Cylindrical Bending of Shear Flexible Plates Using Trigonometric Shear Deformation Theory

Abstract

A trigonometric shear deformation theory for cylindrical bending of shear flexible plates taking into account transverse shear deformation effect is developed. The displacement field of the theory uses sinusoidal function in terms of thickness coordinate to include shear deformation effects. It has only two variables. It is to be noted that the present theory satisfies the constitutive relations in respect of transverse shear strain and stress. The transverse shear stress can be obtained directly from constitutive relation, satisfying the shear stress free boundary conditions at top and bottom surfaces of the plate. Hence, the theory requires no shear factor. Governing equations and boundary conditions of the theory are obtained by using principle of virtual work. The results from closed form solution obtained for inplane and transverse displacements and bending and shear stresses for three load cases, viz; single sine load, uniformly distributed load, and concentrated load are presented in this paper. The results are compared with those of classical plate theory and first order shear deformation theory to validate the accuracy of the theory.

Keywords: Trigonometric shear deformation theory, cylindrical bending, transverse shear stress, thick plate, displacement based theory, closed – form solution