On the equivalence between the cell-based smoothed finite element method and the virtual element method

摘要

We revisit the cell-based smoothed finite element method (SFEM) forquadrilateral elements and extend it to arbitrary polygons and polyhedrons in2D and 3D, respectively. We highlight the similarity between the SFEM and thevirtual element method (VEM). Based on the VEM, we propose a new stabilizationapproach to the SFEM when applied to arbitrary polygons and polyhedrons. Theaccuracy and the convergence properties of the SFEM are studied with a fewbenchmark problems in 2D and 3D linear elasticity. Later, the SFEM is combinedwith the scaled boundary finite element method to problems involvingsingularity within the framework of the linear elastic fracture mechanics in2D.