In the present study, a simple trigonometric shear deformation theory is applied for the bending, buckling and free vibration of crossply laminated composite plates. The theory involves four unknown variables which are five in first order shear deformation theory or any other higher order theories. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. The transverse displacement includes bending and shear components. The present theory satisfies the zero shear stress conditions at top and bottom surfaces of plates without using shear correction factor. Equations of motion associated with the present theory are obtained using the dynamic version of virtual work principle. A closed form solution is obtained using double trigonometric series suggested by Navier. The displacements, stresses, critical buckling loads and natural frequencies obtained using present theory are compared with previously published results and found to agree well with those.

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In this paper, a hyperbolic shear deformation theory taking into account transverse shear deformation effects, is presented for the bending analysis of thick isotropic plates subjected to linear thermal load. The displacement field of the theory contains three variables. The hyperbolic sine and cosine function is used in the displacement field in terms of thickness coordinate to represent the effect of shear deformation. The most important feature of the theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations, satisfying the stress free boundary conditions at top and bottom surfaces of the plate. Hence, the theory eliminates the need of shear correction factor. Governing differential equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for bending analysis of isotropic plates subjected to linear thermal load are compared with those of other higher order theories, lower order theories to validate the accuracy of the present theory.

In this study, the authors analyze laminated composite panels supported on an elastic foundation considering the effects of transverse normal strain. A 2-parameter, i.e., Winkler and Pasternak foundation model is assumed to represent the interaction between the panels and the foundation. The theory presented here takes into account the effects of transverse shear and normal strains. The theory plots realistic distributions of the transverse shear stress through the plate thickness and satisfies the shear-free conditions at the extreme surfaces of the panel. The differential equations of the present model are obtained from the principle of virtual work. The laminated composite panel resting on the elastic foundation is analyzed for simply supported boundary conditions. For the verification purpose, the presented problems are also solved using the Reddy's model, Mindlin's model, and the classical model. Good agreement is observed between the numerical results obtained using the present model and the other models.