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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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In this paper, we propose a method for the solution of the axisymmetric boundary value problem for a finite elastic cylinder with assigned stress and/or displacements acting on the ends and side. The technique utilizes the Love representation, which allows for reduction of the solution of the elastic problem to the search for a biharmonic function on a cylindrical domain. In the solution method suggested here, we write the Love function with a Bessel expansion and analyze in detail the conditions under which it is possible to differentiate the expansion term by term. We show that this is possible only for a restricted class of elastic solutions. In the general case, we introduce two new auxiliary functions of the z-coordinate. In this way, we obtain the general form of the axisymmetric biharmonic function, which is discussed in relation to certain specific boundary conditions applied on the side and ends of the cylinder. We obtain an exact explicit solution of practical interest for a cylinder with free ends and assigned displacements applied to the side.

This work deals with the problem of modeling the effect due to an interphase zone between inclusion and\ud matrix in particulate composites to better estimate the bulk modulus of materials with inclusions. To this\ud end, in this paper the problem of a body containing a hollow or solid spherical inclusion subjected to a\ud spherically symmetric loading is investigated in the framework of the elasticity theory. The interphase\ud zone around the inclusion is modeled by considering the elastic properties varying with the radius moving\ud away from the interface with inclusion and, asymptotically approaching the value of the homogeneous\ud matrix. The explicit solutions are obtained in closed form by using hypergeometric functions\ud and numerical investigations are performed to highlight the localized effects of the graded interphase\ud in the stress transfer between inclusion and matrix. Finally, the exact solutions are used to estimate\ud the effective bulk modulus of a material containing a dispersion of hollow or solid spherical inclusions\ud with graded interphase zone