A nonlinear approach for the three-dimensional polyhedron scaled boundary finite element method and its verification using Koyna gravity dam

Since it was presented, the scaled boundary finite element method (SBFEM) has been shown to be versatile and has been widely applied in structural numerical simulations. However, as it is analytical in the radial direction, nonlinearity inside elements cannot be considered, limiting its application in elastic fields. In this paper, a nonlinear approach for the three-dimensional polyhedron scaled boundary finite element (NPSBFEM3D) is proposed for elasto-plastic analysis to remove this restriction. In NPSBFEM3D, conforming shape functions are constructed using the semi-analytical solution derived from elastic surface elements, while the integrations are accomplished using internal Gauss points in the radial direction instead of integrating on the boundary surface elements. Eventually, the proposed approach can be as conveniently used in elasto-plastic analysis as FEM. This method permits an arbitrary number of faces, which offers a promising adaptive capacity for modelling. Three simulations are conducted to verify the robustness of the presented method.