Thick Orthotropic Rectangular Plates on Elastic Foundations

Abstract

In this research, Mindlin’s thick plate theory is extended to include orthotropic plates under the effects of externally distributed moments and shearing forces at top and bottom faces of the plate. These shearing forces produce in-plane forces in plates and the extensional effects of these in-plane forces are considered. The transverse sections of the plates have five degrees of freedom. These are the transverse deflection, the two independent rotations of the normal to the middle plane and the two mutually perpendicular membrane displacements. Thus, five expressions of the governing equations for thick orthotropic plates are obtained with the inclusion of the effects of externally distributed moments and applied shearing forces. As an application to the generation of distributed moments and shearing forces, the problems of thick orthotropic plates resting on elastic foundations with both compressional and frictional restraints are investigated. The finite-difference method was used to solve the governing equations. Besides, finite elements are formulated and used. Good agreements are found in the results from both methods of solution.