A Simplified First-order Shear Deformation Theory for Bending, Buckling and Free Vibration Analyses of Isotropic Plates on Elastic Foundations

Abstract

This paper presents analytical solutions for bending, buckling and free vibration analyses of isotropic plates on elastic foundations using a simplified first-order shear deformation theory. Unlike the conventional first-order shear deformation theory, the present theory contains only two variables and has many similarities to the classical plate theory. For the elastic foundations, the Pasternak model which has two parameters is used. Equations of motion are derived from Hamilton’s principle. Analytical solutions of deflections, moments, shear forces, buckling loads and natural frequencies are obtained for rectangular plates with various boundary conditions. Numerical examples for various aspect ratios, side-to-thickness ratios and foundation parameters are presented to verify the validity of the present theory. Comparative study shows that the present theory is accurate and efficient in predicting bending, buckling and free vibration responses of isotropic plates on elastic foundations. Parametric study shows the effect of the elastic foundations on the behavior of the plates.