Bidirectional Bending of Laminated Plates Using Trigonometric Shear Deformation Theory

Abstract

Bidirectional bending analysis of symmetric cross-ply laminated plates using trigonometric shear deformation theory is presented. Theory takes into account of transverse shear deformation effect without transverse strain effect. Theory uses sinusoidal function in the displacement field in terms of thickness coordinate to include shear deformation effects. It has only three 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. Using principle of virtual work, governing equations and boundary conditions of the theory are obtained. The results from closed-form solution obtained for inplane and transverse displacements; and bending and shear stresses for plates subjected to sinusoidal load and uniformly distributed load are presented in this paper. The results are compared with those of other higher order plate theories and exact elasticity solutions to validate the accuracy of the theory.