A parameterized level set method combined with polygonal finite elements in topology optimization

Level set-based topology optimization methods have received increased attention in the last decade due to the ease with which they can handle topology changes by splitting and merging boundaries. However, most implementations are limited to box-like design domains and cannot easily handle irregular domains that are common in practical engineering applications. In this paper, a modified level set model, which is parameterized and updated with radial basis functions (RBFs), is introduced to solve topology optimization problems in complex design domains. Because RBFs are not necessarily located in a structured manner, the parametrized level set method can be combined effortlessly with unstructured polygonal finite element meshes to easily handle complex design domains and also achieve the high accuracy characteristic of polygonal discretizations. Furthermore, the nucleation capability of the proposed approach along with an approximate reinitialization is shown to obtain more flexible topology changes of the optimal design, and smooth boundaries can be obtained without introducing smoothing scheme. Several numerical examples illustrate the effectiveness of the proposed model.