Open Access

ARTICLE

Multi-Material Topology Optimization for Spatial-Varying Porous Structures

by Chengwan Zhang¹, Kai Long^1,*, Zhuo Chen^1,2, Xiaoyu Yang¹, Feiyu Lu¹, Jinhua Zhang³, Zunyi Duan⁴

1 State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, 102206, China
2 School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, 510640, China
3 Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing, 100124, China
4 Institute of Structural Health Monitoring and Control, School of Mechanics, Civil Engineering & Architecture, Northwestern Polytechnical University, Xi’an, 710072, China

* Corresponding Author: Kai Long. Email:

Computer Modeling in Engineering & Sciences 2024, 138(1), 369-390. https://doi.org/10.32604/cmes.2023.029876

Received 12 March 2023; Accepted 22 May 2023; Issue published 22 September 2023

Abstract

This paper aims to propose a topology optimization method on generating porous structures comprising multiple materials. The mathematical optimization formulation is established under the constraints of individual volume fraction of constituent phase or total mass, as well as the local volume fraction of all phases. The original optimization problem with numerous constraints is converted into a box-constrained optimization problem by incorporating all constraints to the augmented Lagrangian function, avoiding the parameter dependence in the conventional aggregation process. Furthermore, the local volume percentage can be precisely satisfied. The effects including the global mass bound, the influence radius and local volume percentage on final designs are exploited through numerical examples. The numerical results also reveal that porous structures keep a balance between the bulk design and periodic design in terms of the resulting compliance. All results, including those for irregular structures and multiple volume fraction constraints, demonstrate that the proposed method can provide an efficient solution for multiple material infill structures.

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Keywords

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