Bending analysis of thick functionally graded rectangular plates using unconstrained third-order shear deformation theory

In the current study, the unconstrained third-order shear deformation theory (UTSDT) has been considered for bending analysis of thick functionally graded (FG) rectangular plates. Since the strain field of unconstrained thirdorder shear deformation theory for the plate is a second order function of the thickness coordinate, this theory does not need a shear correction factor. This theory releases the constraints of vanishing transverse shear stress on the top and bottom plate surfaces. This unconstrained third-order shear deformation plate theory is particularly useful for the study of a plate with contact friction or present in a flow field where the boundary layer shear stress is significant. The governing equations of equilibrium have been obtained using the principle of virtual work. These equations have been derived for a rectangular FG plate using a double Fourier series expansion under uniform load. A numerical analysis is performed for a simply supported square plate. Finally, the numerical results of the bending analysis are compared to available solutions from the previous studies. It is concluded that the present plate model provides more accurate solutions than that of TSDT when compared with the finite element method (FEM) results.