Three-dimensional Analyses of Functionally Graded Multi-layered Systems

Functionally Graded Materials (FGMs) are composites with continuously varying volume fractions of their constituent homogeneous phases. When the characteristic length scale of such variations is much larger than the size of the phases, the model of the inhomogeneous solids is able to describe the macroscopic behaviour of these materials by means of homogenization techniques. By considering materials in which this assumption is possible, some elastic solutions for graded inhomogeneous materials have been obtained in the literature in order to tailor the material parameters for specific requirements. The main purpose of the paper is devoted to analyse the effects of FGM elements in sandwich structures, where the mismatch between the properties of the core and the face-sheets can produce interface damage especially when the structures are subjected to extreme conditions. Two different cases concerning the bending of a thick circular sandwich plate are investigated in the framework of the linear elasticity theory: (a) sandwich plates with homogeneous face sheets and FGM-core and (b) sandwich plates with FGM face sheets and homogeneous core. The related elastic solutions are obtained in the framework of the elasticity theory and explicit solutions are discussed by considering only the first contribution of the series in order; in such a way, we have a solution in closed-form and no convergence effects on the solutions. Three different aspects are studied in detail in terms of the geometric and material parameter: the semi-inverse solution method adopted with the consequence on boundary conditions, the non-linear behaviour of the radial displacement and, the shear and circumferential stress behaviour in the thickness of the plate. A comparative study between sandwich with FGM elements and conventional multi-layered systems is performed in order to highlight the effects of the inhomogeneity.