An asymptotically exact first-order shear deformation theory for functionally graded plates

An asymptotically exact first-order shear deformation theory for functionally graded elastic plates is derived using the variational-asymptotic method. As an application, an analytical solution to the problem of wave propagation in a sandwich plate is found in accordance with this refined theory. Comparison between the dispersion curves obtained by 2-D plate theory and 3-D elasticity theory reveals that the former is accurate up to the order of h^2/l^2, where h is the plate thickness and l the wavelength.