Topology optimization with polygonal finite elements

Achieving high-fidelity results from topology optimization simulations has been a common goal in the technical literature. To that effect, several techniques have been proposed with various degrees of success. By addressing the geometric features of the spatial discretization, we examine the use of unstructured meshes in reducing the influence of mesh geometry on topology optimization solutions. More specifically, we consider polygonal meshes constructed from Voronoi tessellations, which in addition to possessing a higher degree of geometric isotropy, allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities. These points are illustrated by means of several numerical examples, which are compared with results obtained by means of previous techniques.