Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk

Li, X.Y.; Ding, Hu; Chen, W.Q.

doi:10.1016/j.ijsolstr.2007.07.023

Cited by 88 publications

(53 citation statements)

References 20 publications

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“…Therefore, there are many studies on FGM plates during the past decades, for example, Refs. [1][2][3][4][5][6][7][8][9][10], to list but only a few. Studies on FGM plates involve many interesting topics, including static and dynamic analyses, stability analysis, buckling analysis, and so on.…”

Section: Introductionmentioning

confidence: 99%

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

Liu

et al. 2018

Applied Sciences

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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.

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Section: Introductionmentioning

confidence: 99%

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

Liu

et al. 2018

Applied Sciences

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“…Recently, some investigators presented three-dimensional analytic solutions for the bending of FGM plates subject to transversal loads by assuming specific boundary conditions on the mantle for the description of either simply supported or clamped plates (e.g., Li et al 2008;Kashtalyan 2004). The limit of these 3D solutions consists in the fact that the boundary conditions are satisfied on the mantle only in some average sense, not pointwise.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional elastic solutions for functionally graded circular plates

Sburlati¹,

Bardella²

2011

European Journal of Mechanics - A/Solids

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Three-dimensional elastic solutions are obtained for a functionally graded thick circular plate subject to axisymmetric conditions. We consider a isotropic material where the Young modulus depends exponentially on the position along the thickness, while the Poisson ratio is constant. The solution method utilises a Plevako's representation form which reduces the problem to the construction of a potential function satisfying a linear fourth-order partial differential equation. We write this potential function in terms of Bessel functions and we pointwise assign mixed boundary conditions. The analytic solution is obtained in a general form and explicitly presented by assuming transversal load on the upper face and zero displacements on the mantle; this is done by superposing the solutions of problems with suitably imposed radial displacement. We validate the solution by means of a finite element approach; in this way, we highlight the effects of the material inhomogeneity and the limits of the employed numerical method near the mantle, where the solution shows a large sensitivity to the boundary conditions.

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“…Nie and Zhong [6] and Zhou and Li [7] investigated the free vibration of the FGM circular plates based on the three-dimensional theory using the state space method combined with the DQM. Recently, Li et al [8] presented the elasticity solutions for a transversely isotropic FGM circular plate subject to an axisymmetric transverse load in terms of the polynomials of even order.…”

Section: Introductionmentioning

confidence: 99%

Free axisymmetric vibration of FGM circular plates

Wang

Ding

2009

Appl. Math. Mech.-Engl. Ed.

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Based on the three-dimensional theory, this work presents a direct displacement method to investigate the free axisymmetric vibration of transversely isotropic circular plates, whose material is functionally graded and properties obey the exponential law along the thickness direction of the plate. Under two boundary conditions, the solution satisfies all basic equations and the corresponding boundary condition at every point. Thus, it is three-dimensional exact. Numerical examples are presented and compared with previous works. The present method can also be extended to the case of arbitrary distribution of the material properties along the thickness direction of the plate.

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Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk

Cited by 88 publications

References 20 publications

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

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

Three-dimensional elastic solutions for functionally graded circular plates

Free axisymmetric vibration of FGM circular plates

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