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

One of the main difficulties 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 satisfies 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, different types of nodal distributions, uniform, and refined configurations 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.