Effect of higher order shear and normal deformations theory in buckling analysis of thick porous functionally graded plates

This paper presents an analytical solution for stability analysis of thick rectangular functionally graded plates with porosity subjected to in-plane loadings using the higher-order shear and normal deformation plate theory, for the first time. The plate material and its porosity are assumed to vary along the thickness direction. Also, three types of porosity pattern along the thickness are considered. Since the plate structure is not generally symmetry to the mid-plane it is assumed that the in-plane loads are applied to its neutral plane to remove the bending-stretching coupling. Stability equations are derived and then analytically solved for rectangular plates with simple supports using Legendre orthonormal polynomials and Navier’s method to determine the critical buckling load. The results are then compared with estimates made using higher-order shear deformation (HSDT) and classical plate theories (CPT) available in the literature for FG non-porous plates. It is shown that compared to the HSDT, the HOSNDT yields smaller values for the plate critical buckling load and the effect of HSNDT is more important as the plate thickness increases. In addition, it is demonstrated that compared to the uniaxial load, the effect of HSNDT is greater as the plate is subjected to a biaxial compression load. Finally, the effects of the porosity distribution, porosity, power-law index, loading condition, and thickness ratio are studied in detail using HOSNDT. The results show that the porosity effect is greater in smaller values of the power law index parameter.