A state space augmented generalised RKPM for three-dimensional analysis of thick and laminated composite plates

In this paper, a hybrid numerical method which combines the states space approach with the generalised Reproducing Kernel Particle Method (RKPM) is proposed for the three-dimensional analysis of thick and laminated composite plates. Employing the state space approach in the thickness direction, the governing partial differential equation is transformed into a state equation. The meshless RKPM is utilised to present the in-plane distribution of the displacement and stress components while their variation in the transverse direction of the plate and lamina is captured by adopting the state space method. This results in the formation of an algebraic system of equations where the number of unknowns is independent of the number of material layers of the laminate. Moreover, the solution provides a continuous transverse stress and displacement field which is not generally achievable using conventional numerical methods. Because the method is based on a mixed variational principle, and a meshless method is incorporated as the numerical tool, enforcement of the essential boundary conditions requires special treatment and a detailed description is given of the mixed method developed for the enforcement of the essential boundary conditions. A series of numerical examples is performed to illustrate the application of the proposed method and the results obtained are compared with known analytical and numerical solutions.