Abstract
With the rapid development of the vehicle industry, crashworthiness has become a crucial aspect in vehicle body design. In fact, crashworthiness is a multivariable optimization design problem for a vehicle body, regardless of structure or material. However, when crashworthiness involves a large number of design variables, including both material and structure variables, it is more difficult to deal with. In this paper, an integrated design technique for materials and structures of vehicle body under crash safety consideration is suggested. First, a finite element model of the vehicle body is established according to relevant vehicle safety standards. Then, the material parameters of the vehicle body are set as analytical factors for factor screening. Next, significant factors are obtained using a three-level saturated design integrated with multi-index comprehensive balance analysis and the MaxUr (3) method, with an improved evaluation method. These screened material parameters along with the corresponding continuous variables of the structure, are considered as the design variables of the integrated design of the vehicle body. Both the weight and the crashworthiness properties are set as the design objectives. Optimal Latin hypercube sampling and radius basis functions are utilized to construct highly accurate surrogate models. Furthermore, the non-dominated sorting genetic algorithm II is implemented to seek the optimal solutions. Finally, two cases considering the roof module and the frontal module of a vehicle body are analyzed to verify the proposed method.
Similar content being viewed by others
References
Abramowitz M, Stegun IA (1972) Handbook of mathematical functions. National Bureau of Standards, Washington, D.C
Bambach MR (2014) Fibre composite strengthening of thin steel passenger vehicle roof structures. Thin-Walled Struct 74(1–2):1–11
Bathe KJ, Walczak J, Guillermin O, Bouzinov PA, Chen HY (1999a) Advances in crush analysis. Comput Struct 72(2):31–47
Bathe KJ, Walczak J, Guillermin O, Bouzinov PA, Chen HY (1999b) Advances in crush analysis. Comput Struct 72(1–3):31–47
Brian C, Petrinic G, Colin J (2008) Automotive engineering: lightweight, functional and novel materials. Taylor&Francis GROUP, New York
Chen X (2009) Optimization design of the structure of B-pillar based on roof crush and side impact analysis. Hunan University, Changsha
Chen Y, Kunert J (2004) A new quantitative method for analyzing unreplicated factorial designs. Biom J 46(2–3):125–140
Chen Y, Chan CK, Leung BPK (2010) An analysis of three-level orthogonal saturated designs. Comput Stat Data Anal 54(2–5):1952–1961
Chuang CH, Yang RJ, Li G, Mallela K, Pothuraju P (2008) Multidisciplinary design optimization on vehicle tailor rolled blank design. Struct Multidiscip Optim 35:551–560
Cui XT, Wang SX, Hu SJ (2008) A method for optimal design of automotive body assembly using multi-material construction. Mater Des 29(1–2):381–387
Cui XT, Zhang HW, Wang SX, Zhang LH, Ko JH (2011) Design of lightweight multi-material automotive bodies using new material performance indices of thin-walled beams for the material selection with crashworthiness consideration. Mater Des 32(2):815–821
Dobbertin MK, Freeman DM, Lambert EW, Lasarev RM, Kohles SS (2013) The relationship between vehicle roof crush and head, neck and spine injury in rollover crashes. Accid Anal Prev 58(1):46–52
Duddeck F (2008) Multidisciplinary optimization of car bodies. Struct Multidiscip Optim 35(10–12):375–389
Duddeck F, Heiserer D, Lescheticky J (2003) Stochastic methods for optimization of crash and NVH problems. In: Bathe KJ (ed) 2nd M.I.T. Conf. on Comput. Fluid and Solid Mech. Elsevier, Oxford, p 2265–2268
Dyn N, Levin D, Rippa S (1986) Numerical procedures for surface fitting of scattered data by radial basis functions. SIAM J Sci Stat Comput 7:639–659
Fang H, Rais-Rohani M, Liu Z, Horstmeyer MF (2005) A comparative study of metamodeling methods for multi-objective crashworthiness optimization. Comput Struct 83(4):21–36
Gu XG, Sun GY, Li GY, Mao LC, Li Q (2013) A comparative study on multiobjective reliable and robust optimization for crashworthiness design of vehicle structure. Struct Multidiscip Optim 48(3):669–684
Hardy RL (1971) Multiquadratic equations of topography and other irregular surfaces. J Geophys Res 76:1905–1915
Hou SJ, Li Q, Long SY, Yang XJ, Li W (2007) Design optimization of regular hexagonal thin-walled columns with crashworthiness criteria. Finite Elem Anal Des 43(2):555–565
Hou SJ, Dong D, Ren LL, Han X (2012) Multivariable crashworthiness optimization of vehicle body by unreplicated saturated factorial design. 46(6): 891–905
Hou SJ, Liu TY, Dong D, Han X (2014a) Factor screening and multivariable crashworthiness optimization for vehicle side impact by factorial design. Struct Multidiscip Optim 49(8):147–167
Hou SJ, Tan W, Zheng YN, Han X, Li Q (2014b) Optimization design of corrugated beam guardrail based on RBF-MQ surrogate model and collision safety consideration. Adv Eng Softw 78(4):28–40
Hurnall J, Draheim A, Case M, Del Beato J (2003) A review of ‘B’-pillar and front seat belt loads measured in ANCAP offset frontal crash tests. In: Proceedings of 18th international technical conference on the enhanced safety of vehicles. Nagoya, Japan
Hvejsel CF, Lund E (2011) Material interpolation schemes for unified topology and multi-material optimization. Struct Multidiscip Optim 43(2):811–825
Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodelling techniques under multiple modelling criteria. Struct Multidiscip Optim 23(1):1–13
Jones N (1983) Impact crashworthiness. Int J Impact Eng 1(3):197
Kiani M, Yildiz AR (2015) A comparative study of non-traditional methods for vehicle crashworthiness and NVH optimization. Arch Comput Methods Eng. doi:10.1007/s11831-015-9155-y
Kodiyalam S, Yang JR, Gu L, Tho HC (2004) Multidisciplinary design optimization of a vehicle system in a scalable, high performance computing environment. Struct Multidiscip Optim 26(3–4):256–263
Liao XT, Li Q, Yang XJ, Zhang WG, Li W (2008) Multiobjective optimization for crash safety design of vehicles using stepwise regression model. Struct Multidiscip Optim 35:561–569
Liu GP, Han X, Jiang C (2008) A novel multi-objective optimization method based on an approximation model management technique. Comput Methods Appl Mech Eng 197(2):2719–2731
Lotus Engineering Inc (2010) An assessment of mass reduction opportunities for a 2017–2020 model year vehicle programme
Lu GX, Yu TX (2003) Energy absorption of structures and materials. WHP, England
Mallick PK (2010) Materials, design and manufacturing for lightweight vehicles. Woodhead Publishing, USA
Morris MD, Mitchell TJ (1995) Exploratory designs for computational experiments. J Stat Plan Infer 43(3):381–402
National Crash Analysis Center (NCAC) (2001) Public finite element model archive. www.ncac.gwu.edu/archives/model/index.html
NHTSA FMVSS 216 (2009) Final rule: federal motor vehicle safety standards; roof crush resistance. Docket No. NHTSA-2009-0093, RIN 2127-AG51. U.S. Government, Washington, DC
Ning HB, Pillay S, Vaidya UK (2009) Design and development of thermoplastic composite roof door for mass transit bus. Mater Des 30(1–2):983–991
Pan F, Zhu P, Zhang Y (2010) Metalmodel-based lightweight design of B-pillar with TWB structure via support vector regression. Comput Struct 88(4):36–44
Ramani A (2010) A pseudo-sensitivity based discrete-variable approach to structural topology optimization with multiple materials. Struct Multidiscip Optim 41(1):913–934
Ramani A (2011) Multi-material topology optimization with strength constraints. Struct Multidiscip Optim 43(4):597–615
Rowe J (2012) Advanced materials in automotive engineering. Woodhead Publishing Limited, UK
Sobieszczanski-Sobieski J, Kodiyalam S, Yang RY (2001) Optimization of car body under constraints of noise, vibration, and harshness (NVH), and crash. Struct Multidiscip Optim 22(4):295–306
Sun GY, Li GY, Zhou SW, Li HZ, Hou SJ, Li Q (2011) Crashworthiness design of vehicle by using multiobjective robust optimization. Struct Multidiscip Optim 44(5):99–110
Taguchi G (1986) Introduction to quality engineering. Asian Productivity Organization, Tokyo
Tahan F, Digges K, Mohan P (2010) Sensitivity study of vehicle rollovers to various initial conditions finite element model based analysis. The National Crash Analysis Center
Tran T, Hou SJ, Han X, Chau M (2015) Crushing analysis and numerical optimization of angle element structures under axial impact loading. Compos Struct 119:422–435
United Nations Economic Commission for Europe (1998) ECE R94:uniform provisions concerning the approval of vehicles with regard to the protection of the occupants in the event of a frontal collision
Zhao ZH, Han X, Jiang C, Zhou XX (2010) A nonlinear interval-based optimization method with local-densifying approximation technique. Struct Multidiscip Optim 42(3):559–573
Zhu P, Pan F, Chen W, Zhang SL (2012) Use of support vector regression in structural optimization: application to vehicle crashworthiness design. Math Comput Simul 86(5):21–31
Acknowledgements
The financial supports from the National Natural Science Foundation of China (11232004, 11572122), and from the New Century Excellent Talents Program in University (NCET-12-0168) are gratefully acknowledged. Moreover, Joint Center for Intelligent New Energy Vehicle is also gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
Rights and permissions
About this article
Cite this article
Chen, Y., Liu, G., Zhang, Z. et al. Integrated design technique for materials and structures of vehicle body under crash safety considerations. Struct Multidisc Optim 56, 455–472 (2017). https://doi.org/10.1007/s00158-017-1674-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-017-1674-8