Analysis of Sheet Metal Stamping Based on New Triangular Shell Element and Multiple Dynamic Adaptive Method

doi:10.3901/JME.2024.14.153

Abstract

Abstract: Sheet metal stamping is a technological method that takes advantage of the plasticity of sheet metal and forms under the external force of die. Based on the key technology of sheet metal stamping process, a new triangular shell element for sheet metal stamping is developed. Based on the updated Lagrangian framework, an implicit radial return algorithm for nonlinear solution of materials is embedded. A contact search algorithm and a contact force calculation method for contact analysis are developed to solve the sheet metal stamping problem. The balance between calculation efficiency and calculation accuracy is the key to finite element simulation of sheet metal stamping. The error criterion of combining geometry with energy is applied to improve the accuracy of encryption range, and the method of inserting new nodes according to geometric vectors is introduced to reduce the iteration of contact calculation. A multiple dynamic adaptive algorithm is proposed. With the change of deformation area and stress concentration area in the calculation process, multiple “encryption-coarsening- encryption” are carried out on the mesh. Through the comparison of finite element simulation examples, it shows that the algorithm in this paper can greatly improve the calculation efficiency on the premise of ensuring the calculation accuracy.

Key words: new triangular shell element, shear self-locking, sheet stamping forming, finite element simulation, adaptive mesh refinement

CLC Number:

ZHAO Yan, LI She, CUI Xiangyang. Analysis of Sheet Metal Stamping Based on New Triangular Shell Element and Multiple Dynamic Adaptive Method[J]. Journal of Mechanical Engineering, 2024, 60(14): 153-165.

References

[1] 钟志华，李光耀. 薄板冲压成型过程的计算机仿真与应用[M]. 北京：北京理工大学出版社，1998. ZHONG Zhihua，LI Guangyao. Computer simulation and application of sheet metal stamping process[M]. Beijing：Beijing Institute of Technology Press，1998.
[2] RAY N，GRINDEANU I，ZHAO X，et al. Array-based，parallel hierarchical mesh refinement algorithms for unstructured meshes[J]. Computer-Aided Design，2017，85：68-82.
[3] JENSEN K E，GONMAN G. Details of tetrahedral anisotropic mesh adaptation[J]. Computer Physics Communications，2016，201：135-143.
[4] DUVAL M，LOZINSKI A，PASSIEUX J C，et al. Residual error based adaptive mesh refinement with the non-intrusive patch algorithm[J]. Computer Methods in Applied Mechanics and Engineering，2018，329：118-143.
[5] ZIENKIEWICZ O C，ZHU J Z. A simple error estimator and adaptive procedure for practical engineerng analysis[J]. International Journal for Numerical Methods in Engineering，1987，24(2)：337-357.
[6] 刘习洲，王城璟，王琥. 基于h型自适应有限元法在薄板冲压成型中的应用[J]. 图学学报，2022，42(6)：970. LIU Xizhou，WANG Chengjing，WANG Hu. Application in sheet metal forming based on h-adaptive finite element method[J]. Journal of Engineering Graphics，2022，42(6)：970.
[7] PETHE R，HEUZE T，STAINIER L. Remapping-free variational h-adaption for strongly coupled thermo-mechanical problems[J]. Finite Elements in Analysis and Design，2020，176：103435.
[8] 陈加慧. 节点积分动态自适应算法研究及其在动态大变形问题中的应用[D]. 长沙：湖南大学，2018. CHEN Jiahui. Research on node integral dynamic adaptive algorithm and its application in dynamic large deformation[D]. Changsha：Hunan University，2018.
[9] CHATTERJEE T，CHOWDHURY R. h-p adaptive model based approximation of moment free sensitivity indices[J]. Computer Methods in Applied Mechanics & Engineering，2018，332：572-599.
[10] 徐岗，王毅刚，胡维华. 等几何分析中的r-p型细化方法[J]. 计算机辅助设计与图形学学报，2011，23(12)：2019-2024. XU Gang，WANG Yigang，HU Weihua. R-p-refinement in isogemetric analysis[J]. Journal of Computer-Aided Design & Computer Graphics，2011，23(12)：2019-2024.
[11] GRINSPUN E. The basis refinement method[D]. California：California Institute of Technology，2003.
[12] XIA M，SHAO S，CHOU T. A frequency-dependent p-adaptive technique for spectral methods[J]. Journal of Computational Physics，2021，446：110627.
[13] CHENG J，YU S J，YUE H Q，et al. An adjoint-based h-adaptive reconstructed discontinuous galerkin method for the steady-state compressible Euler equations[J]. Communications in Computational Physics，2019，26(3)：855-879.
[14] GOSHTASBY A A. Plus curves and surfaces[J]. The Visual Computer，2005，21：4-16.
[15] LOOP C T. Smooth subdivision surfaces based on triangles[J]. Utah：University of Utah，1987.
[16] LU Y，WANG G，YANG X. Uniform trigonometric polynomial B-spline curves[J]. Science in China Series F Information Sciences，2002，45：335-343.
[17] 张苏，施法中. 板料冲压数值模拟中网格自适应算法插入新结点的新方法[J]. 塑性工程学报，2005，12(4)：14-18. ZHANG Su，Shi Fazhong. A new method of mesh adaptive algorithm inserting new nodes in sheet metal stamping numerical simulation[J]. Journal of Plasticity Engineering，2005，12(4)：14-18.
[18] FUNKEN S A，SCHMIDT A. Adaptive mesh refinement in 2D-An efficient implementation in matlab[J]. Computational Methods in Applied Mathematics，2020，20(3)：459-479.
[19] 李射. 金属板材磁脉冲成形高效高精度数值建模理论研究[D]. 长沙：湖南大学，2019. LI She. Modeling theory with high efficiency and high accuracy for electromagnetic sheet metal forming process [D]. Changsha：Hunan University，2019.
[20] LEE S W，YOON J W，YANG D Y. Comparative investigation into the dynamic explicit and the static implicit method for springback of sheet metal stamping [J]. Engineering Computations，1999，16(2-3)：347-373.