Three-dimensional elastic solutions for functionally graded circular plates

Roberta Sburlati , Lorenzo Bardella

Three-dimensional elastic solutions are obtained for a functionally graded thick cir-cular 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 high-light 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.

Mots clés: Functionally graded plates; Boundary value problems; Finite element method

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Roberta Sburlati, Lorenzo Bardella. Three-dimensional elastic solutions for functionally graded circular plates. European Journal of Mechanics - A/Solids, 2011, ⟨10.1016/j.euromechsol.2010.12.008⟩. ⟨hal-00734537⟩