A Study of the Elastodynamic Problem by Meshless Local Petrov-Galerkin Method Using the Laplace-Transform

Jaouad Eddaoudy,Touria Bouziane

doi:10.4236/wjm.2018.82004

Abstract

The Meshless Local Petrov-Galerkin (MLPG) with Laplace transform is used for solving partial differential equation. Local weak form is developed using the weighted residual method locally from the dynamic partial differential equation and using the moving least square (MLS) method to construct shape function. This method is a more effective alternative than the finite element method for computer modelling and simulation of problems in engineering; however, the accuracy of the present method depends on a number of parameters deriving from local weak form and different subdomains. In this paper, the meshless local Petrov-Galerkin (MLPG) formulation is proposed for forced vibration analysis. First, the results are presented for different values of as, and aq with regular distribution of nodes nt=55. After, the results are presented with fixed values of as and aq for different time-step.

Highlights

Generality of physical or mechanical problems are modeled by partial differential equations (PDEs)
The meshless local Petrov-Galerkin (MLPG) method constructs the weak form over local subdomain such as Ωs, which is a small region taken for each node inside the global domain
We present a numerical study for elastodynamic 2-D problem of a rectangular homogeneous isotropic plate [26] by using MLPG method, subjected to a dynamic force at the right end (Figure 2)

Summary

Introduction

Generality of physical or mechanical problems are modeled by partial differential equations (PDEs). Y. et al, have applied MLPG5 method used the Heaviside function as the test function for elastic dynamic problems [22] They found a good agreement compared with the results obtained by (FEM). This method applied by Ping Xia et al in elastic dynamic analysis of moderately thick plate using meshless LRPIM [23] They have used the Newmark method for solving the dynamic problem and have studied the effects of the size of the quadrature subdomain and the influence domain on the dynamic properties. In which X − Xi is the distance from node Xi to point X , and di is the size of the influence domain for the weight function

Basic Equations of Elastodynamics

The MLPG Weak Formulation in Laplace-Transformed Domain

Numerical Results and Discussions

Conclusion