The numerical analysis of symmetric cross-ply laminates using the natural neighbour radial point interpolation method and high-order shear deformation theories

Abstract

Composite structures are commonly analysed using the Finite Element Method (FEM). However, new accurate and efficient discrete numerical techniques have appeared recently – the meshless methods. Thus, this work uses a meshless method – the Natural Neighbour Radial Point Interpolation Method (NNRPIM) – to perform an elasto-static analysis of composite laminated plates. Meshless methods only require an unstructured nodal distribution to discretize the problem domain. In order to numerically integrate the integro-differential equation from the Galerkin weak formulation, a background integration mesh is constructed using the Voronoï diagram. Then, the nodal connectivity is enforced using the ‘influence-cell’ concept and the shape functions are obtained. In this work, laminated composite plates are analysed using distinct equivalent single layer theories, considering different transverse high-order shear deformation laws. Thus, several third-order, exponential and trigonometric transverse shear deformation theories are combined with the NNRPIM to analyse the structural response of composite laminated plates. In the end, composite laminated plates are numerically analysed and the meshless solutions are compared with the analytical solution available in the literature. Therefore, this works contributes with new solutions for classic composite symmetric cross-ply laminated plates and provides a comparative study on the accuracy of some high-order shear deformation theories (HSDTs).