A new HSDT for buckling and free vibration behavior of cross-ply laminated composite plates resting on elastic foundation

This research paper deals with the analysis of buckling and free vibration of cross-ply laminated composite plates on elastic foundations. A refined plate theory based on the undetermined integrals terms is presented, which leads to reducing the unknown number to four instead of five or more unknowns used in the other theories. In the current theory, a function of shear with a hyperbolic form is employed, so the parabolic transverse shear stresses variation through the plate's thickness is obtained, and the zero shear stress conditions at the plate's top and bottom surfaces are satisfied. Therefore, the present formulation does not need shear correction factors. Pasternak elastic foundation mathematical model is considered in the formulation. The motion equations are determined using the virtual work principle, and the Navier approach is utilized to obtain the closed form solutions of cross-ply laminated plates. The fundamental frequencies and buckling loads are predicted by determining the eigenvalue problem. The present results are discussed and validated with results predicted using other previously published models.