Topology optimization of multi-material structures with graded interfaces

Abstract

Using the advanced manufacturing methods and in particular addictive manufacturing, the multi-material structure with graded interface is allowed to be achieved. In this paper, a SIMP-based method is presented to handle topology optimization of the multi-material structure with graded interface. An extended two-step filtering approach is developed to describe the multi-material structure and identify the material interface, where the density smoothing and projection scheme are used. Based on this approach, the width of the interface zone can be controlled and the graded interface is able to be constructed. Then a new SIMP-based interpolation scheme is proposed to define the properties of the multi-material structure with graded interface. The minimum compliance problem is considered with two kinds of optimization models under different constraints. One is subject to both mass and cost constraints to control the amounts of different materials and interface zones; while the other is only subject to a structural cost constraint. To solve these problems, the sensitivities of the objective function and constraints over design variables are derived. Numerical examples are presented to test the proposed method. Results show that the multi-material structure with graded interface can be described and optimized effectively. The width of the interface zone and the graded interface properties can be well controlled and defined, respectively. Due to its generality, the proposed method can be readily integrated into other SIMP-based methods to extent to a broader range of multi-material problems.