Compared Computational Performances of EFG Meshfree Metod for One-Dimensional Elastic Problem Analysis

Abstract

Mesh free (MF) methods are among the breed of numerical analysis technique that are being vigorously developed to avoid the drawbacks that traditional methods like Finite Element method (FEM) possess. The Element Free Galerkin (EFG) method is a meshless method in which only a set of nodes and a description of model's boundary are required to generate the discrete equations. EFG approach is based on global weak form of governing differential equation and employs Moving Least Square (MLS) approximants to construct shape functions. While deriving solution with EFG, following selectable parameters affect solution accuracy and computational efforts: Order of monomial basis function and weight function selection in MLS approximants, size of influence domain, uniform and non uniform node distribution, number of Gauss points in integration cells. The computational performance of meshfree Moving Least Squares technique when solving the Galerkin weak form of one-dimensional elastic problem is tested against exact analytical solution and mesh-based Finite Element Method. In the present paper, selectable parameters are studied to check its influence on solution accuracy in EFG and suggest near optimal selection. Finally, when EFG results are compared with standard FEM solution, it is found that EFG displacements are more accurate than FEM.