Comparative Study of the Effect of the Parameters of Sizing Data on Results by the Meshless Methods (MLPG)

Ahmed Moussaoui,Touria Bouziane

doi:10.4236/wjm.2013.31006

Abstract

The local Petrov-Galerkin methods (MLPG) have attracted much attention due to their great flexibility in dealing with numerical model in elasticity problems. It is derived from the local weak form (WF) of the equilibrium equations and by inducting the moving last square approach for trial and test functions in (WF) is discussed over local sub-domain. In this paper, we studied the effect of the configuration parameters of the size of the support or quadrature domain, and the effect of the size of the cells with nodes distribution number on the accuracy of the methods. It also presents a comparison of the results for the Shear stress, the deflections and the error in energy.

Highlights

Meshless formulations are becoming popular due to their higher adaptivity and lower cost for preparing input data in the numerical analysis
The local Petrov-Galerkin methods (MLPG) have attracted much attention due to their great flexibility in dealing with numerical model in elasticity problems. It is derived from the local weak form (WF) of the equilibrium equations and by inducting the moving last square approach for trial and test functions in (WF) is discussed over local sub-domain
The meshless local Petrov-Galerkin (MLPG) method originated by Atluri and Zhu [1] uses the so-called local weak form of the Petrov-Galerkin formulation

Summary

Introduction

Meshless formulations are becoming popular due to their higher adaptivity and lower cost for preparing input data in the numerical analysis. Many of them are derived from a weak-form formulation on global domain [1] or a set of local subdomains [4,5,6,7]. The meshless local Petrov-Galerkin (MLPG) method originated by Atluri and Zhu [1] uses the so-called local weak form of the Petrov-Galerkin formulation. The method is a fundamental base for the derivation of many meshless formulations, since trial and test functions are chosen from different functional spaces. The procedure is quite similar to numerical methods based on the strong-form formulation, such as the finite difference method (FDM). The aims of this paper are to study the effect on accuracy and convergence of MLPG methods of different size parameters: s and Q associated to support and quadrature domains respectively.

Basic Equations

Numerical Example

Discussions

Conclusion