Topology optimization for structures with bi-modulus material properties considering displacement constraints

Abstract

In this paper, an efficient topology optimization method is developed for bi-modulus structures considering displacement constraints. In order to overcome the numerical difficulty caused by the non-smoothness bi-modulus material properties, a new smooth elastic modulus matrix concerned with the principal strain states is firstly constructed to approximate the discontinuous modulus matrix for bi-modulus materials. Based on the smooth approximation, topology optimization model for structures under both single and multiple load cases is built to minimize structural compliance with volume and displacement constraints. Considering the nonlinear equilibrium equations, the sensitivities of the objective function and constraints are explicitly achieved based on the adjoint method, and then the gradient-based method of moving asymptotes algorithm is employed to update the topological design variables. A cooperation platform is constructed for the proposed bi-modulus topology optimization, which provides an effective tool for the design optimizations. The proposed method is proved to have good efficiency and applicability to deal with problems with multiple load cases and multiple constraints by several typical numerical examples.