汽车覆盖件冲压成形中拉延筋模型及其参数反演研究
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摘要
汽车车身覆盖件成形中,若工艺参数和模具几何参数设置不当则易引起起皱、破裂等成形缺陷。为保证成形质量,通常在拉延模压料面合理设置拉延筋调整拉延阻力大小和分布,以改善板料流动的不均匀性,提高覆盖件成形质量。近几十年来很多学者在拉延筋相关方面开展了较为广泛的研究,并已取得诸多成果,但拉延筋相关研究仍存在较多问题。本文在前人研究的基础上对拉延筋分析模型、数值模拟中的等效拉延筋仿真模型、拉延筋几何参数优化反演以及真实拉延筋仿真模型等方面进行了深入的研究。并将研究成果应用到自主开发的板料冲压成形软件CADEMⅡ中,开发了拉延筋相关功能模块,提高了CAE软件的工程实用性。
研究具体内容如下:
(1)建立了一种考虑混合硬化的拉延筋分析模型。目前的拉延筋阻力模型大多忽略板料弯曲时中性层的偏移,并假设板料在复杂的循环加载条件下仍然保持等向强化,不考虑包辛格效应的影响。本文将板料经过拉延筋的复杂塑性变形过程简化为一根平面应变板条在拉伸力作用下的反复弯曲与校直过程,根据Love Kirchhoff假设及平面应变假设,建立了一种拉延筋数值分析模型。该模型不仅考虑了板材厚度变化、材料各向异性,而且通过应变记忆因子考虑板料的混合强化,构建一种简易循环加载本构关系,并能够比较准确地描述了板料的加工硬化特性和包辛格效应。通过与试验结果和仿真结果进行对比,验证模型的合理性和有效性。
(2)建立了一种基于快速接触搜寻的等效拉延筋仿真模型。将点到块的接触算法应用于等效拉延筋的接触搜寻,快速建立与更新等效拉延筋节点与板料单元的接触对关系,减少仿真过程接触搜寻时间。
(3)提出一种基于近似模型的拉延筋几何参数优化反演方法。针对覆盖件的起皱、拉裂等成形缺陷,建立了相应的目标评价函数。采用均匀拉丁方试验设计方法提取适当的设计参数样本构造响应面近似模型,并不断通过移动和缩放设计兴趣域优化响应面模型优化反演拉延筋参数。该方法能有效克服常规响应面法在整个设计空间进行逼近导致精度低的缺陷;大量减少调用有限元正问题模拟调用次数,提高计算效率,而且能够克服板料成形数值模拟中因单元计算或接触计算产生问题而使整个优化过程无法进行的瓶颈问题。此外,将多目标粒子群优化方法应用到了板料成形优化研究,拓展了多目标粒子群优化方法的应用领域,为其它复杂系统的优化研究起到重要的借荐作用。数值算例表明该方法可在设计域内快速寻优,有助于加快模具设计进程,减少生产成本。
(4)建立了一种基于自适应和子循环的真实拉延筋仿真模型。目前主要的等效拉延筋模型,对变截面过渡拉延筋、拉延端部效应、斜拉延筋以及材料特性的局部变化未给予考虑,因而需要通过真实拉延筋模型进行有限元仿真分析获取板料经过拉延筋后更为准确的应力应变信息。然而由于流经拉延筋的板料单元尺寸限制,导致临界时间步长过小,极大地降低了真实拉延筋模拟的计算效率。针对该问题,本文建立了一种基于自适应和子循环方法的真实拉延筋模型。自适应方法针对拉延筋的几何尺寸问题,对流经拉延筋的板料单元进行自适应网格划分限制计算单元总数,并将整个板料单元网格按时间步长划分区域;采用子循环算法对不同区域单元采用各自的时间步长进行积分,以提高真实拉延筋模拟的计算效率。
In forming field, defects such as wrinkles and fractures are often caused owing to non-uniform material flow in the complex surfaces. In the forming operations of an automotive cover panel, the setting of drawbeads in the blank holder is an effective technique to supply a frictional resistance force in the sheet contact area and produce tensile stress in the sheet, which controls the material flow to obtain a more uniform deformation. In the past several decades, works of the drawbead have been studied by many researchers, but there still exist many problems in this field. In this study, the drawbead analytical model, the equivalent drawbead model in FEM and the optimization of drawbead parameters, have been proposed based on the former researches. All of the research results have been applied successfully in forming self-devolped software CADEMⅡ. This paper includes the following topics:
1. A numerical analysis drawbead model with isotropic-kinematic harding law is proposed to calculate drawbead restraining force. The equivalent drawbead restrained force models are used to describe the effects on the mechanics of the deformation of the sheet experiencing cyclic bending/unbending with isotropic cyclic hardening rule, and does not consider the incline of neutral layer and the Bauschinger effect. A numerical analysis model is proposed to calculate drawbead restraining force based on the Love-Kirchhoff assumption and plane strain assumption. The proposed model adequately considers the valuation of sheet thickness, the anisotropy and the incline of neutral layer. A Stress-strain law and a mixed isotropic-kinematic harding law under cyclic bending are described through the introduction of a strain memory factor to take into account the Bauschinger effect. The proposed model is compared with experimental ones and the validity of this model is verified.
2. An equivalent drawbead model is established, which is based on the particle to segment contact algorithm. The particle to segment contact algorithm is applied to quickly build and update the contact pair between the equivalent drawbead nodes and sheet metal elements, to reduce the time consuming for contact search.
3. A metamodel based inverse method of the drawbead geometrical parameters is suggested. The building of reasonable criterions to form objective functions such as fracture, wrinkle and insufficient stretching, which can be used to evaluate the formability of automobile panels. The first approach was for an optimization of the design variables of sheet forming with the region of the interest moved across the design space and the uniform latin square designs of experiment. The method can effectively overcome the shortcoming of low calculation accuracy compared with the conventional response surface method. And the obtained optimization procedure is very efficient due to decreasing the number of FEM evaluations. In addition, Multi-objective particle swarm optimization method is applied in the research on the forming optimization. It extends the applications of the particle swarm optimization method. numerical examples are presented to demonstrate the usefulness of the proposed optimization procedure for the design of mould.
4. Based on the adaptive method and subcycling algorithm, The FEM model with true drawbeads is established. Because the variable cross-section of the transition drawbead, the effect of drawbead end, the cable-stayed extension drawbead and the material properties change of local sheet are not be taken into account in the equivalent drawbead models usually used in numerical simulation, The strain of the sheet metal having passed the true drawbead is accurate access by the true drawbead simulation model compared with the equivalent drawbead models. However, the sheet element must be enough small to run through the drawbead, leading to the critical time step too small to significantly reduce computational efficiency. To solve the problem, we establish the true drawbead model based on the adaptive method and the subcycling algorithm. We first refine the elements accessing the drawbead and coase these having passed over the drawbead, the sheet metal elements mesh is divided into subdomains with the different time-steps, and then the elements in different domains are updated with their time-steps to increase the simulation efficiency. numerical examples are presented to demonstrate the usefulness of the proposed procedure for the finite element simulation with true drawbeads.
研究具体内容如下:
(1)建立了一种考虑混合硬化的拉延筋分析模型。目前的拉延筋阻力模型大多忽略板料弯曲时中性层的偏移,并假设板料在复杂的循环加载条件下仍然保持等向强化,不考虑包辛格效应的影响。本文将板料经过拉延筋的复杂塑性变形过程简化为一根平面应变板条在拉伸力作用下的反复弯曲与校直过程,根据Love Kirchhoff假设及平面应变假设,建立了一种拉延筋数值分析模型。该模型不仅考虑了板材厚度变化、材料各向异性,而且通过应变记忆因子考虑板料的混合强化,构建一种简易循环加载本构关系,并能够比较准确地描述了板料的加工硬化特性和包辛格效应。通过与试验结果和仿真结果进行对比,验证模型的合理性和有效性。
(2)建立了一种基于快速接触搜寻的等效拉延筋仿真模型。将点到块的接触算法应用于等效拉延筋的接触搜寻,快速建立与更新等效拉延筋节点与板料单元的接触对关系,减少仿真过程接触搜寻时间。
(3)提出一种基于近似模型的拉延筋几何参数优化反演方法。针对覆盖件的起皱、拉裂等成形缺陷,建立了相应的目标评价函数。采用均匀拉丁方试验设计方法提取适当的设计参数样本构造响应面近似模型,并不断通过移动和缩放设计兴趣域优化响应面模型优化反演拉延筋参数。该方法能有效克服常规响应面法在整个设计空间进行逼近导致精度低的缺陷;大量减少调用有限元正问题模拟调用次数,提高计算效率,而且能够克服板料成形数值模拟中因单元计算或接触计算产生问题而使整个优化过程无法进行的瓶颈问题。此外,将多目标粒子群优化方法应用到了板料成形优化研究,拓展了多目标粒子群优化方法的应用领域,为其它复杂系统的优化研究起到重要的借荐作用。数值算例表明该方法可在设计域内快速寻优,有助于加快模具设计进程,减少生产成本。
(4)建立了一种基于自适应和子循环的真实拉延筋仿真模型。目前主要的等效拉延筋模型,对变截面过渡拉延筋、拉延端部效应、斜拉延筋以及材料特性的局部变化未给予考虑,因而需要通过真实拉延筋模型进行有限元仿真分析获取板料经过拉延筋后更为准确的应力应变信息。然而由于流经拉延筋的板料单元尺寸限制,导致临界时间步长过小,极大地降低了真实拉延筋模拟的计算效率。针对该问题,本文建立了一种基于自适应和子循环方法的真实拉延筋模型。自适应方法针对拉延筋的几何尺寸问题,对流经拉延筋的板料单元进行自适应网格划分限制计算单元总数,并将整个板料单元网格按时间步长划分区域;采用子循环算法对不同区域单元采用各自的时间步长进行积分,以提高真实拉延筋模拟的计算效率。
In forming field, defects such as wrinkles and fractures are often caused owing to non-uniform material flow in the complex surfaces. In the forming operations of an automotive cover panel, the setting of drawbeads in the blank holder is an effective technique to supply a frictional resistance force in the sheet contact area and produce tensile stress in the sheet, which controls the material flow to obtain a more uniform deformation. In the past several decades, works of the drawbead have been studied by many researchers, but there still exist many problems in this field. In this study, the drawbead analytical model, the equivalent drawbead model in FEM and the optimization of drawbead parameters, have been proposed based on the former researches. All of the research results have been applied successfully in forming self-devolped software CADEMⅡ. This paper includes the following topics:
1. A numerical analysis drawbead model with isotropic-kinematic harding law is proposed to calculate drawbead restraining force. The equivalent drawbead restrained force models are used to describe the effects on the mechanics of the deformation of the sheet experiencing cyclic bending/unbending with isotropic cyclic hardening rule, and does not consider the incline of neutral layer and the Bauschinger effect. A numerical analysis model is proposed to calculate drawbead restraining force based on the Love-Kirchhoff assumption and plane strain assumption. The proposed model adequately considers the valuation of sheet thickness, the anisotropy and the incline of neutral layer. A Stress-strain law and a mixed isotropic-kinematic harding law under cyclic bending are described through the introduction of a strain memory factor to take into account the Bauschinger effect. The proposed model is compared with experimental ones and the validity of this model is verified.
2. An equivalent drawbead model is established, which is based on the particle to segment contact algorithm. The particle to segment contact algorithm is applied to quickly build and update the contact pair between the equivalent drawbead nodes and sheet metal elements, to reduce the time consuming for contact search.
3. A metamodel based inverse method of the drawbead geometrical parameters is suggested. The building of reasonable criterions to form objective functions such as fracture, wrinkle and insufficient stretching, which can be used to evaluate the formability of automobile panels. The first approach was for an optimization of the design variables of sheet forming with the region of the interest moved across the design space and the uniform latin square designs of experiment. The method can effectively overcome the shortcoming of low calculation accuracy compared with the conventional response surface method. And the obtained optimization procedure is very efficient due to decreasing the number of FEM evaluations. In addition, Multi-objective particle swarm optimization method is applied in the research on the forming optimization. It extends the applications of the particle swarm optimization method. numerical examples are presented to demonstrate the usefulness of the proposed optimization procedure for the design of mould.
4. Based on the adaptive method and subcycling algorithm, The FEM model with true drawbeads is established. Because the variable cross-section of the transition drawbead, the effect of drawbead end, the cable-stayed extension drawbead and the material properties change of local sheet are not be taken into account in the equivalent drawbead models usually used in numerical simulation, The strain of the sheet metal having passed the true drawbead is accurate access by the true drawbead simulation model compared with the equivalent drawbead models. However, the sheet element must be enough small to run through the drawbead, leading to the critical time step too small to significantly reduce computational efficiency. To solve the problem, we establish the true drawbead model based on the adaptive method and the subcycling algorithm. We first refine the elements accessing the drawbead and coase these having passed over the drawbead, the sheet metal elements mesh is divided into subdomains with the different time-steps, and then the elements in different domains are updated with their time-steps to increase the simulation efficiency. numerical examples are presented to demonstrate the usefulness of the proposed procedure for the finite element simulation with true drawbeads.
引文
[1] 现代模具技术编委会. 汽车覆盖件模具设计与制造. 北京: 国防工业出版社, 1998, 1-10
[2] 陈军,石晓祥,姚兴,阮雪榆. 汽车覆盖件冲压工艺/ 模具计算机辅助技术的发展现状. 锻压技术, 2002, 6, 14-18
[3] 钟志华,李光耀. 薄板冲压成形过程的计算机仿真与应用. 第1版. 北京:北京理工大学出版社, 1998, 1-7
[4] 汽车覆盖件拉伸模的设计现状及发展方向. 电加工与模具, 2001, 2, 13-15
[5] 徐伟力,林忠钦,刘罡等. 车身覆盖件冲压仿真的现状和发展趋势. 机械工程学报, 2000, 36(7): 1-4
[6] 张晓静,周贤宾,孔永明. 板料成形数值模拟研究. 锻压技术,2001,1, 13-17
[7] Paiter M J, Pearce R. Metal flow through a drawbead. Sheet metal industries, 1976, (7): 12-20
[8] Nine H D. Drawbead forces in sheet metal forming. In: Mechanics of Sheet Metal Forming. New York: Plenum Press, 1978, 179-211
[9] Wang N M, Shah V C. Drawbead design and performance. J. of Material Shaping Tech., 1991, 9(1): 21-26
[10] Schey J A. Speed effects in drawbead simulation. J. Mater. Process Technol., 1996, 57(1): 146-154
[11] Demeri M Y. Drawbeads in sheet metal forming. J. Mater. Eng. Perform, 1993, 2(6): 863-866
[12] 邢忠文.薄板冲压成形中拉深筋阻力及其影响因素研究. 模具工业,1994, 4, 33-35
[13] 刘迪辉,钟志华. 拉延筋对回弹的影响机理研究. 中国机械工程,2005,16(20): 1876-1879
[14] Levy B S. Development of a predictive model for draw bead restraining forces utilizing work of Nine and Wang. J. Appl. Metalworking, 1983, 3(1): 38-44
[15] Ludovic Courvoisier, Marion Martiny, Gerard Ferron. Analytical modeling of drawbeads in sheet metal forming. Journal of materials Processing Technology. 2003, 133(3): 359-370
[16] Fuh Kou Chen, Pao Ching Tszeng. An analysis of drawbead restraining force in the stamping process. International Journal of Machine Tools & Manufature, 1998,38(7):827-842
[17] 李东升,黄小明,胡世光. 汽车覆盖件成型中拉延筋约束力的模拟计算. 塑性工程学报,1994, 1, 59-65
[18] 徐 丙 坤 , 施 法 中 . 拉 延 筋 约 束 阻 力 的 一 种 解 析 计 算 方 法 . 锻 压 技术,2001,26(6):11-13
[19] 朱勇建,那景新,闫亚坤等. 应用直接法求解拉延筋约束力. 吉林大学学报(工学版), 2003, 33(1): 92-97
[20] 李淑慧,林忠钦,包友霞等. 改进的等效拉延筋阻力模型及其应用. 中国机械工程, 2002, 13(7): 558-561
[21] 王烨. 拉延筋模型及汽车覆盖件成形工艺 CAD/CAE 集成系统关键技术的研究: [上海交通大学博士学位论文]. 上海: 上海交通大学,2000,82-84
[22] Chabrand P, Dubois F, Gelin J C. Modelling drawbeads in sheet metal forming. Int. J. of Mechanical Science, 1996, 38(1): 59-77
[23] Cao J, Boyce M C. Draw bead penetration as a control element of material flow. SAE 930517, 1993, 694-702
[24] Carleer B D, Meinders T, Hu tink H. Equivalent drawbead model in finite element simulations. Numerical Simulations of 3-D Sheet Metal forming Processes (NUMISHEET'96), Michigan, USA, 1996, 25-31
[25] Carleer B D, Vreede P T, Drent P, et al. Modelling Drawbeads with Finite Elements and Verification. J.Mater.Process.Technol, 1994, 45(1): 63-68
[26] Weinmann K J, Sanchez L R. A general computer model for plane strain sheet flow and its application to flow between circular drawbeads. In: Proceedings of the 15th IDDRG. Dearborn,USA and Toronto, Canada, 1988, 217-226
[27] Weidemann . The blankholder action of drawbeads. In: Proc. of 10th Biennial IDDRG Congress. 1978, 79-84
[28] 印雄飞. 板料成形中拉延筋模型及其工艺效果的研究: [上海交通大学博士学位论文]. 上海: 上海交通大学, 1999, 1-13
[29] Wang N M. A mathematical model of drawbead forces in sheet metal forming. J. Appl. Met. Working, 1982, 2(3): 193-199
[30] Stoughton T B. Model of drawbead forces in sheet metal forming. in: Proceedings of the 15th IDDRG. Dearborn, USA and Toronto, Canada, 1988, 205-215
[31] Ghoo B Y, Keum Y T. Expert drawbead models for sectional FEM analysis of sheet metal forming process. Journal of Materials Processing Technology, 2000, 105(1): 7-16
[32] Keum Y T, Kim J H, Ghoo B Y. Expert drawbead models for finite elementanalysis of sheet metal forming processes. International Journal of Solids and Structures, 2001, 38(30): 5335-5353
[33] Sanchez LR, Weinmann K J. An Analytical and Experimental Study of the Flow of Sheet Metal between Circular Drawbeads. Journal of Engineering for for Industry, 1996 ,118(1): 45-54
[34] 李大永, 胡平, 李运兴. 拉延筋阻力的一种简便解析模型. 机械工程学报, 2000, 36(5): 46-49
[35] 印雄飞, 何丹农, 彭颖红等. 板料成形有限元分析中的等拉延筋模型. 计算机技术应用, 1999, 34(5):49-51
[36] Roy S, Shivpuri R. A new approach to optimal design of multi-stage metal forming processes with micro genetic algorithms. INTERNATIONAL JOURNAL OF MACHINE TOOLS & MANUFACTURE, 2000, 37(1): 29-44
[37] Liu Gang Bao Youxia. Optimization Design of Drawbead in Drawing Tools of Autobody Cover Panel. Journal of Engineering Materials and Technology, 2002, 124(2): 278-285
[38] Nakamura Y, Katayama T. Optimum die design for sheet metal forming process by using finite element and discretized optimization methods. In: NUMIFORM 98: Sixth International Conference on Numerical Methods in Industrial Forming Processes, Enschede, Netherlands, 1998, 787-792
[39] Chung J S. Application of a genetic algorithm to the optimal design of the die shape in extrusion. Journal of Materials Processing Technology, 1997, 72(1): 69-77
[40] Gantar G, Pepelnjak T, Kuzman K. Optimization of sheet metal forming processes by the use of numerical simulations. Journal of Materials Processing Technology, 2002, 130, 54-59
[41] Kubli W, Reissner J. Optimization of sheet-metal forming processes using the special-purpose program AUTOFORM. Journal of Materials Processing Technology, 1995, 50(1-4): 292-305
[42] Huh H, Kim S-H. Optimum process design in sheet-metal forming with finite element analysis. Journal of Engineering Materials and Technology . 2001, 123(4): 476-481
[43] Hillmann M, Kubli W. Optimization of sheet metal forming processes using simulation programs. In: Proc. of NUMISHEET, 1999, 287-292
[44] Naceur H,Delameziere A,Batoz J L,et al.Some improvements on the optimum process design in deep drawing using the inverse approach. Journal of MaterialsProcessing Technology,2004,146(2): 250-262
[45] Naceur H, Gou Y Q, Batoz J L, et al.Optimization of blank restraining forces to improve the global quality of stamping parts. In: Proceedings of the Fourth International Conference on Numerical Simulation, NUMISHEET’99, Besancon, France, 1999, 517-521
[46] Naceur H, Guo YQ, Batoz JL, Knopf-Lenoir C. Optimization of drawbead restraining forces and drawbead design in sheet metal forming process. International Journal of Mechanical Sciences, 2001, 43(10): 2407-2434
[47] Guo Y Q, Batoz J L, Naceur H, et al. Recent developments on the analysis and optimum design of sheet metal forming parts using a simplified inverse approach Computers and Structures, 2000, 78(1) :133-148
[48] Guo YQ, Naceur H, Debray K, Bogard F. Initial solution estimation to speed up inverse approach in stamping modeling, Engineering Computations. Int J for Computer Aided Engineering, 2003, 20(7): 810-834
[49] NACEUR H, GUO Y Q, BATOZ J L. Blank optimization in sheet metal forming using an evolutionary algorithm. Journal of materials processing technology , 2004, 151(3): 183-191
[50] Schenk Olaf, Hillmann Matthias. Optimal design of metal forming die surfaces with evolution strategies. Computers & Structures, 2004, 82(20-21): 1695-1705
[51] JANSSON T, NILSSON L, REDHE M. Using surrogate models and response surfaces in structural optimization: with application to crashworthiness design and sheet metal forming. Structural and multidisciplinary optimization , 2003, 25(2): 129-140
[52] Jansson T, Andersson A, Nilsson L. Optimization of draw-in for an automotive sheet metal part An evaluation using surrogate models and response surfaces. Journal of Materials Processing Technology. 2005, 159(3): 426-434
[53] Jakumeit J, Herdy M and Nitsche M. Parameter optimization of the sheet metal forming process using an iterative parallel Kriging algorithm. Structural and Multidisciplinary Optimization, 2005,29(6):1615-1488
[54] Ohata T Katayama. Improvement of optimum process design system by numerical simulation. Journal of Engineering Materials and Technology, 1998, 88(1): 635-641
[55] Ohata T Katayama. Development of optimum process design system by numerical simulation. Journal of Engineering Materials and Technology, 1996, 60(1):543-548
[56] Ohata T, Nakamura Y, Katayama T, Nakamachi E. Development of optimum process design system for sheet fabrication using response surface method. Journal of Materials Processing Technology. 2003, 143-144, 667-672
[57] Y. Nakamura, T. Ohata, T, Katayama, et al., Optimum die design for sheet metal forming process by finite element and discretized optimization methods. In: Proceedings of the Numiform’98, 1998, 787–792
[58] Liew K M, Tan H, Ray T and Tan M J. Optimal process design of sheet metal forming for minimum springback via an integrated neural network evolutionary algorithm. Structural and Multidisciplinary Optimization, 2004,26(3-4): 284-294
[59] 王广春, 赵国群. 马新武基于灵敏度分析的预锻模具形状优化设计. 锻压技术, 2001, 26(5): 52-55
[60] 包有霞. 车身覆盖件冲压成形中拉深盘的优化设计方法研究: [上海交通大学博士学位论文]. 上海:上海交通大学, 2000, 26-88
[61] 韩利芬, 高晖, 李光耀. 神经网络与遗传算法在拉延筋参数反求中的应用. 机械工程学报, 2005, 41(5): 171-176
[62] 张峻, 柯映林. 序列响应面方法在覆盖件成形过程中的应用研究. 汽车工程, 2005, 27(2): 246-250
[63] Belytschko T, Liu W K, Moran B. Nonlinear finite elements for continua and structures. 庄茁. 第 1 版. 北京: 清华大学出版社, 2002, 64-108
[64] 赵海鸥. LS-DYNA 动力分析指南. 兵器工业出版社. 2005,30-36
[65] Hill R. A theory of the yielding and plastic flow of anisotropic materials. in: Proceedings of the Royal Society of London, Series A, 1948, 193, 281-297
[66] Hill R. Theoretical plasticity of textured aggregates. Mathematical Proceedings of Cambridge Philosophical Society, 1979, 85, 179-191
[67] 谢晖. 基于 CAE 的冲压工艺分析理论与关键技术研究: [湖南大学博士学位论文]. 长沙: 湖南大学, 2003, 1-26
[68] 钟志华,李光耀, 冲压成形 CAE 技术中接触摩擦计算的新方法.机械工程学报,2001,37(2):33-37
[69] Zhong Z H,Finite Element Procedures for Contact Impact Problems. United Kingdom and New York: Oxford University Press, 1993
[70] Belytschko T, Tsay C S. A stabilization procedure for the quadrilateral plate element with one-point quadrature. Comput. Meth. Appl. Mech. Engng., 1986, 55, 259-300
[71] Belytschko T, Wong B L and Chiang H Y, Advances in one-point quadrature shell elements. Comput. Meth. Appl. Mech. Engng., 1992, 96(1): 93-107
[72] Belytschko T, and Leviathan I. Physical stabilization,of the 4-node shell element with one-point quadrature. Computer Methods in Applied Mechanics and Engineering, 1994, 113(3-4): 321-350
[73] Hughes T J R, Liu WK. Nonlinear finite element analysis of shell: Part I. Three-dimensional shells. Comput. Meth. Appl. Mech. Engrg., 1981,26, 331-362
[74] Hughes T J R, Liu WK. Nonlinear finite element analysis of shell: Part II. Two-dimensional shells. Comput. Meth. Appl. Mech. Engrg., 1981, 27, 167-181
[75] Hill R. The Mathematical Theory of Plasticity. Clarendon Press. Oxford, 1950
[76] Sanchez LR. A new cyclic anisotropic model for plane strain sheet metal forming . International Journal of mechanical sciences, 2000, 42(4): 705-728
[77] 干年妃. 金属塑性成形过程的三维自适应无网格仿真方法研究: [湖南大学博士论文]. 长沙: 湖南大学, 2006, 58-61
[78] Li G Y, Sidibe K L L, Liu G R. Meshfree method for 3D bulk forming analysis with lower order integration scheme. Engineering Analysis with Boundary Elements, 2004, (28):1283-1292
[79] 徐丙坤. 汽车覆盖件冲压成形过程有限元数值模拟技术研究: [北京航空航天大学博士学位论文]. 北京: 北京航空航天大学, 2002, 71-94
[80] S. P. Keeler. Circular Grid System A Valuable Aid for Evaluating Sheet Metal Formability. SAE Trans. 1968, 92, 371-379
[81] Goodwin G M. A pplication of Strain Analysis to Sheet Metal Forming Problems in Press Shop. SAE Trans. 1968, 93, 380-387
[82] 郑刚, 李光耀, 孙光永. 基于近似模型的拉延筋几何参数反求. 2006, 17(19): 1988-1992
[83] Kim Y. Study on wrinkling limit diagram of anisotropic sheet metals. Journal of Materials Processing Technology, 2000, 97(1-3): 88-94
[84] 张峻. 汽车覆盖件成形过程数值模拟与优化技术研究: [浙江大学博士学位论文]. 杭州:浙江大学, 2005,1-119
[85] Myers, R. H., and Montgomery, D. C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley and Sons, Inc., Toronto., New York, NY, USA ,1995
[86] Kurtaran H, Eskandarian A, Marzougui D, Bedewi N E. Crashworthiness design optimization using successive response surface approximations. Computational mechanics, 2002, 29(4-5): 409-421
[87] Stander N, Craig K J. On the robustness of the successive response surface method for simulation-based optimization. Engineering Computations, 2002, 19,431-450
[88] Giunta A A, Balabanov V, Haim D, Grossman, B,et al. Multidisciplinary Optimization of a Supersonic Transport Using Design of Experiments theory and Response Surface Modeling. Aeronaut. J., 1997, 347–356
[89] Unal R, Lepsch R A, Engelund W, and Stanley D O. Approximation Model Building and Multidisciplinary Optimization Using Response Surface Methods. AIAA-96- 4044-CP, 1996, 592–598
[90] Unal R, Lepsch R A, and McMillin M L, Response Surface Model Building and Multidisciplinary Optimization Using D-Optimal Designs. AIAA-98-4759, 1998, 405–411
[91] Simpson T W, Mauery T M, Korte J J, and Mistree F. Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization. AIAA-98-4755, 1998, 2,381–391
[92] Wang G G, Dong Z, and Aitchison P. Adaptive Response Surface Method–A Global Optimization Scheme for Computation-intensive Design Problems. Journal of Engineering Optimization, 2001,707–734
[93] Simpson T W, Peplinski J D, Koch P N, and Allen J K. Metamodels for Computer- based Engineering Design: Survey and Recommendations. Eng. Comput., 2001, 17(2), 129–150
[94] 熊俊涛, 乔志德, 韩忠华. 基于响应面法的跨声速机翼气动优化设计. 航空学报, 2006, 27(3): 399–402
[95] 任露泉. 试验优化技术. 机械工业出版社, 北京, 1987
[96] 王海亮. 基于耐撞性数值仿真的汽车车身结构优化设计研究: [上海交通大学博士学位论文]. 上海:上海交通大学, 2002, 41-63
[97] Lancaster P, Salkauskas K. Surfaces Generated by Moving Least-squares Methods. Mathematics of Computation,1981, 37(155): 141–158
[98] 龙述尧, 刘凯远, 胡德安. 移动最小二乘近似函数中的样条权函数的研究. 湖南大学学报, 2003, 30(6): 10-13
[99] 茆诗松, 周纪芗, 陈颖. 试验设计. 中国统计出版社, 2004, 287–333
[100] Mitchell, T J. An Algorithm for the Construction of D-Optimal Experimental Designs. Technometrics, 1974, 16(2): 203–210
[101] Giunta A A, Balabanov V. Multidisciplinary Optimization of a Supersonic Transport Using Design of Experiments Theory and Response Surface Modeling. Aeronaut. J., 1997, 101(1): 347–356
[102] Haftka R, Scott E P, and Cruz J R. Optimization and Experiments: A Survey.Appl. Mech. Rev., 1998 51(7): 435–448
[103] Taguchi G, Yokoyama Y, and Wu Y Taguchi. Methods: Design of Experiments. American Supplier Institute, Allen Park, Michigan, 1993
[104] Sacks J, Schiller S B, and Welch, W J. Designs for Computer Experiments. Technometrics, 1989, 31(1): 41–47
[105] Lin Y, Krishnapur K, Allen J K, and Mistree F. Robust Concept Exploration in Engineering Design: Metamodeling Techniques and Goal Formulations. In: Proceedings of the 2000 ASME Design Engineering Technical Conferences, DETC2000/DAC-14283, Baltimore, Maryland. 2000, 10–14
[106] Park, J S. Optimal Latin-hypercube Designs for Computer Experiments. J. Stat. Plan. Infer., 1994, 39(1), 95–111
[107] Ye K Q, Li William, and Sudianto A. Algorithmic Construction of Optimal Symmetric Latin Hypercube Designs. J. Stat. Plan. Infer., 2000, 90(1), 145–159
[108] Tang B. Orthogonal Array-based Latin Hypercubes. J. Am. Stat. Assoc., 1993, 88(424): 1392–1397
[109] Zitzler E, Thiele L. Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach. Evolutionary Computation, 1999, 3(4): 257-271
[110] BENJAMIN W Timothy W.S. Efficient Pareto Frontier Exploration Using Surrogate Approximations. Optimization and Engineering, 2001, 2 (1): 31–50
[111] Shan, Songqing; Wang, G G. An Efficient Pareto Set Identification Approach for Multiobjective optimization on Black-Box Functions. Journal of Mechanical Design (Transactions of the ASME), 2005, 127(5): 866–874
[112] Wilson B, Cappelleri D J, Simpson T W, Frecker M. Efficient Pareto frontier exploration using surrogate approximations. Optimization and Engineering, 2001, 2, (1): 31-50
[113] Goel T, Vaidyanathan R, et al. Response surface approximation of Pareto optimal front in multi-objective optimization. Computer Methods in Applied Mechanics and Engineering, 2007,196(4-6): 879–893
[114] Kennedy J, Eberhart R C. Particle Swarm optimization. In: Proc IEEE Interna- tional Conference on Neural Networks, 1995, 1942–1948
[115] Eberhart R C, Shi Y. Particle swarm optimization: develoments, applications and resources. In: Proc, Congress on Evolutionary Computation 2001, Piscataway, NJ: IEEE press, 2001, 81–86
[116] Parsopoulos K E, Varhatis M N. Particle swarm optimization method inmultiobjective problems. In: Proc, ACM Symp on Applied Computing, Madrid, Spain, 2002, 603–607
[117] Hu X, Eberhart R C.Multiobjective using dynamic neighborhood particle swarm optimization. In: Proc, Congress Evolutionary Compution, Honolulu, Hawaii, USA, 2002, 1677–1681
[118] Raquel C R, Naval P C. An Effective Use of Crowding Distance in Multiobjective Particle Swarm Optimization. In: Proc, Congress Evolutionary Compution, Washington DC, USA, 2005, 257–264
[119] 闰晓珂, 史彩成, 何佩琨. 基于粒子群优化算法的自适应图像分割方法. 光学技术, 2006, 32(16): 889-892
[120] 张建立, 王长松. 粒子群算法在优化板坯二冷制度中的应用. 特种铸造及有色合金 2006, 26(11): 701-703
[121] 王勖成. 有限单元法. 第一版. 北京: 清华大学出版社, 2003, 165-175
[122] Belytschko T. Fission-Fussion adaptivity in finite elements for nolinear dynamics of shells. Computer & Structures, 1989, 33(5): 1307–1323
[123] Bessette G C. Modeling of impact problems using an h-adaptive, explicit Lagrangian finite element method in three dimensions. Comput. Methods Appl. Mech. Engrg., 2003, 192, 1649-1679
[124] Belytschko T, Mullen R. Explicit integration of structural problems. Finite Elements in Nonlinear Mechanics,1997, 2:697-720
[125] Neal M O, Belytschko T. Explicit-explicit subcycling with non-integer time step ratios for structural dynamic systems.Comput. Struct., 1989, 31:871-880
[126] Belytschko T, Lu Y Y. An explicit multi-time step integration for parabolic and hyperbolic systems. In: New Methods Trans. Anal., 1992, 246: 25-39
[127] Daniel W J T. Analysis and implementation of a new constant acceleration subcycling algorithm. Int. J. Numer.Meth. Eng., 1997, 40:2 841-2 855
[128] Belytschko T, Lin I, Tsay. Explicit algorithms for the nonlinear dynamics of shells. Comput. Methods Appl.Mech. Eng., 1984, 42:225-251
[129] Smolinski P, Belytschko T, Neal M. Multi-time-step integration using nodal partitioning. Int. J. Numer. Methods Eng.,1988, 26: 349-359
[130] Michael L B. Optimization of the sheet metal stamping process: closed-loop active drawbead control combined with in-die process sensing: [dissertation]. Michigan: Michigan technological university, 1999, 911-915
[131] 钟志华, 黄文梅, 杨沿平, 杨旭静. 汽车车身冲压工艺与模具关键技术研究. 机械工程学报, 2003, 39(12): 44-50
[2] 陈军,石晓祥,姚兴,阮雪榆. 汽车覆盖件冲压工艺/ 模具计算机辅助技术的发展现状. 锻压技术, 2002, 6, 14-18
[3] 钟志华,李光耀. 薄板冲压成形过程的计算机仿真与应用. 第1版. 北京:北京理工大学出版社, 1998, 1-7
[4] 汽车覆盖件拉伸模的设计现状及发展方向. 电加工与模具, 2001, 2, 13-15
[5] 徐伟力,林忠钦,刘罡等. 车身覆盖件冲压仿真的现状和发展趋势. 机械工程学报, 2000, 36(7): 1-4
[6] 张晓静,周贤宾,孔永明. 板料成形数值模拟研究. 锻压技术,2001,1, 13-17
[7] Paiter M J, Pearce R. Metal flow through a drawbead. Sheet metal industries, 1976, (7): 12-20
[8] Nine H D. Drawbead forces in sheet metal forming. In: Mechanics of Sheet Metal Forming. New York: Plenum Press, 1978, 179-211
[9] Wang N M, Shah V C. Drawbead design and performance. J. of Material Shaping Tech., 1991, 9(1): 21-26
[10] Schey J A. Speed effects in drawbead simulation. J. Mater. Process Technol., 1996, 57(1): 146-154
[11] Demeri M Y. Drawbeads in sheet metal forming. J. Mater. Eng. Perform, 1993, 2(6): 863-866
[12] 邢忠文.薄板冲压成形中拉深筋阻力及其影响因素研究. 模具工业,1994, 4, 33-35
[13] 刘迪辉,钟志华. 拉延筋对回弹的影响机理研究. 中国机械工程,2005,16(20): 1876-1879
[14] Levy B S. Development of a predictive model for draw bead restraining forces utilizing work of Nine and Wang. J. Appl. Metalworking, 1983, 3(1): 38-44
[15] Ludovic Courvoisier, Marion Martiny, Gerard Ferron. Analytical modeling of drawbeads in sheet metal forming. Journal of materials Processing Technology. 2003, 133(3): 359-370
[16] Fuh Kou Chen, Pao Ching Tszeng. An analysis of drawbead restraining force in the stamping process. International Journal of Machine Tools & Manufature, 1998,38(7):827-842
[17] 李东升,黄小明,胡世光. 汽车覆盖件成型中拉延筋约束力的模拟计算. 塑性工程学报,1994, 1, 59-65
[18] 徐 丙 坤 , 施 法 中 . 拉 延 筋 约 束 阻 力 的 一 种 解 析 计 算 方 法 . 锻 压 技术,2001,26(6):11-13
[19] 朱勇建,那景新,闫亚坤等. 应用直接法求解拉延筋约束力. 吉林大学学报(工学版), 2003, 33(1): 92-97
[20] 李淑慧,林忠钦,包友霞等. 改进的等效拉延筋阻力模型及其应用. 中国机械工程, 2002, 13(7): 558-561
[21] 王烨. 拉延筋模型及汽车覆盖件成形工艺 CAD/CAE 集成系统关键技术的研究: [上海交通大学博士学位论文]. 上海: 上海交通大学,2000,82-84
[22] Chabrand P, Dubois F, Gelin J C. Modelling drawbeads in sheet metal forming. Int. J. of Mechanical Science, 1996, 38(1): 59-77
[23] Cao J, Boyce M C. Draw bead penetration as a control element of material flow. SAE 930517, 1993, 694-702
[24] Carleer B D, Meinders T, Hu tink H. Equivalent drawbead model in finite element simulations. Numerical Simulations of 3-D Sheet Metal forming Processes (NUMISHEET'96), Michigan, USA, 1996, 25-31
[25] Carleer B D, Vreede P T, Drent P, et al. Modelling Drawbeads with Finite Elements and Verification. J.Mater.Process.Technol, 1994, 45(1): 63-68
[26] Weinmann K J, Sanchez L R. A general computer model for plane strain sheet flow and its application to flow between circular drawbeads. In: Proceedings of the 15th IDDRG. Dearborn,USA and Toronto, Canada, 1988, 217-226
[27] Weidemann . The blankholder action of drawbeads. In: Proc. of 10th Biennial IDDRG Congress. 1978, 79-84
[28] 印雄飞. 板料成形中拉延筋模型及其工艺效果的研究: [上海交通大学博士学位论文]. 上海: 上海交通大学, 1999, 1-13
[29] Wang N M. A mathematical model of drawbead forces in sheet metal forming. J. Appl. Met. Working, 1982, 2(3): 193-199
[30] Stoughton T B. Model of drawbead forces in sheet metal forming. in: Proceedings of the 15th IDDRG. Dearborn, USA and Toronto, Canada, 1988, 205-215
[31] Ghoo B Y, Keum Y T. Expert drawbead models for sectional FEM analysis of sheet metal forming process. Journal of Materials Processing Technology, 2000, 105(1): 7-16
[32] Keum Y T, Kim J H, Ghoo B Y. Expert drawbead models for finite elementanalysis of sheet metal forming processes. International Journal of Solids and Structures, 2001, 38(30): 5335-5353
[33] Sanchez LR, Weinmann K J. An Analytical and Experimental Study of the Flow of Sheet Metal between Circular Drawbeads. Journal of Engineering for for Industry, 1996 ,118(1): 45-54
[34] 李大永, 胡平, 李运兴. 拉延筋阻力的一种简便解析模型. 机械工程学报, 2000, 36(5): 46-49
[35] 印雄飞, 何丹农, 彭颖红等. 板料成形有限元分析中的等拉延筋模型. 计算机技术应用, 1999, 34(5):49-51
[36] Roy S, Shivpuri R. A new approach to optimal design of multi-stage metal forming processes with micro genetic algorithms. INTERNATIONAL JOURNAL OF MACHINE TOOLS & MANUFACTURE, 2000, 37(1): 29-44
[37] Liu Gang Bao Youxia. Optimization Design of Drawbead in Drawing Tools of Autobody Cover Panel. Journal of Engineering Materials and Technology, 2002, 124(2): 278-285
[38] Nakamura Y, Katayama T. Optimum die design for sheet metal forming process by using finite element and discretized optimization methods. In: NUMIFORM 98: Sixth International Conference on Numerical Methods in Industrial Forming Processes, Enschede, Netherlands, 1998, 787-792
[39] Chung J S. Application of a genetic algorithm to the optimal design of the die shape in extrusion. Journal of Materials Processing Technology, 1997, 72(1): 69-77
[40] Gantar G, Pepelnjak T, Kuzman K. Optimization of sheet metal forming processes by the use of numerical simulations. Journal of Materials Processing Technology, 2002, 130, 54-59
[41] Kubli W, Reissner J. Optimization of sheet-metal forming processes using the special-purpose program AUTOFORM. Journal of Materials Processing Technology, 1995, 50(1-4): 292-305
[42] Huh H, Kim S-H. Optimum process design in sheet-metal forming with finite element analysis. Journal of Engineering Materials and Technology . 2001, 123(4): 476-481
[43] Hillmann M, Kubli W. Optimization of sheet metal forming processes using simulation programs. In: Proc. of NUMISHEET, 1999, 287-292
[44] Naceur H,Delameziere A,Batoz J L,et al.Some improvements on the optimum process design in deep drawing using the inverse approach. Journal of MaterialsProcessing Technology,2004,146(2): 250-262
[45] Naceur H, Gou Y Q, Batoz J L, et al.Optimization of blank restraining forces to improve the global quality of stamping parts. In: Proceedings of the Fourth International Conference on Numerical Simulation, NUMISHEET’99, Besancon, France, 1999, 517-521
[46] Naceur H, Guo YQ, Batoz JL, Knopf-Lenoir C. Optimization of drawbead restraining forces and drawbead design in sheet metal forming process. International Journal of Mechanical Sciences, 2001, 43(10): 2407-2434
[47] Guo Y Q, Batoz J L, Naceur H, et al. Recent developments on the analysis and optimum design of sheet metal forming parts using a simplified inverse approach Computers and Structures, 2000, 78(1) :133-148
[48] Guo YQ, Naceur H, Debray K, Bogard F. Initial solution estimation to speed up inverse approach in stamping modeling, Engineering Computations. Int J for Computer Aided Engineering, 2003, 20(7): 810-834
[49] NACEUR H, GUO Y Q, BATOZ J L. Blank optimization in sheet metal forming using an evolutionary algorithm. Journal of materials processing technology , 2004, 151(3): 183-191
[50] Schenk Olaf, Hillmann Matthias. Optimal design of metal forming die surfaces with evolution strategies. Computers & Structures, 2004, 82(20-21): 1695-1705
[51] JANSSON T, NILSSON L, REDHE M. Using surrogate models and response surfaces in structural optimization: with application to crashworthiness design and sheet metal forming. Structural and multidisciplinary optimization , 2003, 25(2): 129-140
[52] Jansson T, Andersson A, Nilsson L. Optimization of draw-in for an automotive sheet metal part An evaluation using surrogate models and response surfaces. Journal of Materials Processing Technology. 2005, 159(3): 426-434
[53] Jakumeit J, Herdy M and Nitsche M. Parameter optimization of the sheet metal forming process using an iterative parallel Kriging algorithm. Structural and Multidisciplinary Optimization, 2005,29(6):1615-1488
[54] Ohata T Katayama. Improvement of optimum process design system by numerical simulation. Journal of Engineering Materials and Technology, 1998, 88(1): 635-641
[55] Ohata T Katayama. Development of optimum process design system by numerical simulation. Journal of Engineering Materials and Technology, 1996, 60(1):543-548
[56] Ohata T, Nakamura Y, Katayama T, Nakamachi E. Development of optimum process design system for sheet fabrication using response surface method. Journal of Materials Processing Technology. 2003, 143-144, 667-672
[57] Y. Nakamura, T. Ohata, T, Katayama, et al., Optimum die design for sheet metal forming process by finite element and discretized optimization methods. In: Proceedings of the Numiform’98, 1998, 787–792
[58] Liew K M, Tan H, Ray T and Tan M J. Optimal process design of sheet metal forming for minimum springback via an integrated neural network evolutionary algorithm. Structural and Multidisciplinary Optimization, 2004,26(3-4): 284-294
[59] 王广春, 赵国群. 马新武基于灵敏度分析的预锻模具形状优化设计. 锻压技术, 2001, 26(5): 52-55
[60] 包有霞. 车身覆盖件冲压成形中拉深盘的优化设计方法研究: [上海交通大学博士学位论文]. 上海:上海交通大学, 2000, 26-88
[61] 韩利芬, 高晖, 李光耀. 神经网络与遗传算法在拉延筋参数反求中的应用. 机械工程学报, 2005, 41(5): 171-176
[62] 张峻, 柯映林. 序列响应面方法在覆盖件成形过程中的应用研究. 汽车工程, 2005, 27(2): 246-250
[63] Belytschko T, Liu W K, Moran B. Nonlinear finite elements for continua and structures. 庄茁. 第 1 版. 北京: 清华大学出版社, 2002, 64-108
[64] 赵海鸥. LS-DYNA 动力分析指南. 兵器工业出版社. 2005,30-36
[65] Hill R. A theory of the yielding and plastic flow of anisotropic materials. in: Proceedings of the Royal Society of London, Series A, 1948, 193, 281-297
[66] Hill R. Theoretical plasticity of textured aggregates. Mathematical Proceedings of Cambridge Philosophical Society, 1979, 85, 179-191
[67] 谢晖. 基于 CAE 的冲压工艺分析理论与关键技术研究: [湖南大学博士学位论文]. 长沙: 湖南大学, 2003, 1-26
[68] 钟志华,李光耀, 冲压成形 CAE 技术中接触摩擦计算的新方法.机械工程学报,2001,37(2):33-37
[69] Zhong Z H,Finite Element Procedures for Contact Impact Problems. United Kingdom and New York: Oxford University Press, 1993
[70] Belytschko T, Tsay C S. A stabilization procedure for the quadrilateral plate element with one-point quadrature. Comput. Meth. Appl. Mech. Engng., 1986, 55, 259-300
[71] Belytschko T, Wong B L and Chiang H Y, Advances in one-point quadrature shell elements. Comput. Meth. Appl. Mech. Engng., 1992, 96(1): 93-107
[72] Belytschko T, and Leviathan I. Physical stabilization,of the 4-node shell element with one-point quadrature. Computer Methods in Applied Mechanics and Engineering, 1994, 113(3-4): 321-350
[73] Hughes T J R, Liu WK. Nonlinear finite element analysis of shell: Part I. Three-dimensional shells. Comput. Meth. Appl. Mech. Engrg., 1981,26, 331-362
[74] Hughes T J R, Liu WK. Nonlinear finite element analysis of shell: Part II. Two-dimensional shells. Comput. Meth. Appl. Mech. Engrg., 1981, 27, 167-181
[75] Hill R. The Mathematical Theory of Plasticity. Clarendon Press. Oxford, 1950
[76] Sanchez LR. A new cyclic anisotropic model for plane strain sheet metal forming . International Journal of mechanical sciences, 2000, 42(4): 705-728
[77] 干年妃. 金属塑性成形过程的三维自适应无网格仿真方法研究: [湖南大学博士论文]. 长沙: 湖南大学, 2006, 58-61
[78] Li G Y, Sidibe K L L, Liu G R. Meshfree method for 3D bulk forming analysis with lower order integration scheme. Engineering Analysis with Boundary Elements, 2004, (28):1283-1292
[79] 徐丙坤. 汽车覆盖件冲压成形过程有限元数值模拟技术研究: [北京航空航天大学博士学位论文]. 北京: 北京航空航天大学, 2002, 71-94
[80] S. P. Keeler. Circular Grid System A Valuable Aid for Evaluating Sheet Metal Formability. SAE Trans. 1968, 92, 371-379
[81] Goodwin G M. A pplication of Strain Analysis to Sheet Metal Forming Problems in Press Shop. SAE Trans. 1968, 93, 380-387
[82] 郑刚, 李光耀, 孙光永. 基于近似模型的拉延筋几何参数反求. 2006, 17(19): 1988-1992
[83] Kim Y. Study on wrinkling limit diagram of anisotropic sheet metals. Journal of Materials Processing Technology, 2000, 97(1-3): 88-94
[84] 张峻. 汽车覆盖件成形过程数值模拟与优化技术研究: [浙江大学博士学位论文]. 杭州:浙江大学, 2005,1-119
[85] Myers, R. H., and Montgomery, D. C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley and Sons, Inc., Toronto., New York, NY, USA ,1995
[86] Kurtaran H, Eskandarian A, Marzougui D, Bedewi N E. Crashworthiness design optimization using successive response surface approximations. Computational mechanics, 2002, 29(4-5): 409-421
[87] Stander N, Craig K J. On the robustness of the successive response surface method for simulation-based optimization. Engineering Computations, 2002, 19,431-450
[88] Giunta A A, Balabanov V, Haim D, Grossman, B,et al. Multidisciplinary Optimization of a Supersonic Transport Using Design of Experiments theory and Response Surface Modeling. Aeronaut. J., 1997, 347–356
[89] Unal R, Lepsch R A, Engelund W, and Stanley D O. Approximation Model Building and Multidisciplinary Optimization Using Response Surface Methods. AIAA-96- 4044-CP, 1996, 592–598
[90] Unal R, Lepsch R A, and McMillin M L, Response Surface Model Building and Multidisciplinary Optimization Using D-Optimal Designs. AIAA-98-4759, 1998, 405–411
[91] Simpson T W, Mauery T M, Korte J J, and Mistree F. Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization. AIAA-98-4755, 1998, 2,381–391
[92] Wang G G, Dong Z, and Aitchison P. Adaptive Response Surface Method–A Global Optimization Scheme for Computation-intensive Design Problems. Journal of Engineering Optimization, 2001,707–734
[93] Simpson T W, Peplinski J D, Koch P N, and Allen J K. Metamodels for Computer- based Engineering Design: Survey and Recommendations. Eng. Comput., 2001, 17(2), 129–150
[94] 熊俊涛, 乔志德, 韩忠华. 基于响应面法的跨声速机翼气动优化设计. 航空学报, 2006, 27(3): 399–402
[95] 任露泉. 试验优化技术. 机械工业出版社, 北京, 1987
[96] 王海亮. 基于耐撞性数值仿真的汽车车身结构优化设计研究: [上海交通大学博士学位论文]. 上海:上海交通大学, 2002, 41-63
[97] Lancaster P, Salkauskas K. Surfaces Generated by Moving Least-squares Methods. Mathematics of Computation,1981, 37(155): 141–158
[98] 龙述尧, 刘凯远, 胡德安. 移动最小二乘近似函数中的样条权函数的研究. 湖南大学学报, 2003, 30(6): 10-13
[99] 茆诗松, 周纪芗, 陈颖. 试验设计. 中国统计出版社, 2004, 287–333
[100] Mitchell, T J. An Algorithm for the Construction of D-Optimal Experimental Designs. Technometrics, 1974, 16(2): 203–210
[101] Giunta A A, Balabanov V. Multidisciplinary Optimization of a Supersonic Transport Using Design of Experiments Theory and Response Surface Modeling. Aeronaut. J., 1997, 101(1): 347–356
[102] Haftka R, Scott E P, and Cruz J R. Optimization and Experiments: A Survey.Appl. Mech. Rev., 1998 51(7): 435–448
[103] Taguchi G, Yokoyama Y, and Wu Y Taguchi. Methods: Design of Experiments. American Supplier Institute, Allen Park, Michigan, 1993
[104] Sacks J, Schiller S B, and Welch, W J. Designs for Computer Experiments. Technometrics, 1989, 31(1): 41–47
[105] Lin Y, Krishnapur K, Allen J K, and Mistree F. Robust Concept Exploration in Engineering Design: Metamodeling Techniques and Goal Formulations. In: Proceedings of the 2000 ASME Design Engineering Technical Conferences, DETC2000/DAC-14283, Baltimore, Maryland. 2000, 10–14
[106] Park, J S. Optimal Latin-hypercube Designs for Computer Experiments. J. Stat. Plan. Infer., 1994, 39(1), 95–111
[107] Ye K Q, Li William, and Sudianto A. Algorithmic Construction of Optimal Symmetric Latin Hypercube Designs. J. Stat. Plan. Infer., 2000, 90(1), 145–159
[108] Tang B. Orthogonal Array-based Latin Hypercubes. J. Am. Stat. Assoc., 1993, 88(424): 1392–1397
[109] Zitzler E, Thiele L. Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach. Evolutionary Computation, 1999, 3(4): 257-271
[110] BENJAMIN W Timothy W.S. Efficient Pareto Frontier Exploration Using Surrogate Approximations. Optimization and Engineering, 2001, 2 (1): 31–50
[111] Shan, Songqing; Wang, G G. An Efficient Pareto Set Identification Approach for Multiobjective optimization on Black-Box Functions. Journal of Mechanical Design (Transactions of the ASME), 2005, 127(5): 866–874
[112] Wilson B, Cappelleri D J, Simpson T W, Frecker M. Efficient Pareto frontier exploration using surrogate approximations. Optimization and Engineering, 2001, 2, (1): 31-50
[113] Goel T, Vaidyanathan R, et al. Response surface approximation of Pareto optimal front in multi-objective optimization. Computer Methods in Applied Mechanics and Engineering, 2007,196(4-6): 879–893
[114] Kennedy J, Eberhart R C. Particle Swarm optimization. In: Proc IEEE Interna- tional Conference on Neural Networks, 1995, 1942–1948
[115] Eberhart R C, Shi Y. Particle swarm optimization: develoments, applications and resources. In: Proc, Congress on Evolutionary Computation 2001, Piscataway, NJ: IEEE press, 2001, 81–86
[116] Parsopoulos K E, Varhatis M N. Particle swarm optimization method inmultiobjective problems. In: Proc, ACM Symp on Applied Computing, Madrid, Spain, 2002, 603–607
[117] Hu X, Eberhart R C.Multiobjective using dynamic neighborhood particle swarm optimization. In: Proc, Congress Evolutionary Compution, Honolulu, Hawaii, USA, 2002, 1677–1681
[118] Raquel C R, Naval P C. An Effective Use of Crowding Distance in Multiobjective Particle Swarm Optimization. In: Proc, Congress Evolutionary Compution, Washington DC, USA, 2005, 257–264
[119] 闰晓珂, 史彩成, 何佩琨. 基于粒子群优化算法的自适应图像分割方法. 光学技术, 2006, 32(16): 889-892
[120] 张建立, 王长松. 粒子群算法在优化板坯二冷制度中的应用. 特种铸造及有色合金 2006, 26(11): 701-703
[121] 王勖成. 有限单元法. 第一版. 北京: 清华大学出版社, 2003, 165-175
[122] Belytschko T. Fission-Fussion adaptivity in finite elements for nolinear dynamics of shells. Computer & Structures, 1989, 33(5): 1307–1323
[123] Bessette G C. Modeling of impact problems using an h-adaptive, explicit Lagrangian finite element method in three dimensions. Comput. Methods Appl. Mech. Engrg., 2003, 192, 1649-1679
[124] Belytschko T, Mullen R. Explicit integration of structural problems. Finite Elements in Nonlinear Mechanics,1997, 2:697-720
[125] Neal M O, Belytschko T. Explicit-explicit subcycling with non-integer time step ratios for structural dynamic systems.Comput. Struct., 1989, 31:871-880
[126] Belytschko T, Lu Y Y. An explicit multi-time step integration for parabolic and hyperbolic systems. In: New Methods Trans. Anal., 1992, 246: 25-39
[127] Daniel W J T. Analysis and implementation of a new constant acceleration subcycling algorithm. Int. J. Numer.Meth. Eng., 1997, 40:2 841-2 855
[128] Belytschko T, Lin I, Tsay. Explicit algorithms for the nonlinear dynamics of shells. Comput. Methods Appl.Mech. Eng., 1984, 42:225-251
[129] Smolinski P, Belytschko T, Neal M. Multi-time-step integration using nodal partitioning. Int. J. Numer. Methods Eng.,1988, 26: 349-359
[130] Michael L B. Optimization of the sheet metal stamping process: closed-loop active drawbead control combined with in-die process sensing: [dissertation]. Michigan: Michigan technological university, 1999, 911-915
[131] 钟志华, 黄文梅, 杨沿平, 杨旭静. 汽车车身冲压工艺与模具关键技术研究. 机械工程学报, 2003, 39(12): 44-50
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