An n-order refined plate theory for bending and buckling of functionally graded polymer composite plates reinforced with graphene nanoplatelets

This study investigates the bending and buckling behavior of functionally graded multilayer graphene nanoplatelet (GPL)/polymer composite plates using an n-order refined plate theory. The theory introduces a higher-order polynomial displacement field that ensures variational consistency and eliminates the need for shear correction factors. In this formulation, shear stresses vary parabolically through the plate thickness, and stress-free conditions are satisfied at both the top and bottom surfaces, resulting in improved accuracy compared to conventional plate theories. A key innovation of this work lies in the layer-wise variation of GPL weight fractions, enabling the design of functionally graded nanocomposites with both uniform and non-uniform reinforcement patterns—specifically, UD, FG-O, FG-X, and FG-A. While most existing studies are limited to uniformly distributed GPLs or rely on lower-order theories, this study addresses these limitations by proposing an analytically tractable higher-order model that can accurately capture shear deformation effects and by systematically analyzing the mechanical influence of different GPL distribution patterns. This dual advancement fills an important gap in the literature, particularly in understanding the performance of non-uniformly graded nanocomposites under bending and buckling. The effective Young's modulus is predicted using the Halpin-Tsai micromechanics model, and the rule of mixtures is used to determine the effective Poisson's ratio and mass density. Analytical solutions for static deflection and buckling are derived for simply supported plates using the Navier solution technique. The results show that non-uniform GPL distributions, particularly FG-X and FG-O, significantly enhance bending stiffness and buckling resistance by concentrating reinforcement near high-stress regions. Additionally, increasing the GPL weight fraction and optimizing GPL geometry further improve structural performance. This study offers new insights into the tailored design of functionally graded nanocomposite plates and provides practical guidance for lightweight, high-performance structural components in aerospace, automotive, and civil engineering applications.