The bending behaviour of antisymmetric cross-ply laminates using high-order shear deformation theories and a Radial Point Interpolation Method

Abstract

The analysis of composite laminates is often performed using plate models suitable to study, with accuracy, the distribution of the shear stresses across the laminate’s thickness. Several High-Order Shear Deformation Theories (HSDTs) are proposed in the literature since they fulfil the insufficiencies of the First-Order Shear Deformation Theory (FSDT) without the computational cost of approaches such as Layerwise (LW) theories. In this work, five of the most popular HSDTs existing in the literature were used to study the bending of antisymmetric cross-ply laminates. The plate theories were computationally implemented within a meshless method algorithm – the Radial Point Interpolation Method (RPIM). The numerical analysis of engineering problems is commonly performed using the Finite Element Method (FEM), but in problems dealing with transitory geometry, the FEM may not be the most efficient numerical method. Additionally, in meshless methods, the shape functions have virtually a higher order which results in a higher continuity and reproducibility. Meshless methods only require an unstructured nodal distribution to discretize the problem domain, so there is no previous relationship between nodes, which makes the refinement procedure easier than in the FEM.Thus, using the RPIM and HSDTs, different laminates were analysed, which marks the first time in the literature that the RPIM is used to study the bending of antisymmetric cross-ply laminates through HSDTs. In the end, the meshless solutions are compared with analytical and FEM solutions available in the literature, and the accuracy and robustness of the numerical approach are proved.