基于子结构法的多层级结构拓扑优化

doi:10.3969/j.issn.1004-132X.2021.16.006

摘要/Abstract

摘要： 为避免多层级结构拓扑优化中的尺度分离问题，保证不同多孔结构之间的连接性，提出了一种基于子结构法的多层级结构拓扑优化方法。采用参数化水平集方法，将多孔结构拓扑优化分为两个层级，在细观层级优化多孔结构拓扑构型，在宏观层级优化多孔结构最优空间分布。采用子结构法建立宏细观结构之间的联系，将细观结构凝聚为超单元，凝聚的超单元又作为宏观结构分析和优化的基本单元。数值算例表明：所提方法可有效实现二维、三维多层级结构的拓扑优化；在多层级结构设计中考虑多种类型的多孔结构时，所提方法能有效保证不同多孔结构之间的连接性。

关键词: 拓扑优化, 多层级结构, 参数化水平集法, 子结构法

Abstract: To avoid the separation of scales in the hierarchical structures topology optimization, and to maintain the connection between different cellular structures, a hierarchical structure topology optimization method was proposed based on the substructure method. The topology optimization of cellular structures was divided into two hierarchies with the parametric level set method. The topology configuration of the cellular structure was optimized in meso-hierarchy. The spatial distribution of the cellular structure was optimized in macro-hierarchy. The relationship between macro-structure and meso-structure was established using the substructure method. The meso-structures was condensed into a super element, which was then used as the basic element of macro-structures for the structural analysis and optimization. Numerical examples show that the proposed method is effective for the 2D and 3D hierarchical structure topology optimization. The proposed method may effectively guarantee the connection between different cellular structures when considering multiple types of cellular structures in the hierarchical structure design.

Key words: topology optimization, hierarchical structure, parametric level set method, substructure method

中图分类号:

TH122

付君健, 孙鹏飞, 杜义贤, 田启华, 高亮. 基于子结构法的多层级结构拓扑优化[J]. 中国机械工程, 2021, 32(16): 1937-1944，1951.

FU Junjian, SUN Pengfei, DU Yixian, TIAN Qihua, GAO Liang. Hierarchical Structure Topology Optimization Based on Substructure Method[J]. China Mechanical Engineering, 2021, 32(16): 1937-1944，1951.

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链接本文: http://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2021.16.006

http://www.cmemo.org.cn/CN/Y2021/V32/I16/1937

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