Deflections, stresses and free vibration analysis of bi-functionally graded sandwich plates resting on Pasternak's elastic foundations via a hybrid quasi-3D theory

The main aim of this study is to establish a hybrid quasi-3D theory for the deflections, stresses and free vibration analysis of bi-functionally graded sandwich plates resting on Pasternak's elastic foundations. In the proposed hybrid quasi-3D theory, the polynomial function is used to describe the distribution of transverse shear strains through the thickness direction while the trigonometric function is used to describe the thickness stretching effects. The bi-functionally graded sandwich plates are made of one homogeneous core and two different functionally graded face sheets. The governing equations of motion of the plates are established using Hamilton's principle and they are solved by a closed-form solution via Navier's technique. The present numerical results are compared with the published results using different higher-order and normal shear deformation theories to show the accuracy and efficiency of the proposed theory. And then the proposed theory was applied to examine the bending and free vibration behavior of the bi-functionally graded sandwich plates. A comprehensive study about the effects of some parameters such as side-to-thickness ratio, aspect ratio, skin-core-skin thicknesses, power-law index and elastic foundation parameters on the bending and free vibration behavior of the bi-functionally graded plates is carried out. The results of the deflections, stresses and frequency of the functionally graded sandwich with two different material face sheets can serve as benchmark solutions for engineering and future works.