Flexural behaviour of functionally graded graphene platelet–reinforced plates with multidimensional gradation using a higher-order shear deformation finite element model

The present study investigates the bending behaviour of functionally graded graphene platelet–reinforced plates (FG-GPLRPs) with one-(1D), two-(2D), and three-dimensional-(3D) material gradation, addressing the need for accurate modelling of highly heterogeneous advanced composites. A nine-degree-of-freedom higher-order shear deformation theory is employed within a finite element framework to capture bending and stress responses without the use of shear correction factors. The effective material properties of the graded metal–ceramic matrix are evaluated using a modified rule of mixtures, while the reinforcing effect of graphene platelets is incorporated through the Halpin–Tsai model. Three graphene platelet dispersion patterns symmetric (Pattern A), asymmetric (Pattern B), and uniform (Pattern C) are considered to assess their influence on structural performance. The governing equations, derived from the principle of minimum potential energy, are solved using an isoparametric finite element formulation. A comprehensive parametric study is conducted to examine the effects of geometric parameters, gradation index, graphene platelet weight fraction, and dispersion patterns. The results provide useful insights into the design and optimization of FG-GPLRPs for enhanced bending performance in engineering applications.