An analytical study on static, free vibrational and buckling behaviour of FG-GNPRC plates using nonpolynomial shear deformation theory

This study presents an analytical formulation based on the inverse hyperbolic shear deformation theory (IHSDT), a non-polynomial higher-order shear deformation theory, for the static, buckling, and free vibration analyses of functionally graded graphene nanoplatelets reinforced composite (FG-GNPRC) plates. The IHSDT satisfies the condition of zero transverse shear stresses at both bottom and top surfaces of the composite plate, so it eliminates the need for a shear correction factor. This theory also considers non-linear transverse shear deformation across the thickness of the composite plate. The effective material properties such as Young's modulus, density etc., of FG-GNPRC plates are calculated using the modified Halpin-Tsai method and rule of mixture method. The governing differential equations are derived by applying Hamilton's principle. The composite plates are subjected to simply supported boundary conditions and differential equations are solved by applying Navier's solution methodology. An analytical approach is applied to obtain the deflection, stresses, critical buckling load and natural frequency of FG-GNPRC plates. The accuracy of the proposed model is verified through comparisons with the existing results, demonstrating excellent agreement. Various parametric studies such as the impact of weight percentage of GNP, geometry of GNP, number of layers, distributions of GNP and span-to-thickness ratio of composite plate are conducted. Different GNP distribution patterns are taken into consideration, such as (FG-X, UD, FG-A and FG-O) for the analysis.