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汽车接触碰撞仿真中的关键技术研究
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摘要
计算机仿真技术在汽车设计制造中得到了越来越广泛的应用,特别是在汽车碰撞安全性设计中,仿真技术为缩短开发周期、降低成本起着很重要的作用。计算效率和计算精度是汽车接触碰撞仿真技术的关键。本文对参数反求方法、壳单元和沙漏控制算法、多时间步长算法等影响效率和精度的关键理论和方法进行了系统研究。
     本文的主要创新点包括以下几个方面:
     (1)材料参数的精度是影响仿真精度的关键因素。本文利用遗传算法的全局优化的优势,提出了一种基于改进遗传算法IP -μGA(a modified micro genetic algorithm with the strategy of Intergeneration Projection)和计算机仿真技术的参数反求方法,编制了相应的计算程序。为了克服遗传算法计算耗时多的问题,本文提出一种直接从冲压成形过程反求材料参数的方法。试验测量值为冲头的力-位移曲线,而待求的参数包括材料的特性参数和本构参数,采用移动最小二乘响应面法作为优化方法以减少调用正问题计算的次数。为了进一步提高计算效率,本文提出用解析式和有限元仿真结合的方法从冲压过程直接反求材料塑性参数。算例表明本方法在保证精度的前提下大幅度提高了计算效率。
     (2)壳单元算法是汽车接触碰撞仿真的核心算法之一。针对汽车碰撞和冲压成形过程的特点,本文提出了一种新的壳单元算法,编制了相应程序并集成到自主研发的碰撞仿真软件之中。该算法采用面内一点积分、物理稳定沙漏控制的计算格式,针对物理稳定单元存在的翘曲构型计算不精确和翘曲构型膜锁定问题,提出了两种翘曲构型沙漏控制策略,即:沙漏稳定性因子法、非翘曲影响域法。大量的算例和试验验证表明本文的壳单元算法提高了计算精度和稳定性。
     (3)对汽车碰撞和冲压成形过程的仿真基本上采用显式时间积分的格式。对于复杂的系统,采用多时间步长积分方法能很大程度地提高计算效率。在深入研究多时间积分方法即子循环法的基础上,本文提出了阻尼子循环法。该方法在常速度子循环法的基础上引入阻尼项以消除由于使用子循环法引起的计算误差和不稳定因素。对刚性连接的子循环方法也进行了深入的研究和处理,以满足碰撞过程仿真的需要。算例表明了阻尼子循环法的有效性。
     (4)本文提出用遗传算法进行某微车的约束系统改进优化,初始约束系统模型经过试验验证后被用来进行相关参数的优化。对于整车安全性的改进,采用结合结构碰撞安全性分析改进和约束系统遗传算法优化的方法进行。结构改进的好坏最终由车身变形的指标和假人的伤害指标来评判。
     综上所述,本文在参数反演方法、壳单元和沙漏控制技术、子循环方法和应用仿真技术优化实车安全性方面取得了一些成果,提出了三种材料参数反求的方法,为材料参数的准确获取提供了新的途径;提出了一个新的壳单元计算格式和两种翘曲结构沙漏控制方法,为提高汽车碰撞仿真精度探索了新的方法和途径;提出了阻尼子循环方法,为提高计算效率和减少误差提供了手段;提出了一条应用仿真技术和遗传算法解决微车碰撞安全性问题的切实可行的技术路线。
In automotive design, Computer Aided Engineering (CAE) has become a key factor to reduce the development time and the cost of products, especially for the design of vehicle crash safety. In order to improve the performance of the simulation methods for impacting process, studies which focus on the inverse problem, the shell element method, hourglass control ideas, multiple time steps algorithm and crash safety improvement using CAE and optimization methods for a microbus are conducted in this paper.
     The main innovative points of this paper are given as follows:
     (1)The precise material parameters play an important role to an effective simulation. An identification scheme to couple the finite element method and IP -μGA(a modified micro genetic algorithm with the strategy of Intergeneration Projection)is developed and programmed. The idea is to match the calculated response with the measured one in least-squares sense. The optimization algorithm chooses the parameters which are putted into the finite element code to find the best coincidence between the observed response and the calculated one. This technique is an alternative approach to the conventional method. An identification scheme for the determination of plastic parameters of blank sheet material is presented. This identification scheme is based on the combination of the finite element method (FEM) and the response surface methodology (RSM). The FEM is employed to calculate the responses of a blank sheet and RSM adjusts the material parameters so that the calculated responses match the measured one in a least-square sense. An example shows that the accurate plastic parameters can be obtained from a sheet forming test by using the method. An identification scheme for characterizing the material plastic property directly by using the results of simulation is presented. A series of equations in which the material parameters become unknown are constructed based on results from the calculation of FEM. The macro genetic algorithm is used to solve these unknown parameters. It is found that the identification scheme presents with high computational efficiency and accuracy.
     (2)A general four-node shell element with a single point quadrature is developed in this paper. This formulation is based on a physical stabilization approach for the control of spurious zero-energy modes (the hourglass mode). In order to eliminate the over hardening response existing in the warped configurations produced by applying the assumed strain method and the physical stabilization approach, an hourglass stability factor is introduced. In this paper a concept of mini-warped domain is presented and the hourglass forces are calculated based on it. The numerical results show that the developed methods possess high stabilization, high convergence and high accuracy.
     (3)It can decrease significantly the computation time in transient structural analysis to use subcycling algorithms which permit multiple time steps in explicit integration. Several subcycling algorithms were tested and it was shown that constant velocity subcycling algorithm possesses the best accuracy and stability properties. A new subcycling algorithm based on special treatment of rigid joint and proper choice of damper is proposed. The numerical examples show that the algorithm presents with high computational efficiency.
     (4)Genetic Algorithm(GA) is employed to solve the problem of constrain system optimization. A Madymo frontal crash model is testified its validity and then is optimized to yield the lowest levels of the occupant injury value and at least satisfy the Chinese legal requirements for frontal crash. It wastes little time to run this problem by using GA, as each simulation time is very little. The accuracy of the method is verified by comparison with optimization results and the test results.
引文
[1] Backus G E, Gilbert J F. Numerical applications of a formalism for geophysical inverse problems[J]. Geophy. J. Roy. Astr. Soc., 1967,13(1):247-276.
    [2] Backus G E,Gilbert J F. The resolving power of gross earth data[J]. Geophy. J. Roy. Astr.Soc., 1968, 16(1):169-205
    [3] Backus G E, Gilbert J F. Uniqueness in the inversion of inaccurate gross earth data[J]. Phil. Trans. Roy. Soc. London, 1970,266(3):123-192
    [4] Gardner H. Frames of mind: The theory of multiple intelligences[M]. New York: Basic Books Inc,1985:130-140
    [5] Peacock K, Treitel S. Predictive deconvolution–theory and practice[J]. Geophysics, 1969,34(3):155-169.
    [6] Lines L R, Treitel S. Tutorial: A review of least-squares inversion and its application to geophysical problems[J]. Geophys. Prosp., 1984,32(3):159-186
    [7] Castagna J P, Backus M M. Offset-dependent reflectivity–Theory and practice of AVO analysis[M]. SEG publication, Tulsa,1993:111-121
    [8] Lines L R, Schultz A,Treitel S. Cooperative inversion of geophysical data[J]. Geophysics, 1988,53(3):8-20.
    [9] Oldenburg D W, Scheuer T and Levy S. Recovery of the acoustic impedance from reflection seismograms[J]. Geophysics, 1983,48(3):1318-1337
    [10]王登刚.非线性反演算法及其应用研究[D].大连:大连理工大学, 2000: 1-18
    [11]刘家琦.数学物理方程反问题的分类及不适定问题求解[J].计算数学和应用数学, 1983, (4):43-64
    [12]李世雄,刘家琦.小波变换和反演数学基础[M].北京:地质出版社, 1994
    [13]赵红兵.基于能量测试和优化方法的结构单元损伤识别[D].大连:大连理工大学, 2005:26-32
    [14] Liu G R, Han X. Computational inverse techniques in nondestructive evaluation[M]. Florida: CRC Press LLC, 2003:1-222
    [15]赵新铭,刘宁,张剑.岩土力学反分析的数值反演方法[J].水利水电科技进展, 2003, 23(2):55-58
    [16]杨文采.非线性地球物理反演方法:回顾与展望[J].地球物理学进展, 2002, 17(2):255-261
    [17] Hanke M. A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems[J].Inverse problems, 1997, 13(1): 78-95
    [18] Kaltenbacher B. Some Newton-type methods for the regularization of nonlinear inverse problems[J].Inverse problems, 1997, 13(3): 729-753
    [19]王小平,曹立明.遗传算法理论、应用与软件实现,第1版[M]..西安:西安交通大学出版社, 2002:20-40
    [20]姜波,汪秉文.基于遗传算法的非线性系统模型参数估计[J].控制理论与应用, 2000, 17(1):150-152
    [21] Liu G R, Chen S C. Flaw detection in sandwich plates base on time-harmonic reponse using genetic algorithm[J]. Comput. Methods Appl. Mech. Eng., 2001, 190(42): 5505-5515
    [22] Han X, Xu D. A computational method for reconstruction of elastic constants of anisotropic laminated plate[A],in:6th U.S. National Congress on Computational Mechanics[C]. Michigan:Dearborn, 2001 :August
    [23]李守巨,刘迎曦,王登刚.土体渗流固结参数识别方法.水文地质工程地质[J]. 2001, 32(2):14-17
    [24] Giacobbo F, Marseguerra M, Zio E. Solving the inverse peoblem of parameter estimation by genetic algorithms: the case of a groundwater contaminant transport model[J]. Annals of Nuclear Energy, 2002, 29(3): 967-981
    [25] Katsifarakis K L, Karpouzos D K, Theodossiou N. Combined use of BEM and genetic algorithms in groundwater flow and mass transport problems[J]. Engineering Analysis with Boundary Element, 1999, 23(4): 555-565
    [26] Mannino M V, Koushik M V. The cost-minimizing inverse classification problem: A genetic algorithm approach[J]. Decision Support Systems, 2000, 29(2): 283-300
    [27] Han X, Xu D, Liu G R. On determination of the material constants of laminated cylindrical shells based on an inverse optimal approach. Inverse Probl[J]. Eng., 2002, 10(4): 309-321
    [28] Krishnan B, Navin S R. Inversion of composite material elastic constant from ultrasonic bulk wave phase velocity data using genetic algorithms[J]. Composites Part B, 1998, 29(2): 171-185
    [29]高晖,韩利芬,李光耀等.基于macro GA和有限元的薄板塑性材料参数识别[J].中国机械工程, 2005,16(18):1678-1681
    [30]韩莉芬.基于神经网络的薄板冲压成形中的反演问题研究[D].长沙:湖南大学,2006:
    [31]康立山,谢云,尤矢勇等.非数值并行算法——模拟退火算法[M].北京:科学出版社, 1998
    [32]师学明,王家映.一维层状介质大地电磁模拟退火反演法[J].地球科学, 1998, 23(5):542-546
    [33] Weber Z. Seismic travel time tomography: a simulated annealing approach[J]. Physics of the Earth and Planetary Interiors, 2000, 119(5): 149-159
    [34]尹成,周熙襄.热槽法模拟退火分析及其改进[J].石油物探, 1998, 37(1):63-70
    [35]傅慧萍,乔志德,张宇文.基于模拟退火算法的水下航行流体动力参数辨识[J].系统仿真学报, 2001, 13(4):434-435
    [36]尹成,周熙襄.一种改进的遗传算法及其在剩余静校正中的应用[J].石油地球物理勘探, 1997, 32(4):486-491
    [37]李守巨,刘迎曦,冯颖.基于混合遗传算法的动力系统阻尼参数识别方法[J].计算力学学报, 2004, 21(5):551-556
    [38] Xu Y G, Liu G R. Detection of flaws in composite materials from scattered elastic-wave field using modifiedμGA and gradient-based optimizer[J]. Comput. Methods Appl. Mech. Eng., 2002, 191(3): 3929-3940
    [39] Liu G R, Han X, Lam K Y. A combined genetic algorithm and nonlinear least squares method for material characterization using elastic waves[J]. Comput. Methods Appl. Mech. Engng., 2002, 191(4): 1909-1921
    [40] Box G E P, Wilson K B. On the experimental attainment of optimum conditions[J]. J. Roy. Stat. Soc. B.,1951,13(8):145~152
    [41] Box, G E P, J S Hunter. The 2k?p fractional factorial designs, Part I[J]. Technometrics,1961,3 (3):311-351
    [42] Box, G E P, J S Hunter. The 2k?p fractional factorial designs, Part II[J]. Technometrics,1961,3 (4):449-458
    [43] Box G E P, Hunter J S, W G Hunter. Statistics for Experi- menters II[M]. New York:Wiley ,2005:
    [44] DeGroot M H. A Conversation with George Box[J]. Statistical Science,1987,2 (3):239-58
    [45] Box G E P. Finding Bad Values in Factorial Designs[J]. Quality Engineering, 1991, 3 (3): 405-410
    [46] Box G E P. Signal to noise ratios, performance criteria and transformations[J]. Technometrics,1988,30 (l): 1-17
    [47]朱伟勇,段晓东.最优设计在工业中的应用[M].沈阳:辽宁科学技术出版社, 1994:644-667
    [48] Lenth R V. Quick and Easy Analysis of Unreplicated Factorials[J]. Technometrics ,1989,31 (4): 469-473
    [49] Sung H Park. Experimental design for fiting segmented polynomial regression models[J]. Technometrics,1978,20(2): 151-154
    [50] Meyer R D, D M Steinberg,G E P Box. Follow-Up Designs to Resolve Confounding in Multifactor Experiments (with discussion) [J]. Technometrics 1996,38 (4): 303-332
    [51] Hill W J, Hunter W G. A review of response surface methodology[J]. Technometrics, 1966,8(7):571-590
    [52] Myers R H. Response Surface Methodology, Current Status and Future Directions[J]. Journal of Quality Technology, 1999,31 (1): 30-44
    [53] Bates R A,Buck R J,Wynn H P. Experimental design and observation for large systems[J]. J R Statist Soc B,1996,58(4): 77-94
    [54] Box G E P,Liu P Y T. Statistics as a Catalyst to Learning by the Scientic Method Part I -An Excercise[J]. Journal of Quality Technology, 1999,31 (1): 1-15
    [55] Dalgaard P. Introductory Statistics with R[M]. New York:Springer ,2002:
    [56] Steinberg D M, Hunter W G. Experimental design review and comment. Technometrics[J],1984,26(1):71-97
    [57] Fang K T,Wang Y. Number theoretic methods in statistics[M]. New York:Chapman and Hall,1994:237-245
    [58] Leon R V, A C Shoemaker,R N. Kacker Performance Measures Independent of Adjustment (with discussion) [J]. Technometrics ,1987, 29(1):53-65
    [59] Daniel C. Applications of Statistics to Industrial Experimentation[M]. New York: Wiley Sciences, 1976:
    [60] Montgomery D C. Design and Analysis of Experiments[M]. New York:Wiley 2004.
    [61] Chu Y C,Degtyar A D,Rokhlin S I. On Determination of Orthotropic Material Moduli from Ultrasonic Velocity Data in Non-Symmetry Planes[J]. Journal of the Acoustical Society of America , 1994, 95 (16) : 3191-3203
    [62] J H Holland. Genetic algorithm[J]. Sci .Am. (Int. Ed.) ,1992,267(2):66-71.
    [63] Goldberg D E,Richardson J. Genetic Algorithms with Sharing for Multimodal Function Optimization[A]. in:Genetic Algorithms and their Applications:Proceedings of the Second International Conference on Genetic Algorithms[C], 1987:41-49
    [64] Carroll D L,Optimizing High Pressure Chemical Oxygen Iodine Lasers[A]. in:International Conference on Lasers '95[C], Charleston, South Carolina, 1995:Dec. 4-8
    [65] Krishnakumar K. Micro-Genetic Algorithms for Stationary and Non-Stationary Function Optimization[A]. in: Intelligent Control and Adaptive Systems, Society of Photo-Optical Instrumentation Engineers[C].Philadelphia,1989:1196
    [66] Liu G R,Han X. Computational inverse techniques in nondestructive evaluation[M]. Boca Raton. USA: CRC Press,2003 : 137-164
    [67] LANCASTER P, SALKAUSKAS K. Surfaces generated by moving least-squares methods[J]. Mathematics of Computation, 1981, 37(155):141-158
    [68] K Chung,O Richmond. Ideal forming-II. Sheet forming with optimum deformation[J].Int. J. Mech. Sci. 1992 ,34:612-633
    [69] S Ahmad, B M Irons, O C Zienkiewicz. Analysis of thick and thin shell structure by curved finite elements[J], Int. J. Numer. Meth. Engrg. 1970, 2(2):419-442
    [70] E Ramm. A plate/shell element for large deflection and rotations, Formulation and Computational Algorithms in Finite Element Analysis[M]. Cambridge, MA: MIT Press,1977
    [71] T J R Hughes, E Carnoy. Nonlinear finite element shell formulation accounting for large membrane strains[J]. Comput. Meth. Appl. Mech. Engrg. 1983, 39(2):69-81
    [72] E N Dvorkin, K J Bathe. A continuum mechanics based four-node shell element for general nonlinear analysis[J]. Engrg. Comput. 1984,1(1):77-95
    [73] K C Park, G Stanley. A curved C0 shell element based on assumed natural- coordinate strains[J]. J. Appl. Mech. 1986,53(3):278-297
    [74] W K Liu, E S Law, D Lam, T Belytschko. Resultant-stress degenerated shell element[J]. Comput. Meth. Appl. Mech. Engrg. 1986,55(1):259-274
    [75] J O Hallquist, P J Benson, G L Gougrean. Implementation of a modified Hughes–Liu shell into a fully vectorized explicit finite element code[M]. Berlin:Finite Element Methods for Nonlinear Problems, Springer, 1986, 283-299
    [76] J C Simo, D D Fox, M S Rifai. On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear theory[J]. Comput. Meth. Appl. Mech. Engrg. 1990,79(2):21-36
    [77] E L Wilson, R L Taylor, W P Doherty, J Ghaboussi. Incompatible displacement models[A], in: Numerical and Computer Models in Structural Mechanics[M].New York:Academic Press, 1973:43-70
    [78] U Andelfinger, E Ramm, EAS-elements for two-dimensional, three- dimensional, plate and shell structures and their equivalence to HR-elements[J]. Int J Numer Meth Engrg. 1993,36(1):1311-1340
    [79] M Bischoff, E Ramm.Shear deformable shell elements for large strains and rotations[J].Int J Numer Meth Engrg. 1997,40(1): 4427-4451
    [80] D Roehl, E Ramm.Large elasto-plastic finite element analysis of solids and shells with the enhanced assumed strain concept[J]. Int J Solids Struct. 1996,33(1) :3215-3230
    [81] J M A,Cesar de Sa, R M Natal Jorge,et al. Development of shear locking-free shell elements using an enhanced assumed strain formulation[J].Int J Numer Meth Engrg. 2002,53(1) :1721-1739
    [82] T J R Hughes, M Cohen, M Haroun. Reduced and selective integration techniques in finite element analysis of plates[J]. Nucl Engrg Des. 1978,46(1): 203-230
    [83] T J R Hughes, T E Tezduyar. Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element[J]. J Appl Mech. 1981,48(1):587-601
    [84] D Kosloff, G A Frazier. Treatment of hourglass patterns in low-order _nite element codes[J]. Int J Numer Anal Meth Geomeca, 1978,2(2):57-72
    [85] R L Taylor. Finite Element for General Shell Analysis[A].in:5th Seminar on Computation of Aspects of Finite Element Method[M]. Berlin:1979
    [86] T Belytschko,C S Tsay. A stabilization procedure for the quadrilateral plate element with one-point quadrature[J].Comput Meth Appl Mech Engng., 1986,55(1):259-300
    [87] D F Flanagan,T Belytschko. A uniform strain hexahedron and quadrilateral with orthogonal hourglass control[J].Comput Meth Appl Mech Engng. 1981,17(1): 679- 706
    [88] T Belytschko, J I Lin,C S Tsay. Explicit algorithms for the nonlinear dynamics of shells[J].Comput Meth Appl Mech Engng. 1984, 42(1):225 - 251
    [89] T Belytschko,W E Bachrach. Eficient implementation of quadrilaterals with high coarse-mesh accuracy[J].Comput Meth Appl Mech Engng. 1986,54(1):279- 301
    [90] T Belytschko,L Bindeman. Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems[J].Comput Meth Appl Mech Engng. 1991,88(2):311-340
    [91] B E Engelmann,R G Whirley. A new elastoplastic shell element formulation for DYNA3D, Report ugrl-jc-104826[R].America:Lawrence Livermore National Laboratory,1990
    [92] T J R Hughes, W K Liu. Nonlinear finite element analysis of shell: Part I. Three-dimensional shells[J]. Comput Meth Appl Mech Engrg. 1981,26(1):331-345
    [93] T J R Hughes, W K Liu. Nonlinear finite element analysis of shell: Part II. Two-dimensional shells[J]. Comput Meth Appl Mech Engrg.1981,27(1):167-187
    [94] T Belytschko, I Leviathan. Physical stabilization,of the 4-node shell element with one-point quadrature[J]. Computer Methods in Applied Mechanics and Engineering, 1994,113(1):321-350
    [95] Zeng Q,Combescure A. A new one-point quadrature, general non-linear quadrilateral shell element with physical stabilization[J].International Journal for Numerical Methods in Engineering,1998, 42(1):1307-1338
    [96] H Stolarski, T Belytschko,S H Lee. A review of shell _nite elements and corotational theories[J].Comput Mech Adv. 1995,2(1):125-212
    [97]龙驭球,须寅.广义协调平板型矩形壳元[J].计算结构力学及其应用,1994, 11(2):154-160
    [98]陈丽华,程建钢,黄文彬,姚振汉.带有沙漏控制的相对自由度壳元[J].工程力学, 2002, 19(3):122-127
    [99] Belytschko T, Mullen R.Explicit integration of structural problems[J]. Finite Elements in Nonlinear Mechanics, 1997, 2(2):697-20
    [100] Neal M O, Belytschko T.Explicit-explicit subcycling with non-integer time step ratios for structural dynamic systems[J]. Comput Struct. 1989, 31(1):871-80
    [101] Belytschko T, Lu Y Y.An explicit multi-time step integration for parabolic and hyperbolic systems[J]. New Methods Trans Anal. 1992,143(3): 25-9
    [102] Daniel W J T.Analysis and implementation of a new constant acceleration subcycling algorithm[J].Int J Numer Meth Eng. 1997, 40(2): 2841-2855
    [103] Smolinski P, Belytschko T, Neal M.Multi-time-step integration using nodal partitioning[J].Int J Numer Methods Eng. 1988, 26(1): 349-359
    [104] Daniel W J T. A study of the stability of subcycling algorithms in structural dynamics[J].comput Methods appl Mech Engrg. 1998, 156(1): 1-13.
    [105] Yang R J, Tho CH, Gu L. Recent development in multidisciplinary design optimization of vehicle structures[A]. In: Mistree F (ed) 9th AIAA/ISSMO symposium on multidisciplinary analysis and optimization[C]. Atlanta:2002.
    [106] Redhe M, Nilsson L, A method to determine structural sensitivities in vehicle crashworthiness design[J]. Int J Crashworthiness,2002,7(1):179-190
    [107] Redhe M, Nilsson L.Using space mapping and surrogate models to optimize vehicle crashworthiness design[A]. In: Mistree F (ed) 9th AIAA/ISSMO symposium on multidisciplinary analysis and optimization[C].Atlanta:2002
    [108] Redhe M, Forsberg J, Jansson T, et al. Using the response surface methodology and the D-optimality criterion in crashworthiness related problems[J].Struct Multidiscipl Optim, 2002,24(1):185-194
    [109] Etman LFP, Adriaens J, van Slagmaat M, Schoofs A. Crashworthiness design usin gmultipoint sequential linear programming[J].Struct Optim,1997,12(1): 222-228
    [110] Etman L F P, Optimization of multibody system using approximation concepts[D]. Eindhoven :Technical University, 1997
    [111] Toropov V V, Keulen F V, Markine V L, Alvarez L F.Multipoint approximation based on response surface fitting: a summary of recent developments[A]. In: 1st ASMO UK/ISSMO conference[C].Ilkley:1999:371-380
    [112] Yang R J, Gu L, Tho C, Sobieski J. Multidisciplinary design optimization of a full vehicle with high performance computing[A]. In: 8th symposium on multidisciplinary analysis and optimization[C]. St Louis:2001
    [113]钟志华,汽车耐撞性分析的有限元法[J].汽车工程,1994,16(1):1-6
    [114] HONG Z H. Finite element procedures for contact - impact problems[M] . Oxford :Oxford University Press ,1993.
    [115]钟志华,张维刚,曹立波,等.汽车碰撞安全技术[M] .北京:机械工业出版社,2002.
    [116]贾宏波,黄金陵,李掌宇,等.车身碰撞仿真技术在红旗轿车车身开发中的应用[J].汽车工程,1998,20(5):257-261.
    [117]张金换,王晓冬,黄世霖,汽车安全气袋系统的研究[J].清华大学学报(自然科学版),1997,37(11):69-72
    [118]裘新,黄存军,张金换,黄世霖,汽车正撞的数值模拟及实验验证[J].清华大学学报(自然科学版),1999,39(2):102-105
    [119]朱平,张宇,葛龙,林忠钦.基于正面耐撞性仿真的轿车车身材料轻量化研究[J].机械工程学报,2005,41(9):207-211
    [120]林逸,孙立清,李宏光,朱西产.汽车_乘员三维多体系统碰撞仿真研究[J].汽车工程,1999,21(4):206-211
    [121]林逸,刘静岩,张君媛,等.微型客车车身结构正面碰撞参数化模型的建立[J].汽车工程,2006,28(1):60-63
    [122]朱西产,钟荣华.薄壁直梁件碰撞性能计算机仿真方法的研究[J].汽车工程,2002,22(2):85-89.
    [123]马永春,陈思忠,居囊.非承载式车身正面碰撞的数值分析[J].2000,22(2):81-84.
    [124]邓兆祥,胡玉梅,王攀,等.客车耐撞性结构优化设计[J].机械工程学报,2005,41(11):217-220
    [125]王宏雁,高卫民,邬诚君.基于虚拟试验的轿车正面碰撞安全性分析[J].同济大学学报(自然科学版),2006,34(9):1242-1246.
    [126]陈礼璠,王冬梅.汽车安全带对乘员头部伤害的计算模拟研究[J].同济大学学报(自然科学版),1997,25(5):528-531
    [127]侯飞.轿车侧面碰撞新车评价程序及提高轿车侧面碰撞性能的措施[J].汽车工程,2000,20(6):413-417
    [128] Hill R. A theory of the yielding and plastic flow of anisotropic materials[J]. Proceedings of the Royal Society of London, Series A, 1948, 193(1): 281-297
    [129] F Barlat, D J Lege,J C Brem. A six component yield function for anisotropic metals[J].Int J Plasticity, 1991,7(1): 693-712
    [130] A Nadai. Extremal paths of plastic work and deformation[J]. J Mech Phys Solids,1986, 34(1): 511-523
    [131] E Voce. The relationship between stress and strain for homogeneous deformation[J]. J Inst Metals, 1948, 74(1): 537-562
    [132] www.numisheet2005.com.
    [133] A H van den Boogaard. Thermally Enhanced Forming of Aluminium Sheet Modelling and Experiments[D]. Master thesis, Ponsen & Looijen, Wageningen, Hengelo, The Netherlands:University Twente, 2002:65-66
    [134] Liu G R, Han X. Computational inverse techniques in nondestructive evaluation[M]. Florida: CRC Press LLC, 2003, 1-222
    [135] LANCASTER P, SALKAUSKAS K. Surfaces generated by moving least-squares methods[J]. Mathematics of Computation, 1981, 37(155) :141-158
    [136] A.H. van den Boogaard, Thermally Enhanced Forming of Aluminium Sheet Modelling and Experiments[D], Master thesis, Ponsen & Looijen, Wageningen, Hengelo, The Netherlands: University Twente, 2002:125-126
    [137] V Tarigopula, M Langseth, O S Hopperstad, et al. Axial crushing of thin-walled high-strength steel sections[J]. International Journal of Impact Engineering, 2006,32(1):847-882.
    [138] Wierzbicki T , Abramowicz W. On The Crushing Mechanics of Thin-Walled Structures[J], Journal of Applied Mechanics, 1983,50(1): 727-734.
    [139] T Belytschko, B L Wong,H Y Chiang. Advances in one-point quadrature shell elements[J].Comput Meth Appl Mech Engng. 1992,96(1): 93-107
    [140] R H MacNeal,R L Harder. A proposed standard set of problems to test finite element accuracy[J].Finite Elements Anal Des. 1985,11(12):3-20
    [141] D Y Yang, W J Chung, H B Shim. Rigid-plastic finite element analysis of sheet metal forming processes with initial guess generation[J].Int J Mech Sci. 1990,32(8):687-708
    [142] G H MacNay. Numerical modeling of tube crush with experimental comparison[A].in: Proc 7th Int Conf on Vehicle Structural Mechanics[C]. America:Society of Automotive Engineers, 1988:123-134

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