Topology optimization design of multi‐material quasi‐periodic cellular structures for thermoelastic responses

作者：Quhao Li, Rui Xu, Shutian Liu, Guowei Liang, Yongxin Qu · 发表于：International Journal for Numerical Methods in Engineering · 年份：2022 · DOI：10.1002/nme.7012 · 被引用次数：11 · 研究领域：Topology Optimization in Engineering、Composite Structure Analysis and Optimization、Advanced Mathematical Modeling in Engineering

Abstract Thermal‐mechanical coupling environments extensively exist for engineering structures. How to effectively reduce thermoelastic deformation is distinctly important. Cellular structures have superior performances in stiffness and multi‐functionality with lightweight, and an excellent design can be expected by reasonably designing the microstructural topology and their distributions. However, existing studies are limited to designing homogenous cellular structures for thermoelastic response problems, although heterogeneous cellular structures have larger design spaces. This article intends to investigate the topology optimization problem for designing a special type of heterogeneous cellular structure, that is, quasi‐periodic cellular structure, for thermoelastic responses. The quasi‐periodic cellular structure is a composition of microstructures with similar but not the same topology across the macro domain, which ensures a good compromise between manufacturability and performance. By introducing the erode‐dilate operators to describe quasi‐periodic cellular structural topology, a simple single‐loop topology optimization model for minimizing the deformation variance of specific lines with multi‐material and multi‐constraint is established. Three types of design variables are included, and their sensitivity analyses are derived for using the gradient‐based optimization solver to obtain updates simultaneously. Designs with shape‐preserving and required stiffness under th...