STATIC FLEXURE OF CROSS-PLY LAMINATED CANTILEVER BEAMS

A static analysis of composite beams based on the layerwise trigonometric shear deformation theory is presented. The trigonometric sine function is used in the displacement field in terms of thickness coordinate to represent shear deformation. The present theory contains two displacement variables. The most important feature of the theory is that the transverse shear stress can be obtained directly from the constitutive relations that satisfy the stress-free boundary conditions at the top and bottom surfaces of the beam. Thus, the theory obviates the need for the shear correction factor. The governing equations and boundary conditions are obtained using the principle of virtual work. The unknown functions in the displacement field are determined from the general solution of linear governing differential equations. The transverse shear stresses are also obtained via two-dimensional equilibrium equations of the theory of elasticity. Two-layered (90 degrees/0 degrees) cross-ply laminated cantilever beams with different aspect ratios subjected to bending are examined. The results of flexural analysis are compared with those of the layerwise Bernoulli-Euler beam theory and the layerwise first-order shear deformation theory of Timoshenko.