Recent developments on the analysis and optimum design of sheet metal forming parts using a simplified inverse approach
Recent developments on the analysis and optimum design of sheet metal forming parts using a simplified inverse approach
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DOI：
10.1016/s0045-7949(00)00095-x
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发表时间：
2000-11
影响因子：
4.7
通讯作者：
Y. Guo;J. Batoz;H. Naceur;S. Bouabdallah;F. Mercier;O. Barlet
中科院分区：
文献类型：
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作者：
Y. Guo;J. Batoz;H. Naceur;S. Bouabdallah;F. Mercier;O. Barlet
一种称为逆向法 (IA) 的简化高效有限元方法已被开发出来，用于估计通过拉深获得的薄金属板中的大弹塑性应变。本文介绍了作者介绍的 IA 的主要最新进展，以提高复杂工业零件毛坯轮廓分析和优化设计的效率。 IA 主要利用最终工件 3D 形状的知识。使用迭代方案来查找初始平板毛坯中每个材料点的原始位置，然后可以估计最终工件中的应变和应力。关于本构方程（塑性变形理论）和工具（冲头、凹模和压边圈）的作用采用了重要的假设。即使考虑弯曲效应，IA 也意味着每个节点仅具有两个自由度。在本文中，我们介绍了一些最新进展：（1）使用简单的三角形壳单元考虑弯曲效应，而不增加每个节点的自由度数量。 (2) 引入一些分析公式来考虑拉延筋产生的约束力。 (3)实现了分辨率算法的一些改进，如引入松弛系数、阻尼因子和良好的初始解。 (4) 使用基于 IA 和顺序二次规划方法 (SQP) 耦合的数值程序来执行毛坯轮廓的形状优化。在这项工作中，所有敏感性均使用伴随变量方法进行分析计算。将 IA 在两个基准测试中的数值结果与实验结果和其他数值结果进行了比较。优化程序应用于 Renault/Twingo 减震杯的毛坯优化设计，其中目标函数被定义为最小化厚度变化的最大值。
A simplified efficient finite element method called the inverse approach (IA) has been developed to estimate the large elasto-plastic strains in thin metallic panels obtained by deep drawing. This paper deals with the main recent developments introduced by the authors on the IA to improve its efficiency in the analysis and optimum design of blank contours of complicated industrial parts. The IA mainly exploits the knowledge of the 3D shape of the final workpiece. An iterative scheme is used to find the original position of each material point in the initial flat blank after which it is possible to estimate the strains and stresses in the final workpiece. Important assumptions are adopted regarding the constitutive equations (the deformation theory of plasticity) and the action of the tools (the punch, die and blank holders). The IA implies only two degrees of freedom per node even if bending effects are considered. In this paper, we present several recent developments: (1) The bending effects are taken into account using a simple triangular shell element without increasing the number of dof per node. (2) Some analytical formulas are introduced to consider the restraining forces due to the drawbeads. (3) Some improvements of resolution algorithms such as the introduction of a relaxation coefficient, a damping factor and a good initial solution are realized. (4) Shape optimization of blank contours is performed using a numerical procedure based on the coupling of the IA and a sequential quadratic programming method (SQP). In this work, all sensitivities are computed analytically using the adjoint variable method. The numerical results of the IA on two benchmark tests are compared with experimental and other numerical results. The optimization procedure is applied to the blank optimum design of the Renault/Twingo dashpot cup where the objective function is defined to minimize the maximum of the thickness variations.