Exact solution for functionally graded anisotropic elastic composite laminates

Exact solutions are derived for three-dimensional, anisotropic, linearly elastic, and functionally graded rectangular composite laminates under simply supported edge conditions. The solutions are expressed in terms of an elegant formalism that resembles the Stroh formalism, and the composite laminates can be made of multilayered functionally graded materials with their properties varying exponentially in the thickness direction. The present solution extends Pagano's solution to the functionally graded material, and can serve as a benchmark to the modeling of functionally graded composite laminates based on various numerical methods. Typical results of the present solution are discussed for a single functionally graded plate and a bi-layer plate with a functionally graded layer overlying a homogeneous layer. For both plates, a simple load is applied on their top surfaces. It is shown that with a suitable functionally graded layer, the tensile stress on the top surface (or the compressive stress on the bottom surface for a homogeneous layer overlying a functionally graded layer) of the bi-layer plate can be reduced. This interesting feature could be useful in the design of functionally graded composite laminates.