[1] EYVAZIAN A, HABIBI M K, HAMOUDA A M, et al. Axial crushing behavior and energy absorption efficiency of corrugated tubes [J]. Materials and Design,2014, 54: 1028-1038.
[2] LI Z B, CHEN R, LU F Y. Comparative analysis of crashworthiness of empty and foam-filled thin-walled tubes [J]. Thin-Walled Structures, 2018, 124: 343-349.
[3] GOYAL S, ANAND C S, SHARMA S K, et al. Crashworthiness analysis of foam filled star shape polygon of thin-walled structure [J]. Thin-Walled Structures, 2019, 144: 106312.
[4] TARLOCHAN F, SAMER F, HAMOUDA A M S, et al. Design of thin wall structures for energy absorption applications: Enhancement of crashworthiness due to axial and oblique impact forces [J]. Thin-Walled Structures,2013, 71: 7-17.
[5] CETIN E, BAYKASOGLU C. Energy absorption of thin-walled tubes enhanced by lattice structures [J].International Journal of Mechanical Sciences, 2019,157/158: 471-484.
[6] KILIC?ASLAN C. Numerical crushing analysis of aluminum foam-filled corrugated single- and doublecircular tubes subjected to axial impact loading [J].Thin-Walled Structures, 2015, 96: 82-94.
[7] ZAREI H, KR¨OGER M, ALBERTSEN H. An experimental and numerical crashworthiness investigation of thermoplastic composite crash boxes [J]. Composite Structures, 2008, 85(3): 245-257.
[8] CHEN D H, OZAKI S. Numerical study of axially crushed cylindrical tubes with corrugated surface [J].Thin-Walled Structures, 2009, 47(11): 1387-1396.
[9] YIN H F, XIAO Y Y, WEN G L, et al. Crushing analysis and multi-objective optimization design for bionic thin-walled structure [J]. Materials and Design, 2015,87: 825-834.
[10] PIRMOHAMMAD S, ESMAEILI-MARZDASHTI S. Multi-objective optimization of multi-cell conical structures under dynamic loads [J]. Journal of Central South University, 2019, 26: 2464-2481.
[11] PIRMOHAMMAD S, ESMAEILI-MARZDASHTI S.Multi-objective crashworthiness optimization of square and octagonal bitubal structures including different hole shapes [J]. Thin-Walled Structures, 2019, 139:126-138.
[12] GAO Q, WANG L M, WANG Y L, et al. Crushing analysis and multiobjective crashworthiness optimization of foam-filled ellipse tubes under oblique impact loading [J]. Thin-Walled Structures, 2016, 100: 105-112.
[13] WANG S M, PENG Y, WANG T T, et al. Collision performance and multi-objective robust optimization of a combined multi-cell thin-walled structure for high speed train [J]. Thin-Walled Structures, 2019, 135:341-355.
[14] HOUWB, XU X Z, HAN X, et al. Multi-objective and multi-constraint design optimization for hat-shaped composite T-joints in automobiles [J]. Thin-Walled Structures, 2019, 143: 106232.
[15] WANG H Y, XIE H, CHENGW, et al. Multi-objective optimization on crashworthiness of front longitudinal beam (FLB) coupled with sheet metal stamping process[J]. Thin-Walled Structures, 2018, 132: 36-47.
[16] LI F Y, SUN G Y, HUANG X D, et al. Multiobjective robust optimization for crashworthiness design of foam filled thin-walled structures with random and interval uncertainties [J]. Engineering Structures, 2015,88: 111-124.
[17] DENG X L, LIU W Y. Crushing analysis and multiobjective crashworthiness optimization of multi-cell conical tube subjected to oblique loading [J]. Advances in Mechanical Engineering, 2019, 11(1): 1-20.
[18] WANG C Y, LI Y, ZHAO W Z, et al. Structure design and multi-objective optimization of a novel crash box based on biomimetic structure [J]. International Journal of Mechanical Sciences, 2018, 138/139: 489-501.
[19] KHALKHALI A, MOSTAFAPOUR M,TABATABAIE S M, et al. Multi-objective crashworthiness optimization of perforated square tubes using modified NSGAII and MOPSO [J]. Structural and Multidisciplinary Optimization, 2016, 54: 45-61.
[20] SUN G Y, XU F X, LI G Y, et al. Crashing analysis and multiobjective optimization for thin-walled structures with functionally graded thickness [J]. International Journal of Impact Engineering, 2014, 64: 62-74.
[21] YIN H F, WEN G L, HOU S J, et al. Multiobjective crashworthiness optimization of functionally lateral graded foam-filled tubes [J]. Materials and Design,2013, 44: 414-428.
[22] ASANJARANI A, DIBAJIAN S H, MAHDIAN A. Multi-objective crashworthiness optimization of tapered thin-walled square tubes with indentations [J].Thin-Walled Structures, 2017, 116: 26-36.
[23] YUAN L, SHI H Y, MA J Y, et al. Quasi-static impact of origami crash boxes with various profiles [J]. Thin-Walled Structures, 2019, 141: 435-446.
[24] SARKABIRI B, JAHAN A, REZVANIMJ. Crashworthiness multi-objective optimization of the thin-walled grooved conical tubes filled with polyurethane foam[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2017, 39: 2721-2734.
[25] ZADEH P M, SAYADI M, KOSARI A. An efficient metamodel-based multi-objective multidisciplinary design optimization framework [J]. Applied Soft Computing Journal, 2019, 74: 760-782.
[26] BAROUTAJI B A, GILCHRIST M D, SMYTH D, et al. Crush analysis and multi-objective optimization design for circular tube under quasi-static lateral loading [J]. Thin-Walled Structures, 2015, 86: 121-131.
[27] WU S Y, LI G Y, SUN G Y, et al. Crashworthiness analysis and optimization of sinusoidal corrugation tube [J]. Thin-Walled Structures, 2016, 105: 121-134.
[28] BAROUTAJI A, MORRIS E, OLABI A G. Quasistatic response and multi-objective crashworthiness optimization of oblong tube under lateral loading [J].Thin-Walled Structures, 2014, 82: 262-277.
[29] ZOU X, GAO G J, DONG H P, et al. Crushing analysis and multi-objective optimization of bitubular hexagonal columns with ribs [J]. Journal of Central South University, 2017, 24: 1164-1173.
[30] ABBASI M, REDDY S, GHAFARI-NAZARI A, et al.Multiobjective crashworthiness optimization of multicornered thin-walled sheet metal members [J]. Thin-Walled Structures, 2015, 89: 31-41.
[31] QIN R X, ZHOU J X, CHEN B Z. Crashworthiness design and multiobjective optimization for hexagon honeycomb structure with functionally graded thickness[J]. Advances in Materials Science and Engineering,2019, 2019: 8938696.
[32] WU Z M. Models, methods and theories for fitting scattered data [M]. 2nd ed. Beijing: Science Press,2016 (in Chinese).
[33] CHEN Y Y, ZHENG L. Simulation and optimization of vehicle frontal crashworthiness based on surrogate model [J]. Automotive Engineering, 2018, 40(6): 673-678 (in Chinese).
[34] HUANG D, ALLEN T T, NOTZ W I, et al. Sequential Kriging optimization using multiple-fidelity evaluations[J]. Structural and Multidisciplinary Optimization,2006, 32: 369-382. [35] ZHUANG W M, SHI H D, XIE D X, et al. Research on the lightweight design of body-side structure based on crashworthiness requirements[J].Journal of Shanghai Jiao Tong University (Science), 2019, 24(3): 313-322.
[36] SAKATA S, ASHIDA F, ZAKO M. An efficient algorithm for Kriging approximation and optimization with large-scale sampling data [J]. Computer Methods in Applied Mechanics and Engineering, 2004,193(3/4/5): 385-404.
[37] SUN G Y, ZHANG H L, FANG J G, et al. A new multi-objective discrete robust optimization algorithm for engineering design [J]. Applied Mathematical Modelling,2018, 53: 602-621.
[38] METROPOLIS N, ROSENBLUTH A W, ROSENBLUTH M N, et al. Equation of state calculations
by fast computing machines [J]. Journal of Chemical Physics, 1953, 21: 1087-1092.
[39] XIAO X W, XIAO D, LIN J G, et al. Overview on multi-optimization problem research [J]. Application Research of Computers, 2011, 28(3): 805-808 (in Chinese).