An efficient evolutionary structural optimization method for multi-resolution designs

Abstract

This paper presents a computationally efficient multi-resolution topology optimization framework by establishing a novel bi-directional evolutionary structure optimization (BESO) method based on extended finite element method (XFEM). In the proposed framework, the high-resolution designs preserving the topological complexity can be obtained with low degree of freedoms (DOFs). The implementation of the presented multi-resolution optimization framework takes good use of the ability of XFEM at accurately modeling material discontinuities within one element. On the basis of XFEM, a strategy of triangulated partition and a new material interpolation model are introduced to represent the finer material distribution. We employ the coarser finite element (FE) mesh to perform the finite element analysis, the sub-parts partitioned from finite elements to describe material properties and the nodal design variables to perform the optimization. To circumvent artificially stiff patterns, a modified sensitivity filter is applied to regularize the solution. The effectiveness and high efficiency of the presented approach are highlighted by typical 2D and 3D examples.