Static analysis of functionally graded elastic anisotropic plates using a discrete layer approach

An approximate solution for the static analysis of three-dimensional, anisotropic, elastic plates composed of functionally graded materials (FGM) is presented. The solution is obtained by using a discrete layer theory in combination with the Ritz method in which the plate is divided into an arbitrary number of homogeneous and/or FGM layers. Two types of functionally graded materials are considered: an exponential variation of the mechanical properties through the thickness of the plate, and mechanical properties as a function of the fiber orientation, which varies quadratically through the laminate thickness. The present approach is not dependent on a specific transition function, and any continuous function representing the variation of the material properties in the thickness direction may be incorporated in the model. The method is validated by solving the problem of a single simply supported FGM plate, for which excellent agreement with the exact solution is obtained. Two more examples with different boundary conditions and different material configurations are presented in order to demonstrate the applicability of this solution. Homogeneous, graded, and bi-layer plates are examined in order to study potential advantages of using FGM.