An improved integrated framework based nodal density variable and Voronoi polygon for FE-based topology optimization

Abstract

In this paper, an improved integrated framework is developed to deal with the numerical instability problems in FE-based topology optimization design methods. The proposed method mainly consists of two coupled computational layers: the upper layer for material geometric description, and the lower layer for structural analysis and sensitivity calculation. In the upper layer, the design domain is discretized by Delaunay triangulation, and a smooth and continuous material density description is obtained by interpolating the densities at nodes of Delaunay triangulation with Shepard interpolants. In the lower layer, the dual Voronoi polygon for Delaunay triangulation is used to generate the finite element mesh, and the virtual element method is applied to handle Voronoi polygon for structural response. Following this framework, the separate description of density distribution avoids the problem of geometric description relying on FE mesh in some existing work. Meanwhile, the use of Voronoi polygon provides more accurate finite element discretization of constantly changing material distributions. Typical numerical examples for the minimum compliance optimization problem reveal that the proposed method can eliminate checkerboards and mesh-dependencies effectively, and get approximate discrete 0/1 solutions without any filter. The simulation results demonstrate the efficiency and robustness of the proposed formulation and numerical techniques.