Parameters Analysis Characterizing the EFG Meshfree Metod for Two-Dimensional Elastic Beam Problem

Abstract

The Finite Element Method (FEM) is well established for modelling complex problems for engineering problems in various fields. However, the difficulty of meshing and remeshing of complex structural elements in several classes of problems is the main drawback that FEM possess. To prevent this drawback, Mesh Free numerical techniques have been developed in such a way that the mesh is not more necessary to discretize the problem, and the trial functions are constructed entirely in terms of a set of nodes without the necessity of element descretization for the construction of the equations. Element Free Galerkin method (EFG) is one of the most interesting meshless methods which is based on global weak form of governing differential equation and employs Moving Least Square (MLS) approximants to construct shape functions. To implement this technique, it is necessary to characterize the significant parameters like, order of monomial basis function, weight function selection in MLS approximants, the size of influence domain, uniform and non-uniform node distribution, number of Gauss points in integration cells. In this paper, the EFG method has been extended to solve elasto-static beam problem in plane stress cases for node distribution scheme, number of Gauss points in integration cells. For implementation and solution, a MATLAB program has been developed to verify the accuracy of the proposed meshless method and results are compared with exact analytical solutions.