Solving Algorithm of Initial Guess of Intermediate Configuration in Multi-step Inverse Finite Element Method

doi:10.3901/JME.2015.24.118

Abstract

Abstract: In order to take loading path into account, intermediate configurations are introduced into different forming stages in inverse finite element method(IFEM), multi-step IFEM is presented. Research on multi-step IFEM, a good initial guess is one of key links in the process of solving. So, a kind of reverse mapping method, which is based on sliding constraint surface, has been put forward: Firstly, bending configuration is solved through bending effect of blank and sliding constraint surface is obtained in pseudo minima area optimization algorithm; Then, all nodes in the unfolded final configuration are projected onto the unfolded sliding constraint surface; Thirdly, all projected nodes will be reversely mapped back to sliding constraint surface after these coordinates are calculated in area coordinate. As a result, the corresponding initial guess of intermediate configuration can be obtained. In addition, for the problem of some nodes without projective region in unfolded sliding constraint surface, a solving solution of extending sliding constraint surface is presented. Numerical simulations validate the effectiveness of the algorithm.

Key words: boundary extension, initial guess, multi-step inverse finite element method (IFEM), panel forming, sliding constraint surface

ZHANG Xiangkui, WANG Feng, LIU Weijie, DONG Yaya, WANG Tianju. Solving Algorithm of Initial Guess of Intermediate Configuration in Multi-step Inverse Finite Element Method[J]. Journal of Mechanical Engineering, 2015, 51(24): 118-125.

References

[1] MAJLESSI S A，LEE D. Development of multistage sheet metal forming analysis method[J]. Journal of Materials Shaping Technology，1988，6(1)：41-54.
[2] HUANG Y，CHEN Y P，DU R X. A new approach to solve key issues in multi-step inverse fem in sheet metal stamping[J]. International Journal of Mechanical Sciences，2006，48(6)：591-600.
[3] LEE C H，HUN H. Three dimensional multi-step inverse analyses for the optimum blank design in sheet metal forming processes[J]. Mater. Process. Technol.，1998，80-81：76-82.
[4] KIM S H，HUH H. Finite element inverse analysis for the design of intermediate dies in multi-stage deep-drawing processes with large aspect ratio[J]. Journal of Materials Processing Technology，2001，113：779-785.
[5] KIM S H，HUH H. Construction of sliding constraint surfaces and initial guess shapes for intermediate steps in multi-step finite element inverse analysis[J]. Journal of Materials Processing Technology，2002，130-131：482-489.
[6] GUO Y Q，LI Y M，BOGARD F，et al. An efficient pseudo-inverse approach for damage modeling in the sheet forming process[J]. Journal of Materials Processing Technology，2004，151(1)：88-97.
[7] 唐炳涛，赵震，陈军，等. 多工步板料成形问题的多步反向模拟法[J]. 机械工程学报，2006，42(12)：211-217.TANG Bingtao，ZHAO Zhen，CHEN Jun，et al. Development of multistage sheet metal forming simulation based on multi-step inverse analysis approach[J]. Chinese Journal of Mechanical Engineering，2006，42(12)：211-217.
[8] 吴建军，朱华. 双展开平面映射法研究及在多步快速模拟中的应用[J]. 塑性工程学报，2008，15(5)：152-154.WU Jianjun，ZHU Hua. Study on the double spreading plane based mapping method and it’s application in the fast simulation of multi-steps stamping[J]. Journal of Plasticity Engineering，2008，15(5)：152-154.
[9] FU L J，DONG X H，PENG F，et al. A generally suited method to get initial guess solutions for one-step and multi-step simulations of tube and profile forming based on parameterization[J]. International Journal for Numerical Methods in Biomedical Engineering，2011，27(10)：1622-1639.
[10] LIU Q，XI J，WU Z. An initial solution estimation method based on as-rigid-as-possible mesh parameterization for one-step simulation[J]. Engineering Computations，2013，30(3)：379-398.
[11] SHIRIN M B，ASSEMPOUR A. A new mapping technique to consider intermediate stages in multistep deep drawing[J]. Proceedings of the Institution of Mechanical Engineers，Part C：Journal of Mechanical Engineering Science，2014，228(9)：1557-1569.
[12] FARAHANI M K，SHIRIN M B，ASSEMPOUR A. Development of an inverse finite element method with an initial guess of linear unfolding[J]. Finite Elements in Analysis and Design，2014，79：1-8.
[13] 鲍益东. 汽车车身部件一步逆成形有限元法与碰撞仿真研究[D]. 长春：吉林大学，2004.BAO Yidong. Research on one step inverse forming fem and crash simulation of auto body part[D]. Changchun：Jilin University，2004.
[14] 刘伟杰，胡平，周平，等. 板材多步逆成形中的滑移约束曲面优化构造方法[J]. 机械工程学报，2012，48(4)：21-25. LIU Weijie，HU Ping，ZHOU Ping，et al. Research on intermediate configurations of multi-step inverse approach in sheet metal forming[J]. Journal of Mechanical Engineering，2012，48(4)：21-25.
[15] LES P，WAYNE T. The NURBS book[M]. 2nd ed. New York：Springer-Verlag Berlin Heidelberg，1997.