Table of Contents
ISRN Mechanical Engineering
Volume 2011, Article ID 967512, 11 pages
Research Article

The Meshless Local Petrov-Galerkin Method for Large Deformation Analysis of Hyperelastic Materials

State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha 410082, China

Received 4 May 2011; Accepted 7 June 2011

Academic Editors: Ö. Civalek and D. Liao

Copyright © 2011 De'an Hu and Zhanhua Sun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nonlinear formulations of the meshless local Petrov-Galerkin method (MLPG) are presented for the large deformation analysis of hyperelastic materials which are considered to be incompressible or nearly incompressible. The MLPG method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties. In this paper, a simple Heaviside test function is chosen for reducing the computational effort by simplifying domain integrals for hyperelasticity problems. Trial functions are constructed using the radial basis function (RBF) coupled with a polynomial basis function. The plane stress hypothesis and a pressure projection method are employed to overcome the incompressibility or nearly incompressibility in the plane stress and plane strain problems, respectively. Effects of the sizes of local subdomain and interpolation domain on the performance of the present MLPG method are investigated. The behaviour of shape parameters of multiquadrics (MQ) function has been studied. Numerical results for several examples show that the present method is effective in dealing with large deformation hyperelastic materials problems.