基于等效静态载荷法的多相材料结构动态拓扑优化设计

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摘要为了满足多相材料结构动态性能要求，提出一种基于等效静态载荷法的多相材料结构动态拓扑优化设计方法。采用序列固体各向同性料插值模型惩罚刚度矩阵和质量矩阵，以多个动载荷作用的多相材料结构总动态柔顺度最小化为优化目标，以结构质量和成本为约束条件，构建多相材料结构动态拓扑优化模型，利用等效静态载荷法将多相材料结构动态拓扑优化问题转化为多工况下的多相材料结构静态拓扑优化问题，以降低灵敏度分析的复杂程度；采用移动渐近线算法求解多相材料结构动态拓扑优化问题。数值算例结果表明所提方法是有效性的，与传统的拓扑优化方法相比，基于等效静态载荷法的多相材料结构动态拓扑优化求解时间节省了75%，大大地提高了计算效率；与单相材料拓扑优化结果相比，多相材料结构动态拓扑优化设计获得的结构具有更好的动态性能。

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	占金青1
	王啸1
	蒲圣鑫1
	刘敏1
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关键词 ：多相材料结构, 动态拓扑优化, 等效静态载荷法, 序列SIMP插值模型

Abstract：A method for dynamic topology optimization of continuum structures with multiphase materials using the equivalent static load method is proposed to meet the dynamic performance requirements. The ordered solid isotropic material with penalization (SIMP) interpolation is used to penalize the stiffness matrix and mass matrix. The objective function is developed by minimizing the total dynamic compliance of a multi-material structure under multiple dynamic loads subject to a mass constraint and a cost constraint. The dynamic topology optimization model for multi-material continuum structures is developed. To reduce the complexity of sensitivity analysis, the equivalent static load method is used to transform the dynamic topology optimization problem into the problem for topology optimization under multiple static loads. The method of moving asymptotes algorithm is employed to solve the problem for dynamic topology optimization of multi-material continuum structures. The results of numerical examples demonstrate the effectiveness of the proposed method. In comparison to the traditional topology optimization method, the method for dynamic topology optimization of multi-material structures based on the equivalent static load method reduces solution time by 75% and significantly improves calculation efficiency. The structures obtained by dynamic topology optimization with multiple materials have better dynamic performance than those obtained by topology optimization with single phase material.

Key words： multi-material structure dynamic topology optimization equivalent static load method ordered SIMP interpolation model

收稿日期: 2023-03-06 出版日期: 2024-02-15

引用本文:

占金青1，王啸1，蒲圣鑫1，刘敏1，2. 基于等效静态载荷法的多相材料结构动态拓扑优化设计[J]. 振动与冲击, 2024, 43(3): 77-85.
ZHAN Jinqing1, WANG Xiao1, PU Shengxin1, LIU Min1,2. Dynamic topology optimization design of multiphase material structure based on equivalent static load method. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(3): 77-85.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2024/V43/I3/77

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