Static and dynamic analysis of laminated plates based on an unconstrained third order theory and using a radial point interpolator meshless method

Abstract

The Natural Neighbour Radial Point Interpolation Method (NNRPIM), an improved meshless method, is used in the numerical implementation of an Unconstrained Third-Order Plate Theory applied to laminates. 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 interpolation functions, constructed with the Radial Point Interpolators, pass through all nodes inside the influence-cell providing the interpolation functions with the delta Kronecker property. In order to prove the high accuracy and convergence rate of the proposed meshless method several well-known benchmark static and dynamic laminate examples are solved. The numerical results obtained with the NNRPIM are compared with the Unconstrained Third-Order Plate Theory exact solution, when available, and with exact solutions of other plate deformation theories.