The polygonal scaled boundary thin plate element based on the discrete Kirchhoff theory

Abstract

The scaled boundary finite element method (SBFEM) is a powerful method for solving elastostatics problems based on polygonal elements. In this paper, we firstly construct the quadratic polygonal scaled boundary element only depends on the boundary nodal displacements by transforming the additional degrees of freedom derived from the constant body loads to those by the boundary nodes. Further, combining with the discrete Kirchhoff theory, we construct the polygonal scaled boundary thin plate element, which can possess the second order completeness. The element stiffness matrix for the thin plate problem can be transformed by the stiffness matrix for the plane problem directly by avoiding to compute the shape functions of SBFEM. Numerical examples verify that the proposed polygonal scaled boundary thin plate element has good accuracy.