Study on the effect of functionally graded coating layers on elastic deformation of thick circular plates: A closed-form elasticity solution

In this paper, a closed-form solution is presented for displacements and stresses in a thick homogeneous circular plate coated by functionally grade (FG) layers subjected to transverse loading. The solution procedure is in the framework of infinitesimal theory of elasticity. The elasticity modulus of the FG coating layers is assumed to vary exponentially through the thickness, whereas Poisson’s ratio remains constant. The solution procedure is on the basis of a Plevako’s representation, which reformulates the elasticity equations into some uncoupled fourth-order partial differential equations with respect to some potential functions. We explicitly obtain the analytical solution by writing the potential functions as Fourier–Bessel series expansions with respect to the radial coordinate. The solution is validated by comparing the numerical results with their counterparts reported in literature for the conventional system of thick plates coated by homogeneous layers, as well as the 3-D finite element analysis. A comparative study is presented between a thick circular plate coated by functionally graded layers and the one with homogeneous coating layers.