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 Vorono 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.
natural neighbours radial point interpolation method (rpim) radial basis function (rbf) meshfree method