Numerical experiments on the performance of the RBF meshfree Galerkin Methods for solid mechanics

Abstract

In this work the advances in meshfree methods, partic- ularly the Radial Basis Function based meshfree Galerkin Methods, are presented with the purpose of analyzing the performance of their meshless approximations and integration techniques. The Radial Point Interpolation Method (RPIM) is studied based on the global Galerkin weak form performed using classical Gaussian integration and the stabilized conforming nodal integration scheme. The numeri- cal performance of this category of methods is tested on their behavior on two elastic problems with regular node grids, and two other with distorted irregular grids. All RPIM methods perform very well in term of elastic computation, the Smoothed Radial Point Interpolation Method (SRPIM) shows a higher accuracy, especially in a situation of distorted node schemes. Keywords—adial Basis Function Radial Point Interpolation Method Galerkin weak form Nodal Integrationadial Basis Function Radial Point Interpolation Method Galerkin weak form Nodal Integration.