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

Abstract

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.

Large Deformation Problem of Bimodular Functionally-Graded Thin Circular Plates Subjected to Transversely Uniformly-Distributed Load: Perturbation Solution without Small-Rotation-Angle Assumption

“…For the obtainment of an explicit solution of the problem, we need to define the mathematical form of the bimodular FGM model first. Considering the convenience of differential and integral operations, we model E + (z) and E − (z) as the following exponent type functions [30,31] E + (z) = E 0 e α 1 z/t , E − (z) = E 0 e α 2 z/t , (…”

“…Suppose that the displacements of the neutral layer along the r and z directions are u and w, respectively, and the radii of the radial and circumferential curvatures of the neutral layer are ρ r and ρ θ , respectively. The strain components of any point at the z axis in the plate come from two different aspects, one is the tensile strain on the neutral layer and another from the bending strain; that is [31]…”

“…More recently, the bimodular property of materials has been gradually introduced into the analysis field of FGM and structures. There are also a few works concerning bimodular FGM beam and plate problems [29][30][31]. Focusing on bimodular FGM plates, He et al [30] established the simplified theory based on a neutral layer under small-deflection; thereafter, He et al [31] derived the governing equations of the large-deflection problem of bimodular FGM thin circular plate.…”

“…There are also a few works concerning bimodular FGM beam and plate problems [29][30][31]. Focusing on bimodular FGM plates, He et al [30] established the simplified theory based on a neutral layer under small-deflection; thereafter, He et al [31] derived the governing equations of the large-deflection problem of bimodular FGM thin circular plate. However, consideration of geometrical nonlinearity seems to be insufficient.…”

Experimental Analysis of Welded Rods with a Functionally Graded Material Approach

“…It should be noted that, there are many other studies related to FGM in the literature [36][37][38]. There are many theoretical examples of the thermal behavior and mechanical analysis (vibration, wave propagation, bending and buckling) of axially FGM in the literature [39][40][41][42][43]. The purpose of this study is to establish a link between theoretical and experimental studies.…”