Buckling analysis of embedded functionally graded graphene platelet-reinforced porous nanocomposite plates with various shapes using the p-Ritz method

In this study, the buckling of functionally graded graphene platelet-reinforced porous nanocomposite plates with various shapes such as, rectangular, elliptical and triangular ones embedded in an elastic medium is analyzed. To mathematically model the considered plate and elastic foundation, the first-order shear deformation plate theory and the Winkler-Pasternak model are used, respectively. Three types of graphene nanoplatelet distribution and porous dispersion patterns through the thickness direction are considered for the nanocomposite plate. The effective material properties are obtained via a micromechanical model. By writing the energy functional of system and using the analytical P-Ritz method, the influences of porosity coefficient, weight fraction of graphene nanoplatelets, elastic foundation coefficients, and also the length-to-width and -thickness ratios on the critical buckling loads are analyzed. It is illustrated that the plate with non-uniform porosity distribution pattern of the first type and GPLA pattern due to the greater concentration of graphene nanoplatelets on the upper and lower surfaces of the plate and the increase in the stiffness of the plate, it has higher critical buckling load. Also, the maximum critical buckling load is related to shear loading and the minimum critical buckling load is related to biaxial buckling load. Also, by increasing the porosity coefficient, the critical buckling loads of the plate associated with all patterns of graphene nanoplatelets are reduced.