Multi-Material Topology Optimization Considering the Bounding Box Dimension Constraint and Assemblability Based on the Extended Level Set Method in Two Dimensions

Abstract

Abstract This paper proposes a multi-material topology optimization method considering the bounding box dimension constraint and assemblability of the optimized structures in two dimensions. To handle multi-material topology optimization problems, we first introduce the concept of the extended level set method and the topological derivative. Second, we introduce the dimensional constraint of the two-dimensional bounding box and the assembly constraint for assemblability of the multi-material structure. We also elaborate their mathematical models. We then compute the design sensitivities of the two constraints based on the topological derivative and adjoint method. Third, we formulate the problem of multi-material topology optimization with constraints and explain the algorithm flow based on the finite element method. Finally, we verify our proposed algorithm on two numerical examples in two dimensions. The proposed method with two-dimensional geometry constraints on the optimized structures is applicable to machining methods. A representative application is milling, in which the largest and second-largest dimensions of the work-pieces are limited by the working area of the milling machine. In addition, our method is helpful for the assembly structure composed of multiple components. Traditional topology optimization method does not consider the assemblability, which makes the structure difficult to be assembled and decomposed in practical engineering. Our work will assist the manufacturability and assemblability of topology-optimized multi-material structures.