Abstract:

Natural element method (NEM) is a recently developed meshless method and is essentially the Galerkin method based on natural neighbour interpolation. The algorithm for calculating natural neighbour co-ordinates and their derivatives based on Lasserre's algorithm for the volume of a convex polyhedron was derived and the generalized flowchart for NEM in 3D case was presented. The algorithm can be applied to NEM in any dimensions case in fact. Two algorithms to solve the redundant constraint problem lying in Lasserre's algorithm were also presented. The example's numerical results are equal to the results of hexahedral finite element method.

Key words: natural element method (NEM), natural neighbour interpolation, Delaunay triangulation, Galerkin method