Nonlinear Hygro-Thermo-Mechanical Analysis of Functionally Graded Plates Using a Fifth-Order Plate Theory

In the present research, a new fifth-order plate theory is developed and applied to evaluate the static response of functionally graded (FG) plates resting on Winkler–Pasternak elastic foundation under nonlinear hygro-thermo-mechanical loading. This theory involves polynomial shape functions expanded up to fifth order in terms of the thickness coordinates. The effects of shear deformation and normal deformation are accounted; hence, it can be called as quasi-3D plate theory and abbreviated as FOSNDT. The theory involves nine unknowns. Zero transverse shear stress conditions at top and bottom surfaces are satisfied using constitutive relations. Analytical solutions are obtained using the double Fourier series technique suggested by Navier. The non-dimensional displacements and stresses are compared with available results.