Bending and buckling of three-dimensional graphene foam plates

Bending and buckling behaviors of three-dimensional graphene foam (3D-GrF) plates are investigated in the framework of the two-variable refined plate theory (TRPT). The material properties of three-dimensional graphene foams vary continuously along thickness direction of the plate. The TRPT considers the effect of transverse shear strains that vary quadratically along the thickness of the plate. In addition, this theory does not need to consider the shear correction factor. By using Hamilton's principle, the governing equations are obtained. Analytical solutions for the bending problem of 3D-GrF plates are derived via Navier's method. Additionally, buckling problem of 3D-GrF plates with various boundary conditions are analyzed by employing the Galerkin method. Results obtained in this study are verified by comparing with the published ones. Finally, the influences of pore distribution, porosity coefficient, transverse distributed load, aspect ratio, length-to-thickness ratio, mode number and axial compression ratio on bending and buckling behaviors of 3D-GrF plates are discussed.