An interpolating element-free Galerkin scaled boundary method for the elasticity problem

Abstract

As a newly-developed semi-analytical method, the scaled boundary finite element method is very powerful to deal with singular and unbounded problems. By combining the element-free Galerkin (EFG) method with the scaled boundary method in the frame of improved interpolating moving least-squares (IIMLS) method, an interpolating element-free Galerkin scaled boundary method (IEFG-SBM) is firstly proposed to solve elasticity problems in this paper. In the IEFG-SBM, the solution in the radial direction is obtained analytically and only nodes are required to discretize the boundaries of the computational domain. In addition, higher accuracy and faster convergence are obtained due to the higher continuity of the shape functions in the circumferential direction. The IEFG-SBM does not need the fundamental solution and thus no singular integrations are involved. The shape function of the IIMLS method satisfies the Kronecker delta function property and thus the essential boundary conditions can be imposed directly as in the traditional finite element method. In comparison with the interpolating moving least-squares (IMLS) method proposed by Lancaster and Salkauskas, the key advantage of the IIMLS method is that it does not require singular weight function and thus any weight function used in the MLS approximation can also be applied in the IIMLS method. In addition, there are less unknown coefficients in the IIMLS method than in the conventional moving least-squares (MLS) approximation. Thus fewer nodes are required in the local influence domain and a higher computational accuracy can be reached in the IIMLS-based meshless method. At last, several numerical examples are presented to verify the effectiveness and accuracy of the developed method for the elasticity problem.