Bending and free vibration analysis of thick isotropic plates by using exponential shear deformation theory

Abstract

This paper presents a variationally consistent an exponential shear deformation theory for the bi-directional bending and free vibration analysis of thick plates. The theory presented herein is built upon the classical plate theory. In this displacement-based, refined shear deformation theory, an exponential functions are used in terms of thickness co-ordinate to include the effect of transverse shear deformation and rotary inertia. The number of unknown displacement variables in the proposed theory are same as that in first order shear deformation theory. The transverse shear stress can be obtained directly from the constitutive relations satisfying the shear stress free surface conditions on the top and bottom surfaces of the plate, hence the theory does not require shear correction factor. Governing equations and boundary conditions of the theory are obtained using the dynamic version of principle of virtual work. The simply supported thick isotropic square and rectangular plates are considered for the detailed numerical studies. Results of displacements, stresses and frequencies are compared with those of other refined theories and exact theory to show the efficiency of proposed theory. Results obtained by using proposed theory are found to be agree well with the exact elasticity results. The objective of the paper is to investigate the bending and dynamic response of thick isotropic square and rectangular plates using an exponential shear deformation theory.