Exact Solution for Axisymmetric Bending of Functionally Graded Circular Plate

The paper presented an exact analysis for axisymmetric bending of functionally graded circular plate under the following two edge boundary conditions: elastically supported and rigid slipping. The displacement function of functionally graded circular plate was expanded as Fourier-Bessel series. Based on the basic equations of isotropic functionally graded materials under the assumption that the material property has the exponential dependence on the thickness-coordinate, exact solutions of displacement, and stress field were obtained for a circular plate subjected to axisymmetric normal and shearing loadings on its upper and lower surfaces. The influence of different functionally graded variation on the stress and displacement fields was studied through a numerical example. The obtained exact solutions show that the graded material properties have significant effects on the mechanical behavior of the plate.