Numerical simulation of holes and inclusions using adaptive polygonal finite element method

Abstract

An adaptive polygonal finite element method using the techniques of cut-cell and quadtree refinement is presented for modeling holes and inclusions in 2-D solids. A mesh template is used to ensure the high-quality refined elements generated in quadtree refinement. By coupling the level set method, the polygonal computational mesh is directly extracted from the mesh template in every adaptive cycle. An error estimator based on recovery stress is devoted for adaptive purpose, which allows the mesh where it is needed is further refining. This method allows to model arbitrary shape holes and inclusions in arbitrary-geometry 2-D solid using the initial mesh of few rectangular elements, which considerably simplifies construction of the finite element model. And one curved boundary can be accurately represented though several steps of refinement. Numerical examples are solved and the obtained results are compared with reference solutions to show the simplicity and efficiency of the proposed method.