A new layerwise trigonometric shear deformation theory for two-layered cross-ply beams

A new layerwise trigonometric shear deformation theory for the analysis of two-layered cross-ply laminated beams is presented. The number of primary variables in this theory is even less than that of first-order shear deformation theory, and moreover, it obviates the need for a shear correction factor. The sinusoidal function in terms of thickness coordinate is used in the displacement field to account for shear deformation. The novel feature of the theory is that the transverse shear stress can be obtained directly from the use of constitutive relationships, satisfying the shear-stress-free boundary conditions at top and bottom of the beam and satisfying continuity of shear stress at the interface. The principle of virtual work is used to obtain the governing equations and boundary conditions of the theory. The effectiveness of the theory is demonstrated by applying it to a two-layered cross-ply laminated beam.