A meshless moving morphable component-based method for structural topology optimization without weak material

基于无网格移动变形构件的结构拓扑优化方法

Traditional topology optimization methods often introduce weak artificial material to mimic voids to avoid the singularity of the global stiffness matrix and carry out topology optimization with a fixed finite element(FE)mesh.This treatment,however,may not only increase the computational cost for structural analysis but also lead to unfavorable numerical instabilities,especially when large deformations and dynamic/buckling behaviors are involved.In the present work,a new meshless moving morphable component-based method(ML-MMC),which structural analysis is carried out only on the solid region occupied by components,is proposed.In this approach,the coupling of discrete components is achieved through the adaptively constructed influence domain of the meshless shape function.Therefore,the singularity problem of the stiffness matrix can be naturally avoided without introducing weak artificial material.Compared with traditional methods,the number of degrees of freedoms(DOFs)can be reduced substantially under this treatment.The effectiveness of the proposed approach is also illustrated by some representative examples.

传统拓扑优化方法往往需引入人工弱材料来模拟孔洞,以避免整体刚度矩阵的奇异性,并使用固定的有限元网格进行分析和优化.然而,这种处理方法不仅会增加结构分析的计算成本,还会导致不利的数值不稳定性,尤其是当涉及大变形和动力/屈曲行为时.本文提出了一种新的基于无网格的移动可变形组件拓扑优化方法(ML-MMC),该方法只对组件占据的实体区域进行结构分析,并通过自适应构造无网格形函数的影响域来实现离散组件的耦合,可以在不引入人工弱材料的情况下自然地避免拓扑优化过程中刚度矩阵的奇异性问题.与传统拓扑优化方法相比,这种处理方法可以大大减少优化过程中结构分析的自由度(DOFs)数量.一些典型的二维和三维算例说明了该方法的有效性和高效性.