Modification of the Stamp Topological Optimization Taking into Account Cyclic Fatigue based on the Finite Element Approach

Q3 Engineering
I. Andrianov
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引用次数: 1

Abstract

The study is devoted to optimizing the volume of stamping tools used in pressure processing processes. The relevance of the research is due to the active development of additive technologies and the possibility of producing stamping tools from plastic of optimal shape, which has an important practical significance in the manufacture of thin-walled products in the aviation and automotive industries. The purpose of the study was to carry out a mathematical formulation of the problem of topological optimization of a forming die made of a polymer material with restrictions on fatigue durability and minimum volume. The task of topological optimization was to maximize the stiffness of the die under multicyclic loading. The vector description of topological optimization was based on the finite element approach. The optimization model was built on the basis of the solid isotropic material penalization method with the introduction of additional restrictions in the model of searching for pseudo-densities of the material, taking into account the duration of the force action on the stamp under multicyclic loading. In view of the nonlinearity of the resulting system of equations, the solution of the conditional optimization problem is proposed to be carried out by constructing the Lagrange objective function and using the Lagrange multiplier method. The result of the study is the proposed approach to the topological optimization of the stamp, taking into account the multicyclic loading and restrictions on the desired volume.
基于有限元法的考虑循环疲劳的印章拓扑优化修改
该研究致力于优化压力加工过程中使用的冲压工具的体积。该研究的相关性是由于增材技术的积极发展和用塑料制造最佳形状的冲压工具的可能性,这在航空和汽车工业薄壁产品的制造中具有重要的现实意义。研究的目的是对具有疲劳耐久性和最小体积限制的聚合物材料成形模具的拓扑优化问题进行数学表述。拓扑优化的任务是使模具在多环载荷下的刚度最大化。拓扑优化的矢量描述是基于有限元方法的。该优化模型是在固体各向同性材料惩罚法的基础上建立的,并在寻找材料伪密度的模型中引入了附加的约束条件,考虑了多循环载荷作用在冲压件上的力的持续时间。考虑到所得到的方程组的非线性,提出通过构造拉格朗日目标函数和使用拉格朗日乘数法来求解条件优化问题。研究的结果是提出了一种考虑到多环载荷和期望体积限制的冲压件拓扑优化方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
International Journal of Mechanics
International Journal of Mechanics Engineering-Computational Mechanics
CiteScore
1.60
自引率
0.00%
发文量
17
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