A new level set based multi-material topology optimization method using alternating active-phase algorithm

Abstract

This paper proposes a new level set based multi-material topology optimization method, where a difference-set-based multi-material level set (DS-MMLS) model is developed for topology description and an alternating active-phase algorithm is implemented. Based on the alternating active-phase algorithm, a multi-material topology optimization problem with N + 1 phases is split into N(N + 1)/2 binary-phase topology optimization sub-problems. Compared with the initial multi-material problem, each sub-problem involves fewer design variables and volume constraints. In the DS-MMLS model, N + 1 phases are represented by the sequential difference set of N level set functions. Based on this model, the topological evolution of two active phases can be easily achieved by updating a single level set function in a fixed domain, which contributes a great convenience to the implementation of the alternating active-phase algorithm with level set method. Therefore, the proposed method can be easily extended to topology optimization problems with more material phases. To demonstrate its effectiveness, some 2D and 3D numerical examples with different material phases are presented. The results reveal that the proposed method is effective for multi-material topology optimization problems.