Exact Lévy-type solutions for bending of thick laminated orthotropic plates based on 3-D elasticity and shear deformation theories

Exact solutions for static bending of symmetric laminated orthotropic plates with different Lévy-type boundary conditions are developed. The shear deformation plate theories of Mindlin-Reissner and Reddy as well as the three-dimensional elasticity theory are employed. Using the minimum total potential energy principle, governing equilibrium equations of laminated orthotropic plates and pertaining boundary conditions are derived. Closed-form Lévy-type solutions are obtained for the governing equations of both theories using separation of variables method and different types of classical boundary conditions, namely simply-supported, clamped and free edge, are exactly satisfied. Thereafter, 3-D elasto-static equations for orthotropic materials are solved for bending analysis of laminated plates using two different approaches. First, the method of separation of variables is utilised and an exact closed-from solution is achieved for simply-supported laminated orthotropic plates. Next, a combined Fourier-Differential Quadrature (DQ) approach is employed to present a semi-numerical solution for bending of laminated orthotropic plates with Lévy-type boundary conditions based on the three-dimensional elasticity theory. High accuracy of the presented solutions are proven and comprehensive comparative numerical results are provided and discussed. Presented comparative numerical results can serve as benchmark for investigating the correctness of new solution methods which may be established in the future.