Bending analysis of graphene platelet-reinforced FG plates on Kerr foundations using an integral HSDT

This work explores the bending responses of functionally graded graphene platelet-reinforced ceramic–metal (FG-GPLRCM) plates on Kerr substrates within an integral higher-order shear deformation theory framework. The theory accurately observes zero stresses on the plate's top and bottom surfaces, satisfies boundary conditions, and obviates the requirement for unique shear correction factors using only four governing equations, fewer than other comparable shear deformation models. The plate's Young's modulus and Poisson's ratio are predicted via the Halpin–Tsai model and mixture rule, respectively. By applying Hamilton's principle, governing equations are derived, which are then solved utilizing Navier's technique to determine the deflection of a simply supported FG-GPLRCM plate. Numerical examples are introduced, solved, and compared with theoretical predictions from the literature to confirm the precision of the current theory. The effects of multiple parameters include thick-to-side ratio, length-to-width ratio, power-law gradient index, load type, and Kerr foundation parameters. In addition, the impact of GPL's weight fraction, geometry, size, and distribution pattern on bending behaviors is also investigated.