Elasto‐plastic analysis of plates by the element free Galerkin method

Abstract

Purpose

The aim of this paper is to extend the Element Free Galerkin method (EFGM) in order to perform the elasto‐plastic analysis of isotropic plates.

Design/methodology/approach

The EFGM shape‐function construction is briefly presented. The Newton‐Raphson method and the elasto‐plastic algorithm adapted to the EFGM, are described. Several plate bending non‐linear material problems are solved and the obtained solutions are compared with available finite element method (FEM) solutions.

Findings

The paper finds that the developed EFGM approach is a good alternative to the FEM for the solution of non‐linear problems, once the obtained results with the EFGM show a high similarity with the obtained FEM results.

Research limitations/implications

Comparing the FEM and the EFGM there are some drawbacks for the EFGM. The computational cost of the EFGM is higher, the imposition of the essential boundary conditions is more complex and there is a high sensitivity of the method in what concerns the choice of the influence domain and the choice of the weight function.

Practical implications

The knowledge that the EFGM formulation can be treated almost as the FEM formulation once the EFGM parameters are calibrated and optimized.

Originality/value

The extension of the EFGM to the elasto‐plastic analysis of isotropic plates.

Citation

Belinha, J. and Dinis, L.M.J.S. (2006), "Elasto‐plastic analysis of plates by the element free Galerkin method", Engineering Computations, Vol. 23 No. 5, pp. 525-551. https://doi.org/10.1108/02644400610671126