Non-Linear Bending of Functionally Graded Thin Plates with Different Moduli in Tension and Compression and Its General Perturbation Solution

Abstract

In this study, a set of Föppl–von Kármán equations for a bimodular functionally graded thin plate subjected to a uniformly distributed load is established, and its general perturbation solution in axisymmetric case is also obtained under different boundary conditions. First, the equation of equilibrium of the plate is established on the existence of the neutral layer when considering different properties in tension and compression. During the derivation of the consistency equation, the tensile effect in the thin plate with bimodular effect is fully taken into account. The perturbation method is used to solve the set of governing equations under different edge constraints, in which the central deflection and the load of the plate are taken as a perturbation parameter, respectively. The results indicate that the two selections for perturbation parameters are valid and consistent, and the two solutions are convenient for engineering application. This study also shows that the bimodular effect will modify the relation of load versus central deflection of the plate to some extent, and under the same edge constraint, the capacities resisting deformation in different cases of moduli depend on the relative magnitudes among the tensile modulus, the neutral layer modulus, and the compressive modulus.