Analysis of 3D solids using the natural neighbour radial point interpolation method

In this work an improved meshless method is proposed, based on the combination of the natural neighbour finite element method with the radial point interpolation method, the natural neighbour radial point interpolation method – NNRPIM. The nodal connectivity and the node dependent integration background mesh are constructed resorting to the Voronoï tessellation and to the Delaunay triangulation. Within NNRPIM the obtained shape functions pass through all nodes inside the influence-cell providing shape functions with the delta Kronecker property. Optimization tests and examples of well-known, 2D and 3D problems are solved in order to prove the high accuracy and convergence rate of the proposed method.