Multi-material topology optimization considering properties of solid materials and interface

Abstract

The present study proposes a multi-material topology optimization method considering the physical properties of solid materials and the interface. An extended two-step filtering technique is introduced to define material interface based on Helmholtz-type partial differential equations. Furthermore, the width of the interface region can be controlled based on this approach. To deal with the non-convexity of the problem caused by multi-material topology optimization, a material interpolation function in which the material volume fractions are mutually independent is used: this allows for the commutativity of constituent materials. The minimum mean compliance problem is considered in two different structural models. To solve this problem, sensitivities of the objective function and the constraint condition are derived. The usefulness of the proposed method is verified through several numerical examples.