A Layerwise Trigonometric Shear Deformation Theory for Two Layered Cross-Ply Laminated Beams

A Layerwise Trigonometric Shear Deformation Theory (LTSDT) for the analysis of two layered cross-ply laminated beams, taking into account discrete layer transverse shear deformation effects, is presented. The theory is as simple as the first order shear deformation theory and does not require shear correction factor. The sinusoidal function is used in the displacement field in terms of thickness coordinate to represent shear deformation. The most important feature of the theory is that the transverse shear stress can be obtained directly from the use of constitutitve relations, satisfying the stress-free boundary conditions at top and bottom of the beam and satisfying continuity at the interface. Governing differential equations and boundary conditions of the theory are obtained using the principle of virtual work. The system of governing differential equations is reduced to a single sixth order linear differential equation. A two layered asymmetric cross-ply laminated beam is considered for the numerical study to validate the accuracy of the theory.