3D graphical dynamic responses of FGM plates on Pasternak elastic foundation based on quasi-3D shear and normal deformation theory

A five-variable quasi-three-dimensional (quasi-3D) theory for power law and sigmoid Functionally Graded Material (P- and S-FGM) plates based on a refined higher-order shear and normal deformation approach is presented. The theory accounts for a displacement field in which the in-plane displacement is a third-degree function of the thickness coordinates while the out-of-plane displacement varies parabolically through the plate thickness. The theory satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor; moreover, it has fewer unknowns and equations of motion than other quasi-3D theories. In the present study, the displacement field of the four-variable plate theory was modified by considering the thickness stretching effect, and the equations of motion were derived from Hamilton's principle. Numerical results of natural frequencies and transient analysis are presented herein for two-phase graded material with a power-law and sigmoid through the plate thickness variation of the volume fractions. It was assumed that the elastic medium is modeled as the Pasternak elastic foundation. The accuracy of the obtained numerical results was verified by comparing them with those derived from first-order shear deformation theory and with other higher-order shear deformation theories. The important conclusions that emerge suggest that the proposed five-variable quasi-3D theory produces results as good as those of higher-order shear deformation theories.