Three-dimensional elastic solutions for functionally graded circular plates

Abstract

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.

Three-dimensional compatible finite element stress analysis of spinning two-directional FGM annular plates and disks with load and elastic foundation non-uniformities

“…This fact is independent of the location of the section or the transverse loading pattern (as in the homogeneous plates or beams). Based on these facts, it seems that present results are slightly more accurate than those of Sburlati and Bardella (2011) paper.…”

“…Various combinations of the stress distributions are determined and compared with those of Sburlati and Bardella (2011) paper. In the first stage, the throughthe-thickness distributions of the radial and transverse shear stresses of various radial sections are plotted in Figures 5 and 6, respectively for case (1).…”

“…As it may readily be deduced, there is a good agreement between the results. Example 2: To evaluate the accuracy of the present three-dimensional elasticity approach, an example is adopted from a work by Sburlati and Bardella (2011). Sburlati and Bardella (2011) proposed an analytical solution for stationary solid transversely-graded clamped circular plates under certain transverse pressures.…”

Analytical Bending and Stress Analysis of Variable Thickness FGM Auxetic Conical/Cylindrical Shells with General Tractions

“…Wang et al (2010) presented a three-dimensional solution for axisymmetric bending of FGM circular plates. Sburlati and Bardella (2011) developed three-dimensional elastic solutions for the axisymmetric FGM circular plates. Behravan Rad and Shariyat (2013) presented a 3D elasticity analysis for bidirectional FGM annular plates subjected to normal and shear tractions, on elastic foundations.…”

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“…This requires the introduction of two suitable functions β(z) = L(b, z), and α(z) = ∇ 2 r L(r, z)| r =b which, in turn, give rise to a different componentwise expression of the Plevako equation [Sburlati 2009b;Sburlati and Bardella 2011].…”