Abstract

A nonlinear formulation of the Meshless Local Petrov-Galerkin (MLPG) finite-volume mixed method is developed for the large deformation analysis of static and dynamic problems. In the present MLPG large deformation formulation, the velocity gradients are interpolated independently, to avoid the time consuming differentiations of the shape functions at all integration points. The nodal values of velocity gradients are expressed in terms of the independently interpolated nodal values of displacements (or velocities), by enforcing the compatibility conditions directly at the nodal points. For validating the present large deformation MLPG formulation, two example problems are considered: 1) large deformations and rotations of a hyper-elastic cantilever beam, and 2) impact of an elastic-plastic solid rod (cylinder) on a rigid surface (often called as the Taylor impact test). The MLPG result for the cantilever beam problem was successfully compared with results from both analytical modeling and a commercial finite element code simulation. The final shapes of the plastically deformed rod obtained from a well-known finite element code, and the present MLPG code were also successfully compared. The direct comparison of computer run times between the finite element method (FEM) and the large deformation mixed MLPG method showed that the MLPG method was relatively more efficient than the FEM, at least for the two example problems considered in the present study.

Details

Title
Meshless Local Petrov-Galerkin (MLPG) Approaches for Solving Nonlinear Problems with Large Deformations and Rotations
Author
Han, Z D; Rajendran, A M; Atluri, S N
Pages
1-12
Section
ARTICLE
Publication year
2005
Publication date
2005
Publisher
Tech Science Press
ISSN
1526-1492
e-ISSN
1526-1506
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2397920140
Copyright
© 2005. This work is licensed under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.