RPIM and RPIM-MLS based MDLSM method for the solution of elasticity problems

Abstract

Abstract. One of the main di culties in the development of meshless methods using the Moving Least-Squares approximation, such as Mixed Discrete Least-Squares Meshless (MDLSM) method, is the imposition of the essential boundary conditions. In this paper, the RPIM shape function, which satis es the properties of the Kronecker delta condition, is employed in the Mixed Discrete Least-Squares Meshless (MDLSM) method for solving the elasticity problems. Accordingly, two new MDLSM formulations are proposed in this article, namely RPIM-based MDLSM and coupled MLS-RPIM MDLSM formulation. The essential boundary conditions can be imposed directly on the both presented methods. The proposed methods are used for the solution of three benchmark elasticity problems, and the results are presented and compared with the available analytical solutions and those of MLS-based MDLSM formulations. In addition, in each example, di erent types of nodal distributions, uniform, and re ned con gurations are considered to test the performance of the presented methods. The numerical tests indicate higher accuracy of the suggested approaches in comparison with the MLS-based MDLSM method.