Revised SBFEM on arbitrary polygons and faceted polyhedrons with the second order completeness by elimination of bubble functions

Abstract

By the theoretical analysis on the scaled boundary finite element (SBFEM), some appropriate 2D or 3D bubble functions are necessary in order that the elements can possess the second order completeness. However, the extra 2D bubble function is difficult to be adopted as facet shape function for 3D polyhedral element. In this paper, a revised-scaled-boundary element (denoted by 2DRSBd2) only corresponding to the boundary nodal displacements is constructed by elimination of the 2D bubble function derived from the constant right-hand term in 2D Poisson equation. This polygonal element 2DRSBd2 possesses the second order completeness and the third order convergence in L2-norm. Then we construct two polyhedral elements 3DSB-2DRSBd2 and 3DRSB-2DRSBd2 based on the polygonal element 2DRSBd2. The difference between the two 3D elements is: the 3DSB-2DRSBd2 element is constructed with three 3D bubble functions derived from the constant body loads in three dimensional elastostatic problem, while the 3D revised-scaled-boundary element 3DRSB-2DRSBd2 is constructed by elimination of those 3D bubble functions. Both elements 3DSB-2DRSBd2 and 3DRSB-2DRSBd2 possess the second order completeness and the third order convergence in L2-norm. Numerical examples verify that they have good accuracy and insensitive to mesh distortion.