An efficient evolutionary structural optimization method for multi-resolution designs

To solve large-scale or high-resolution topology optimization problem, a novel algorithm is developed based on modified bi-directional evolutionary structure optimization (BESO) and extended finite element method (XFEM). Within XFEM, a set of enriched nodes are defined to divide the finite element into several uniform sub-regions, i.e. sub-triangles and sub-tetrahedrons. The material grid and shape functions are defined on each sub-region to improve the computational accuracy, whereas the equilibrium equation is established on the level of coarse finite elements to increase the computational efficiency. We set all the standard FE nodes and the enriched nodes as the design variables, and a modified material interpolation model is introduced to calculate the material properties for sub-regions. An enrichment function originating from modeling voids scheme is adopted to character the discontinuity between solid material to void material. To efficiently use the gradient-based algorithm, BESO, sensitivity analysis is performed with the aid of adjoint method. Typical numerical examples, involving millions of design variables, are carried to verify the effectiveness of the proposed method.