Analysis of thick and orthotropic rectangular laminated composite plates using a state-space-based generalised RKP-FSM

This paper presents a novel numerical procedure based on the state space approach for the static analysis of thick and laminated composite plates using the newly-developed reproducing kernel particle finite strip method (RKP-FSM). The concept relies on the combination of the RKP-FSM with the state space method to obtain a semi-analytical three-dimensional numerical technique suitable for the analysis of generally-laminated composite plates. The present formulation is based on the application of the RKP-FSM in the plane of the problem to approximate the in-plane variations of the displacements and stress components, while the state space method is adopted for predicting the stress and displacement components in the direction of the thickness. One of the interesting features of the approach adopted is that the number of unknowns in the final system of equations is independent of the number of material layers. The RKP-FSM was developed by replacing the spline function in the spline finite strip method by the 1-D shape functions of the generalised RKPM. Since a meshless method is utilised as the approximation tool in the longitudinal direction of the strips, enforcing the essential boundary conditions requires special procedures. A detailed description of the method developed for enforcing the boundary conditions is included. Several numerical examples are presented to demonstrate the performance of the method and the results obtained are compared with available analytical and numerical solutions.