A simple adaptive mesh refinement scheme for topology optimization using polygonal meshes

Abstract

The objective of topology optimization is to find the most efficient distribution of material (optimal topology) in a given domain, subjected to design constraints defined by the user. The quality of the new boundary representation depends on the level of mesh refinement: The greater the number of elements in the mesh, the better is the representation of the optimized structure. However, the use of refined meshes implies a high computational cost, particularly with regard to the numerical solution of the linear systems of equations that arise from the finite element method. This paper proposes a new computational strategy for adaptive local mesh refinement using polygonal finite elements in arbitrary two-dimensional domains. The idea is to perform a mesh refinement in regions of material concentration, mostly in inner and outer boundaries, and a mesh derefinement in regions of low material concentration, such as in internal holes. Thus, it is possible to obtain high-resolution optimal topologies with a relatively low computational cost. Representative examples are presented to demonstrate the robustness and efficiency of the proposed methodology by comparing the results obtained here with results from the literature where refined meshes are kept constant throughout the topology optimization process.