Adaptive Mesh Refinement for Topology Optimization with Discrete Geometric Components

Abstract: This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as bars and plates typically exhibit low volume fractions with respect to the volume of the design region they occupy. To maintain an accurate analysis and to ensure well-defined sensitivities in the geometry projection, it is required that the element size is smaller than the smallest dimension of each component. For low-volume-fraction structures, this leads to finite element meshes with very large numbers of elements. To improve the efficiency of the analysis and optimization, we propose a strategy to adaptively refine the mesh and reduce the number of elements by having a finer mesh on the geometric components, and a coarser mesh away from them. The refinement indicator stems very naturally from the geometry projection and is thus straightforward to implement. We demonstrate the effectiveness of the proposed AMR method by performing topology optimization for the design of minimum-compliance and stress-constrained structures made of bars and plates.