Parametric study in Element Free Galerkin method for an elastic bar

Abstract

Meshfree Methods (MMs) have become popular as an alternative numerical simulation technique to handle problems of diverse engineering fields where conventional grid based methods are not suitable. Element Free Galerkin (EFG) method is a popular meshfree approach 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 and the method of imposing essential boundary conditions. In the present paper, aforesaid significant parameters are studied individually to check its influence on solution accuracy in EFG and suggest near optimal selection. An axially loaded elastic bar problem is taken as case study for unambiguous presentation of results. Finally, when EFG results are compared with standard FEM solution, it is found that EFG displacements are more accurate than FEM and EFG stress results are continuous in the domain in contrast to discontinuous stress values in FEM at element boundaries.