A Discrete Layer Shear Deformation Theory for Flexure of Thick Cross-ply Laminated Beams

Abstract

A discrete layer shear deformation theory taking into account transverse shear deformation effects, is presented for flexure of two layered (90/0) cross ply laminated beams. The displacement field of the theory contains two variables. Theory does not require shear correction factor. The sinusoidal function is used in the displacement field in terms of thickness coordinate to represent shear deformation. Transverse shear stress can be obtained from the use of constitutive relation as well from the use of equilibrium equations, satisfying the stress free boundary conditions at top and bottom surfaces of the beam. Governing differential equations and boundary conditions of the theory are obtained using the principle of virtual work. General solution of governing differential equations is developed to obtain the complete flexural response of the beam. The results are obtained for two layered (90/0) cross ply laminated simply supported and fixed beams subjected to uniformly distributed load. The results obtained are compared with the available results in the literature.

Keywords: Shear deformation, cross-ply laminated beam, static flexure, trigonometric shear deformation theory.