 2008 .

[127]  Gyung-Jin Park,et al.  Structural optimization of the automobile frontal structure for pedestrian protection and the low-speed impact test , 2008 .

[128]  Andy J. Keane,et al.  Engineering Design via Surrogate Modelling - A Practical Guide , 2008 .

[129]  H. Zarei,et al.  An experimental and numerical crashworthiness investigation of thermoplastic composite crash boxes , 2008 .

[130]  Wei Li,et al.  Multiobjective optimization of multi-cell sections for the crashworthiness design , 2008 .

[131]  M. Kröger,et al.  Bending behavior of empty and foam-filled beams: Structural optimization , 2008 .

[132]  Baojin Wang,et al.  Optimum design for energy absorption of bitubal hexagonal columns with honeycomb core , 2008 .

[133]  H. Zarei,et al.  Optimum honeycomb filled crash absorber design , 2008 .

[134]  Yong-Beom Cho,et al.  Maximisation of crash energy absorption by crash trigger for vehicle front frame using the homogenisation method , 2008 .

[135]  Yucheng Liu,et al.  Optimum design of straight thin-walled box section beams for crashworthiness analysis , 2008 .

[136]  Qing Li,et al.  Multiobjective optimization for crash safety design of vehicles using stepwise regression model , 2008 .

[137]  Gyung-Jin Park,et al.  Structural optimization of an automobile roof structure using equivalent static loads , 2008 .

[138]  Z.-Q. Lin,et al.  Optimum design of an automotive inner door panel with a tailor-welded blank structure , 2008 .

[139]  Qiang Li,et al.  A two-stage multi-objective optimisation of vehicle crashworthiness under frontal impact , 2008 .

[140]  Shutian Liu,et al.  Design optimization of cross-sectional configuration of rib-reinforced thin-walled beam , 2009 .

[141]  Wei Li,et al.  Crashworthiness design for foam filled thin-wall structures , 2009 .

[142]  Larsgunnar Nilsson,et al.  Finite element based robustness study of a truck cab subjected to impact loading , 2009 .

[143]  Ping Zhu,et al.  Metamodel-based lightweight design of an automotive front-body structure using robust optimization , 2009 .

[144]  M. Rais-Rohani,et al.  Ensemble of metamodels with optimized weight factors , 2008 .

[145]  Kiran Solanki,et al.  System reliability based vehicle design for crashworthiness and effects of various uncertainty reduction measures , 2009 .

[146]  Cho-Chung Liang,et al.  Bus rollover crashworthiness under European standard: an optimal analysis of superstructure strength using successive response surface method , 2009 .

[147]  Mark F. Horstemeyer,et al.  A comparative study of design optimisation methodologies for side-impact crashworthiness, using injury-based versus energy-based criterion , 2009 .

[148]  Kiran Solanki,et al.  Improving the accuracy of vehicle crashworthiness response predictions using an ensemble of metamodels , 2009 .

[149]  R. Haftka,et al.  Multiple surrogates: how cross-validation errors can help us to obtain the best predictor , 2009 .

[150]  Brian O'Neill,et al.  Preventing Passenger Vehicle Occupant Injuries by Vehicle Design—A Historical Perspective from IIHS , 2009, Traffic injury prevention.

[151]  Andy J. Keane,et al.  Recent advances in surrogate-based optimization , 2009 .

[152]  John E. Renaud,et al.  Crashworthiness Design Using Topology Optimization , 2009 .

[153]  Yucheng Liu Crashworthiness design of thin-walled curved beams with box and channel cross sections , 2010 .

[154]  Hu Wang,et al.  Time-based metamodeling technique for vehicle crashworthiness optimization , 2010 .

[155]  Stijn Donders,et al.  Optimisation study of a vehicle bumper subsystem with fuzzy parameters , 2010 .

[156]  Ping Zhu,et al.  Metamodel-based lightweight design of B-pillar with TWB structure via support vector regression , 2010 .

[157]  Necmettin Kaya,et al.  Multi-objective crashworthiness design optimisation of thin-walled tubes , 2010 .

[158]  Yucheng Liu Thin-walled curved hexagonal beams in crashes – FEA and design , 2010 .

[159]  Z. Jiang,et al.  Optimization of a fender structure for the crashworthiness design , 2010 .

[160]  Erdem Acar,et al.  Optimizing the shape parameters of radial basis functions: An application to automobile crashworthiness , 2010 .

[161]  Shiwei Zhou,et al.  Crashworthiness design for functionally graded foam-filled thin-walled structures , 2010 .

[162]  Nielen Stander,et al.  Efficient resource allocation for genetic algorithm based multi-objective optimization with 1,000 simulations , 2010 .

[163]  Zhihua Zhong,et al.  Optimisation of vehicle side interior panels for occupant safety in side impact , 2010 .

[164]  David Lönn,et al.  An approach to robust optimization of impact problems using random samples and meta-modelling , 2010 .

[165]  Mahmoud Shariati,et al.  Optimization of foam filled spot-welded column for the crashworthiness design , 2010 .

[166]  Qian Wang,et al.  Modeling and optimization of foam-filled thin-walled columns for crashworthiness designs , 2010 .

[167]  E. Acar Various approaches for constructing an ensemble of metamodels using local measures , 2010 .

[168]  Masoud Rais-Rohani,et al.  Shape and sizing optimisation of automotive structures with deterministic and probabilistic design constraints , 2010 .

[169]  L. Nilsson,et al.  Structural optimization of product families subjected to multiple crash load cases , 2010 .

[170]  E. Olevsky,et al.  Energy absorbent natural materials and bioinspired design strategies: A review , 2010 .

[171]  Bahram Notghi,et al.  Reliability-based robust multi-objective crashworthiness optimisation of S-shaped box beams with parametric uncertainties , 2010 .

[172]  Gyung-Jin Park,et al.  Non-linear dynamic response structural optimization of an automobile frontal structure using equivalent static loads , 2010 .

[173]  Qing Li,et al.  A two-stage multi-fidelity optimization procedure for honeycomb-type cellular materials , 2010 .

[174]  Xu Han,et al.  Multiobjective optimization for tapered circular tubes , 2011 .

[175]  H. R. Allahbakhsh,et al.  Design optimization of square and circular aluminium extrusion damage columns with crashworthiness criteria , 2011 .

[176]  Yu Zhang,et al.  Metamodeling development for reliability-based design optimization of automotive body structure , 2011, Comput. Ind..

[177]  K. Choi,et al.  Sampling-Based Stochastic Sensitivity Analysis Using Score Functions for RBDO Problems with Correlated Random Variables , 2011, DAC 2010.

[178]  Ping Zhu,et al.  Lightweight design of vehicle front–end structure: contributions of multiple surrogates , 2011 .

[179]  M. Strano,et al.  Optimization of Design and Manufacturing Process of Metal Foam Filled Anti-Intrusion Bars , 2011 .

[180]  Guangyao Li,et al.  Crashworthiness design of vehicle by using multiobjective robust optimization , 2011 .

[181]  John E. Renaud,et al.  Strain-based topology optimisation for crashworthiness using hybrid cellular automata , 2011 .

[182]  Michel van Tooren,et al.  Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles , 2011 .

[183]  E. Acar,et al.  Multi-objective crashworthiness optimization of tapered thin-walled tubes with axisymmetric indentations , 2011 .

[184]  Guilin Wen,et al.  CRASHWORTHINESS DESIGN FOR HONEYCOMB STRUCTURES UNDER AXIAL DYNAMIC LOADING , 2011 .

[185]  Xiao Jian Zhou,et al.  Ensemble of surrogates with recursive arithmetic average , 2011 .

[186]  Gyung-Jin Park,et al.  Technical overview of the equivalent static loads method for non-linear static response structural optimization , 2011 .

[187]  Javad Marzbanrad,et al.  Multi-Objective Optimization of aluminum hollow tubes for vehicle crash energy absorption using a genetic algorithm and neural networks , 2011 .

[188]  Allen Sheldon,et al.  Investigation and Application of Multi-Disciplinary Optimization for Automotive Body-in-White Development , 2011 .

[189]  Hu Wang,et al.  Probability-based least square support vector regression metamodeling technique for crashworthiness optimization problems , 2011 .

[190]  H. R. Allahbakhsh,et al.  Design optimization of square aluminium damage columns with crashworthiness criteria , 2011 .

[191]  G. Wen,et al.  Crushing analysis and multiobjective crashworthiness optimization of honeycomb-filled single and bitubular polygonal tubes , 2011 .

[192]  Liangjin Gui,et al.  Multi-objective optimization for bus body with strength and rollover safety constraints based on surrogate models , 2011 .

[193]  Larsgunnar Nilsson,et al.  Experimental and finite element robustness studies of a bumper system subjected to an offset impact loading , 2011 .

[194]  A. Toksoy,et al.  The optimisation of the energy absorption of partially Al foam-filled commercial 1050H14 and 6061T4 Al crash boxes , 2011 .

[195]  R. F. Kulak,et al.  Multi-objective optimisation and sensitivity analysis of a paratransit bus structure for rollover and side impact tests , 2011 .

[196]  Ping Zhu,et al.  Design optimisation of vehicle roof structures: benefits of using multiple surrogates , 2011 .

[197]  Hu Wang,et al.  Integrating Least Square Support Vector Regression and Mode Pursuing Sampling Optimization for Crashworthiness Design , 2011 .

[198]  Soumaya Yacout,et al.  Design for Six Sigma through collaborative multiobjective optimization , 2011, Comput. Ind. Eng..

[199]  Shu Yang,et al.  Crushing analysis and multiobjective crashworthiness optimization of tapered square tubes under oblique impact loading , 2012 .

[200]  Qing Li,et al.  Optimization of foam-filled bitubal structures for crashworthiness criteria , 2012 .

[201]  Tommaso Ingrassia,et al.  A comparison of simplex and simulated annealing for optimization of a new rear underrun protective device , 2013, Engineering with Computers.

[202]  Kazuhiro Saitou,et al.  A Co-Evolutionary Approach for Design Optimization via Ensembles of Surrogates With Application to Vehicle Crashworthiness , 2012 .

[203]  Kiran Solanki,et al.  Multi-objective optimization of vehicle crashworthiness using a new particle swarm based approach , 2012 .

[204]  Hoon Huh,et al.  Comparison of the optimum designs of center pillar assembly of an auto-body between conventional steel and ahss with a simplified side impact analysis , 2012 .

[205]  A. Najafi,et al.  Sequential coupled process-performance simulation and multi-objective optimization of thin-walled tubes , 2012 .

[206]  S-I Yi,et al.  Crashworthiness design optimization using equivalent static loads , 2012 .

[207]  Xu Han,et al.  Multivariable crashworthiness optimization of vehicle body by unreplicated saturated factorial design , 2012 .

[208]  Ali Ghamarian,et al.  Crashworthiness investigation of conical and cylindrical end-capped tubes under quasi-static crash loading , 2012 .

[209]  Ping Zhu,et al.  A method for selecting surrogate models in crashworthiness optimization , 2012 .

[210]  Masoud Rais-Rohani,et al.  Crashworthiness optimisation of vehicle structures with magnesium alloy parts , 2012 .

[211]  Wei Chen,et al.  Use of support vector regression in structural optimization: Application to vehicle crashworthiness design , 2012, Math. Comput. Simul..

[212]  Zuomin Dong,et al.  Hybrid and adaptive meta-model-based global optimization , 2012 .

[213]  Christophe Bastien,et al.  Effects of roof crush loading scenario upon body in white using topology optimisation , 2012 .

[214]  Ren-Jye Yang,et al.  Adaptive sampling-based RBDO method for vehicle crashworthiness design using Bayesian metric and stochastic sensitivity analysis with independent random variables , 2013 .

[215]  Guangyao Li,et al.  Crashworthiness optimization of foam-filled tapered thin-walled structure using multiple surrogate models , 2013 .

[216]  Shigeru Obayashi,et al.  Kriging-surrogate-based optimization considering expected hypervolume improvement in non-constrained many-objective test problems , 2013, 2013 IEEE Congress on Evolutionary Computation.

[217]  Axel Schumacher,et al.  Graph and heuristic based topology optimization of crash loaded structures , 2013 .

[218]  Gyung-Jin Park,et al.  Design flow for the crash box in a vehicle to maximize energy absorption , 2013 .

[219]  G. Belingardi,et al.  Geometrical optimization of bumper beam profile made of pultruded composite by numerical simulation , 2013 .

[220]  James P. Schmiedeler,et al.  Design of Crashworthy Structures With Controlled Energy Absorption in the Hybrid Cellular Automaton Framework , 2013 .

[221]  Hassan Shirvani,et al.  Hexagonal honeycomb cell optimisation by way of meta-model techniques , 2013 .

[222]  Hu Wang,et al.  Adaptive heuristic search algorithm for discrete variables based multi-objective optimization , 2013, Structural and Multidisciplinary Optimization.

[223]  Wei Chen,et al.  Crashworthiness-based lightweight design problem via new robust design method considering two sources of uncertainties , 2013 .

[224]  Qing Li,et al.  Crashworthiness design of multi-component tailor-welded blank (TWB) structures , 2013 .

[225]  Larsgunnar Nilsson,et al.  Robust optimization of front members in a full frontal car impact , 2013 .

[226]  A. Hamouda,et al.  Design of thin wall structures for energy absorption applications: Enhancement of crashworthiness due to axial and oblique impact forces , 2013 .

[227]  Wei Chen,et al.  Concurrent treatment of parametric uncertainty and metamodeling uncertainty in robust design , 2013 .

[228]  P. Astori,et al.  Crash response optimisation of helicopter seat and subfloor , 2013 .

[229]  S. Mahadevan,et al.  Design optimization for robustness in multiple performance functions , 2013 .

[230]  Christophe Bastien,et al.  Buckling considerations and cross-sectional geometry development for topology optimised body in white , 2013 .

[231]  Layne T. Watson,et al.  Efficient global optimization algorithm assisted by multiple surrogate techniques , 2012, Journal of Global Optimization.

[232]  Shu Yang,et al.  Multiobjective optimization for empty and foam-filled square columns under oblique impact loading , 2013 .

[233]  H. Gedikli,et al.  Crashworthiness optimization of foam-filled tailor-welded tube using coupled finite element and smooth particle hydrodynamics method , 2013 .

[234]  Qing Li,et al.  A Comparative study on multiobjective reliable and robust optimization for crashworthiness design of vehicle structure , 2013 .

[235]  G. Wen,et al.  Multiobjective crashworthiness optimization of functionally lateral graded foam-filled tubes , 2013 .

[236]  Ren-Jye Yang,et al.  An adaptive response surface method for crashworthiness optimization , 2013 .

[237]  Wei Chen,et al.  Lightweight design of vehicle parameters under crashworthiness using conservative surrogates , 2013, Comput. Ind..

[238]  Fabian Duddeck,et al.  Shape optimisation for crashworthiness followed by a robustness analysis with respect to shape variables , 2013 .

[239]  Masoud Rais-Rohani,et al.  Surrogate-based optimisation of automotive structures under multiple crash and vibration design criteria , 2013 .

[240]  Stacy Cagle Davis,et al.  Transportation Energy Data Book: Edition 31 , 2012 .

[241]  Xu Han,et al.  Theoretical prediction and crashworthiness optimization of multi-cell triangular tubes , 2014 .

[242]  Zonghua Zhang,et al.  Design optimization of the S-frame to improve crashworthiness , 2014 .

[243]  Guilin Wen,et al.  Optimisation design of reinforced S-shaped frame structure under axial dynamic loading , 2014 .

[244]  Qing Li,et al.  Crushing analysis of foam-filled single and bitubal polygonal thin-walled tubes , 2014 .

[245]  Anand Ramani,et al.  Topology optimization for nonlinear dynamic problems: Considerations for automotive crashworthiness , 2014 .

[246]  Masoud Rais-Rohani,et al.  Joint stiffness analysis and optimization as a mechanism for improving the structural design and performance of a vehicle , 2014 .

[247]  Guilin Wen,et al.  Crashworthiness optimization design for foam-filled multi-cell thin-walled structures , 2014 .

[248]  Timothy W. Simpson,et al.  Metamodeling in Multidisciplinary Design Optimization: How Far Have We Really Come? , 2014 .

[249]  Qing Li,et al.  Multiobjective crashworthiness optimization of hollow and conical tubes for multiple load cases , 2014 .

[250]  Milad Abbasi,et al.  A new approach for optimizing automotive crashworthiness: concurrent usage of ANFIS and Taguchi method , 2014 .

[251]  L. Romera,et al.  Crushing analysis and multi-objective crashworthiness optimization of GFRP honeycomb-filled energy absorption devices , 2014 .

[252]  Masoud Rais-Rohani,et al.  Multi-objective robust design of energy-absorbing components using coupled process–performance simulations , 2014 .

[253]  G. Wen,et al.  Multiobjective crashworthiness optimization design of functionally graded foam-filled tapered tube based on dynamic ensemble metamodel , 2014 .

[254]  S. Hernández,et al.  A multi-objective surrogate-based optimization of the crashworthiness of a hybrid impact absorber , 2014 .

[255]  Qing Li,et al.  Crashing analysis and multiobjective optimization for thin-walled structures with functionally graded thickness , 2014 .

[256]  Qing Li,et al.  Parametric analysis and multiobjective optimization for functionally graded foam-filled thin-wall tube under lateral impact , 2014 .

[257]  Karim Hamza,et al.  A framework for parallelized efficient global optimization with application to vehicle crashworthiness optimization , 2014 .

[258]  Liang Gao,et al.  A local adaptive sampling method for reliability-based design optimization using Kriging model , 2014 .

[259]  Xu Han,et al.  Optimization design of corrugated beam guardrail based on RBF-MQ surrogate model and collision safety consideration , 2014, Adv. Eng. Softw..

[260]  O. Mohammadiha,et al.  Optimization of functionally graded foam-filled conical tubes under axial impact loading , 2014 .

[261]  Xu Han,et al.  Factor screening and multivariable crashworthiness optimization for vehicle side impact by factorial design , 2014 .

[262]  Jianguang Fang,et al.  Crashworthiness design of foam-filled bitubal structures with uncertainty , 2014 .

[263]  Xu Han,et al.  Investigation on structure optimization of crashworthiness of fiber reinforced polymers materials , 2014 .

[264]  Chang Qi,et al.  Crashworthiness and lightweight optimisation of thin-walled conical tubes subjectedto an oblique impact , 2014 .

[265]  Yong Xia,et al.  Spot Weld Layout Optimization of Tube Crash Performance With Manufacturing Constraints , 2014 .

[266]  Tom Dhaene,et al.  Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization , 2014, J. Glob. Optim..

[267]  Lei Shi,et al.  A new metamodel method using Gaussian process based bias function for vehicle crashworthiness design , 2014 .

[268]  Ren-Jye Yang,et al.  Comparative Benchmark Studies of Response Surface Model-Based Optimization and Direct Multidisciplinary Design Optimization , 2014 .

[269]  Shujuan Hou,et al.  Crashworthiness optimization of new thin-walled cellular configurations , 2014 .

[270]  Xiong Zhang,et al.  Axial crushing and optimal design of square tubes with graded thickness , 2014 .

[271]  Qing Li,et al.  Robust optimization of foam-filled thin-walled structure based on sequential Kriging metamodel , 2014 .

[272]  Ren-Jye Yang,et al.  A Data Mining-Based Strategy for Direct Multidisciplinary Optimization , 2015 .

[273]  Jianguang Fang,et al.  Dynamic crashing behavior of new extrudable multi-cell tubes with a functionally graded thickness , 2015 .

[274]  Sangho Kim,et al.  Brittle intermetallic compound makes ultrastrong low-density steel with large ductility , 2015, Nature.

[275]  Yunkai Gao,et al.  Multiobjective robust design optimization of fatigue life for a truck cab , 2015, Reliab. Eng. Syst. Saf..

[276]  Anirban Chaudhuri,et al.  Parallel surrogate-assisted global optimization with expensive functions – a survey , 2016 .

[277]  Qing Li,et al.  Design of transversely-graded foam and wall thickness structures for crashworthiness criteria , 2016 .

[278]  Feng Zhu,et al.  On the Development of a New Design Methodology for Vehicle Crashworthiness based on Data Mining Theory , 2016 .