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.
Highlights
IntroductionThe concept of functionally graded materials (FGMs) was first suggested by a group of Japanese scientists as thermal barrier materials for aerospace structural applications and fusion reactors
The concept of functionally graded materials (FGMs) was first suggested by a group of Japanese scientists as thermal barrier materials for aerospace structural applications and fusion reactors.The properties of functionally graded materials vary gradually with the thickness direction within the structure, which eliminates interface problems, and the stress distributions are smooth.Thin plate structures made of functionally graded materials have been found many applications in aerospace, automotive, and biomedical fields
This review mainly focuses on the equivalent single layer theories, including the classical plate theory, first-order shear deformation theory, higher-order shear deformation theories, simplified theories, and mixed theories, since they were widely used in the modeling of functionally graded plates and shells
Summary
The concept of functionally graded materials (FGMs) was first suggested by a group of Japanese scientists as thermal barrier materials for aerospace structural applications and fusion reactors. Shen and Wang [19] studied the nonlinear bending problem of a supported, functionally graded cylindrical panel resting on an elastic foundation in thermal environments, in which the formulations are based on a higher order shear deformation shell theory with a von Kármán-type of kinematic nonlinearity, and a two-step perturbation technique is employed to determine the load-deflection and load-bending moment curves Another requirement for the refined analysis of FGM plates may be from the sufficient consideration of possible mechanical properties of materials, for example, the so-called bimodular effect existed in most engineering materials, which is firstly proposed and systematized by Ambartsumyan [20].
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