A 3D shell-like approach using a natural neighbour meshless method: Isotropic and orthotropic thin structures

Abstract

A three-dimensional shell-like approach for the analysis of composite thin plates and shells using a meshless method , the natural neighbour radial point interpolation method (NNRPIM), is presented. In the NNRPIM the nodal connectivity is enforced using the natural neighbour concept. The node-depending background mesh used in the numerical integration of the NNRPIM interpolation functions is entirely created from the unstructured nodal arrangement. The radial point interpolators are used to construct the NNRPIM interpolation functions, which possesses the delta Kronecker property, used in the Galerkin weak form. The novelty of this work lays on the development of a unique NNRPIM approach when 3D thin structures are considered. This new approach leads to remarkable results and it is extremely suitable to the composite structure problem. In order to demonstrate the effectiveness of the method the 3D shell-like NNRPIM analysis is used to solve several isotropic and orthotropic thin plates and shells problems.