A fourth-order shear deformation theory for static analysis of thick functionally graded rectangular plates

In this paper, a fourth-order shear deformation theory (FOSDT) has been introduced for static analysis of thick functionally graded rectangular plates. Based on this theory, the displacement components of the plate are a fourthorder function of the thickness coordinate and also the shear stress on the top and bottom of plate is vanished. Since this theory results in a third order shear strain, its results are more accurate than the other theories. Also the fourthorder shear deformation theory does not need a shear correction factor. Using the principle of virtual work, the governing equations of equilibrium have been obtained. These equations have been solved for a rectangular functionally graded plate using a double Fourier series expansion. The deflection and shear stress of the functionally graded rectangular plate has been calculated analytically. Finally, the numerical results have been compared with the available solutions obtained from the other studies such as first, second and third order shear deformation theories, classical plate theory and finite element method.