A Topology Optimization Method Based on the Edge-Based Smoothed Finite Element Method

In this paper, we combined the edge-based smoothed finite element method (ES-FEM) with topology optimization. The edge-based gradient smoothing operation was introduced to overcome the accuracy-loss of the classical finite element method raised by the coarse mesh and “overly stiff” phenomenon. By employing the ES-FEM, design variables can be related to the smoothed edge, thus more design variables can be adaptively obtained without additional remeshing. Two classical topology optimization problems were considered, namely compliance minimization and stress-constrained topology optimization. We presented several numerical examples, among which the compliance minimization examples illustrated the potential of the proposed method, and the advantages of applying such a numerical method in topology optimization were demonstrated through the stress-constrained topology optimization.