DYNAMIC ELASTOPLASTIC ANALYSIS USING THE MESHLESS LOCAL NATURAL NEIGHBOR INTERPOLATION METHOD

Abstract

Dynamic elastoplastic analysis is a subject of great engineering importance and can practically be handled only by numerical methods due to its complexity. The aim of this paper is to develop the meshless local natural neighbor interpolation (MLNNI) method to perform the dynamic analysis of elastoplastic structures under plane stress or plane strain conditions. The MLNNI, as an effective truly meshless method for solving partial differential equations, employs local weak forms over a local subdomain and shape functions from the natural neighbor interpolation (NNI). The shape functions so formulated possess delta function property and, therefore, the essential boundary conditions can be implemented as ease as in the finite element method (FEM). The predictor-corrector form of the Newmark algorithm is used for the time-marching process and iterations are performed at every time step. The applied loads can have any transient time variation. Comparative results are presented at the end to illustrate the effectiveness of the proposed method and demonstrate its accuracy.