The Natural Neighbour Petrov–Galerkin Method for Stress Analysis of Plates

Abstract

A meshless natural neighbour Petrov–Galerkin method (NNPG) is presented for solving the elasticity problems in this paper. In a certain domain, a discrete model consists of a set of distinct nodes, and a polygonal description of the boundary. The natural neighbour interpolation has Kronecker delta function property, and the construction of local sub-domain is simple both for internal nodes and boundary nodes. The whole interpolation is constructed with respect to the natural neighbour nodes and Voronoi tessellation of the given point. A local weak form over the local Delaunay triangular sub-domain is used to obtain the discretized system of equilibrium equations. The numerical results show the presented method is easy to implement and very accurate, especially for solving the problems of crack propagation or large deformations.