Truncated hierarchical B-spline–based topology optimization

Abstract

This work presents a truncated hierarchical B-spline–based topology optimization (THB-TO) to address topology optimization (TO) for both minimum compliance and compliant mechanism. The sensitivity and density filters with a lower bound are adaptively consistent with the hierarchical levels of active elements to remove the checkboard pattern and reduce the gray transition area. By means of the maximum variation of design variables on two consecutive iterative steps and the density differences of adjacent active elements, a mark strategy is established, which triggers the hierarchical local refinement and identifies the elements to be refined during the course of THB-TO. Besides, a locally refined design space is constructed in terms of the parent–child relationship of the cells on consecutive hierarchical levels. Numerical examples are used to verify the effectiveness of the proposed THB-TO, where the resolution around the boundary of the optimized designs can be effectively improved by THB-TO. Compared with global refinement, the number of degree of freedoms (DOFs) and design variables are largely decreased for 2D and 3D cases by THB-TO, which demonstrates that the proposed THB-TO is a promising approach to solving 2D and 3D TO problems.