A meshless method for multi-material topology optimization based on the alternating active-phase algorithm

In this work, a meshless method based on the alternating active-phase algorithm is proposed for the multi-material topology optimization problems. Mathematic model of the proposed method is built by the solid isotropic microstructure with penalization (SIMP) theory and solved by the optimality criteria. During the optimization process, the nodal relative density is chosen as the design variable and Shepard interpolation combined with the moving least squares (MLS) shape function is utilized to obtain the nodal relative density. Nodal integration method is then adopted to obtain the structural stiffness matrix, with the purpose of promoting the computational efficiency. Since the element-free Galerkin (EFG) method is applied to analyze the structure, sensitivity filtering is avoided and mesh-dependence phenomena are alleviated. Several numerical examples are provided to illustrate the validity and feasibility of the proposed method.