Buckling and Vibration of Plates by Hyperbolic Shear Deformation Theory

Abstract

Hyperbolic shear deformation theory is used to determine the natural frequencies and buckling loads of elastic
plates. The theory takes account of transverse shear effects and hyperbolic cosine distribution of the transverse
shear strains through the thickness of the plate, hence it does not require shear correction factor. Governing
equations are derived from the principle of virtual work. The closed-form solution of a simply supported plate
subjected to in-plane loading has been obtained. Numerical results obtained by the present theory are compared
with those of classical plate theory, first-order shear deformable theory, higher order theories and the exact
theory available in the literature. The results obtained by present theory are in excellent agreement with the
exact results and other higher order theories. Thus the credibility of the present refined theory is validated.
Keywords: Hyperbolic shear deformation theory, Buckling analysis, Free vibration, Isotropic plate, Orthotropic
plate.