This paper is concerned with the vibration and stability analysis of thick rectangular plates resting on elastic foundation, which is distributed over the particular area of the plate. A two-parameter (Pasternak) model is considered to describe the elastic foundation. The eigenvalue problem in 3-D domain is numerically solved by a combination of the finite element and differential quadrature method (DQM). The energy principle is employed to derive the governing equations in the framework of three-dimensional, linear and small strain theory of elasticity. The in-plane domain of the problem is discretized using two-dimensional finite elements and spatial derivatives of equations in the thickness direction are discretized in strong-form using DQM. As a first endeavor, the mixed FE-DQ method has been employed for 3-D buckling and free vibration analysis of rectangular thick plates partially supported by an elastic foundation. The accuracy of obtained results is validated by comparing to the few analytical solutions in the literature.

This paper derives a semi-analytical solution to determine displacements and stresses in a thick cylindrical shell with variable thickness under uniform pressure based on disk form multilayers. The proposed study partitions the thick cylinder into disk-layer parts based on their thickness of the cylinder. According to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are acquired based on first shear deformation theory (FSDT), which are in the form of a set of general differential equations. In this study, the cylinder is partitioned into n different disks and n sets of differential equations are derived. The solution of these equations provides displacements and stresses based on the boundary conditions and continuity conditions between the layers. The results are compared with those obtained through the analytical solution and the numerical solution. For the purpose of the analytical solution, matched asymptotic method (MAM) and for the analytical solution, the finite element method (FEM are implemented.