Flexural Analysis of Thick Plates by Hyperbolic Shear Deformation Theory

Abstract

Hyperbolic shear deformation theory is used for the flexural analysis of isotropic plates with various loading cases. The theory takes account effect of transverse shear deformation. The transverse shear strains distribution through the thickness of the plate varies according to hyperbolic cosine function. 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 are derived from the principle of virtual work. The closed-form solutions for simply supported plates subjected to various transverse loading cases are obtained. Numerical results are 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 those of exact results and other higher order theories. Thus the efficacy of the present refined theory is established.

Keywords: Hyperbolic shear deformation theory, Flexural analysis, Elastic plates, Transverse s