Dynamic topology optimization design of multiphase material structure based on equivalent static load method

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Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (3) : 77-85.

ZHAN Jinqing1, WANG Xiao1, PU Shengxin1, LIU Min1,2

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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

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ZHAN Jinqing1, WANG Xiao1, PU Shengxin1, LIU Min1,2. Dynamic topology optimization design of multiphase material structure based on equivalent static load method[J]. Journal of Vibration and Shock, 2024, 43(3): 77-85

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