Composite Laminated Plates: A 3D Natural Neighbor Radial Point Interpolation Method Approach

Based on the natural neighbor radial point interpolation method (NNRPIM), a 3D analysis of thick composite laminated plates is presented. The NNRPIM uses the natural neighbour concept in order to enforce nodal connectivity. Based on the Voronoï diagram small cells are created from the unstructured set of nodes discretizing the problem domain, the ‘influence-cells’, which are in fact influence domains entirely nodal dependent. The Delaunay triangles, the dual of the Voronoï cells, are used to create a node-dependent background mesh used in the numerical integration of the NNRPIM interpolation functions. The NNRPIM interpolation functions, used in the Galerkin weak form, are constructed in a process similar to that in the radial point interpolation method (RPIM) with some differences that modify the method performance. In the construction of the NNRPIM interpolation functions, no polynomial base is required and the used radial basis function (RBF) is the multiquadric RBF. The NNRPIM interpolation functions possess the delta Kronecker property, which simplifies the imposition of the natural and essential boundary conditions. In this work the 3D NNRPIM analysis is used to solve static and dynamic composite laminated plate problems. Thus, several benchmark examples are studied to demonstrate the effectiveness of the method.