周期性多孔结构特征值拓扑优化

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (3) : 73-81.

论文

周期性多孔结构特征值拓扑优化

付君健1,2，张跃2，杜义贤1,2，高亮3

作者信息 +

Eigenvalue topology optimization of periodic cellular structures

FU Junjian1,2, ZHANG Yue2, DU Yixian1,2, GAO Liang3

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文章历史 +

摘要

为了实现尺度关联周期性多孔结构的隔振性能优化，提出一种周期性多孔结构特征值拓扑优化方法。基于子结构动态凝聚方法对多孔结构的刚度和质量矩阵进行缩减，采用局部水平集函数对多孔结构进行几何隐式描述，以最大化前六阶特征值为目标函数，以结构体积分数为约束条件，建立周期性多孔结构特征值拓扑优化模型，采用优化准则法对拓扑优化模型进行求解，并研究了多孔结构特征值拓扑优化的尺度效应。研究表明，本方法能有效实现尺度关联的二维和三维周期性多孔结构的特征值拓扑优化，并能大幅提高特征值拓扑优化的计算效率。

Abstract

To realize the vibration isolation performance optimization of scale-related periodic cellular structures, this paper proposed an eigenvalue topology optimization method of periodic cellular structures. The stiffness matrix and mass matrix of the cellular structures are reduced based on the substructural dynamic condensation method. Local level set functions are applied to implicitly describe the geometry of the cellular structures. The topology optimization model of periodic cellular structures is established to maximize the first 6 eigenvalues with volume fraction as the constraint. The topology optimization model is then solved by the optimality criteria method. The scale effect of the topology optimization of cellular structures is also investigated. Research shows that the proposed method can effectively realize the topology optimization of scale-related 2D and 3D periodic cellular structures. The computational efficiency of the eigenvalue topology optimization is also improved intensively.

关键词

多孔结构

/ 特征值拓扑优化 / 水平集法 / 子结构法 / 动态凝聚

Key words

cellular structures

/ eigenvalue topology optimization / level set method / substructure method / dynamic condensation

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付君健1,2，张跃2，杜义贤1,2，高亮3. 周期性多孔结构特征值拓扑优化[J]. 振动与冲击, 2022, 41(3): 73-81

FU Junjian1,2, ZHANG Yue2, DU Yixian1,2, GAO Liang3. Eigenvalue topology optimization of periodic cellular structures[J]. Journal of Vibration and Shock, 2022, 41(3): 73-81

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