A weighted nodal-radial point interpolation meshless method for 2D solid problems

In this paper, a novel weighted nodal-radial point interpolation meshless (WN-RPIM) method is proposed for 2D solid problems. In the new approach, the moment matrices are performed only at the nodes to get nodal coefficients. At each computational point (node or integration point), the shape functions are obtained by weighting the nodal coefficients whose nodes are located in its support domain. The shape functions obtained by the new scheme preserve the Kronecker delta function property under certain conditions. This conclusion can be extended for the weighted nodal-interpolating moving least squares approximation studied in Most and Bucher [New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares. Eng Anal Bound Elem 2008;32:461–470]. Besides, the new method is much less time consuming than the RPIM method, since the number of nodes is generally much smaller than that of the integration points. Some numerical examples are illustrated to show the effectiveness of the proposed method. Some parameters that influence the performance of the proposed method are also investigated.