Multi-material topology optimization considering joint stiffness using a two-step filtering approach

Abstract

In this paper, a new method is presented to concurrently determine the structural layout and joint interface during the multi-material topology optimization (MMTO) process. Although the development of additive manufacturing techniques allows the fabrication of multi-material structures for soft materials with graded properties, joint materials for joining metals or composites are still needed. This paper proposes a novel material interpolation scheme for defining the joint area between dissimilar materials using a two-step filtering process. The general MMTO process is performed in the first filtering step. Furthermore, the filtered variables generate the joint area, and the filter radius controls the thickness of the area in the second filtering step. A modified discrete material optimization (DMO) approach is developed to control the different materials independently and to expand the applicability of the method to cases with more than two design materials. To demonstrate the performance of the proposed method, a compliance minimization problem is formulated for various volume constraints, joint thicknesses, material properties, mesh types, and number of materials. To show the scalability, 3-D design and compliant mechanism design examples are adopted. Based on numerical examples, it was confirmed that the proposed method performs well in various cases; moreover, the results demonstrate that the concurrent designing of the structural layout and joint interface leads to better performance than when joint stiffness is not considered.