Polyhedral Elements Based on Scaled Boundary Parametrizations—A Comparative Study of Semi‐Analytical Versus IGA‐Based Formulations

ABSTRACT

This paper addresses polytope element formulations, which facilitate flexible meshing of complex geometries. While two‐dimensional polygon elements have gained popularity, we focus specifically on less explored three‐dimensional polyhedral element formulations. A comparative study of discretizations based on the scaled boundary finite element method (SBFEM) and on its isogeometric variant (SBIGA) is performed. For polyhedral shape functions based on the scaled boundary finite element method, high‐order completeness is achieved by means of enrichment with bubble functions derived from the semi‐analytical solution of Poisson's equation with polynomial body loads. We present the extension of the corresponding derivation in 2D to three dimensions. The performance of the two methods in terms of convergence behavior and flexibility in the context of linear elasticity is illustrated using two benchmark examples.