Buckling and post-buckling analyses of functionally graded graphene reinforced piezoelectric plate subjected to electric potential and axial forces

The buckling and post-buckling behaviors are analyzed for the multilayer functionally graded graphene platelets reinforced piezoelectric (FG-GRP) plates. The FG-GRP plates are subjected to the external electric potential and axial forces, including the uniaxial loading and biaxial loading. The graphene platelets (GPLs) disperse uniformly and parallelly in each graphene platelets reinforced piezoelectric composite (GRPC) layer, but they spread grading across the thickness of the FG-GRP plates. The effective Young's modulus of each layer for the FG-GRP plates is calculated by the Halpin-Tsai parallel model. The rule of the mixture is employed to predict the Poisson's ratio, effective mass density and piezoelectric properties of each layer of the FG-GRP plates. The governing equations of motion for the FG-GRP plates are obtained by the first-order shear deformation plate theory, von Karman nonlinear theory and principle of virtual displacements. To obtain the buckling and post-buckling behaviors of the FG-GRP plates with different boundary conditions, the differential quadrature (DQ) method and a direct iterative technique are combined to solve the governing equations of motion for the FG-GRP plates. The impacts of the external electric voltage, distribution pattern, volume fraction, piezoelectric properties, length-to-thickness of the GPLs and geometry of the plates on the critical buckling load and post-buckling equilibrium paths of the FG-GRP plates are discussed in detailed. It is clearly illustrated that the GPLs have a significantly enhancing influence on the buckling and post-buckling strength of the FG-GRP plates.