Vibration and the Buckling Response of Functionally Graded Plates According to a Refined Hyperbolic Shear Deformation Theory

A first attempt is made to study the free vibrations and the buckling response of functionally graded plates using a refined hyperbolic shear deformation theory. This theory incorporates high-order effects of shear and normal deformation with accounting for thickness stretching. A combination of hyperbolic and polynomial functions ensures a parabolic profile of shear stresses and the enforcement of zero shear stresses at the top and bottom surfaces of the plates. The need for a shear correction factor is eliminated. The plates are made from advanced composites consisting of a functionally graded material varying from a ceramic to metallic phase across the thickness. The mechanical properties of the plates are homogenized by the Voigt rule of mixtures and the Mori- Tanaka scheme. A C0 finite-element model is developed for the present theory and is included in the MATLAB code. A convergence study is performed and the efficacy of the model is validated.