Three-dimensional solution of axisymmetric bending of functionally graded circular plates

Based on three-dimensional theory, this paper investigates the axisymmetric bending of transversely isotropic and functionally graded circular plates subject to arbitrarily transverse loads using the direct displacement method. The material properties can arbitrarily vary along the thickness of the plate. The transverse load is expanded in the Fourier–Bessel series and superposition principle is then used to obtain the total response based on the results of each item of the series. For one item of the series of the load, we assume the distributions of the displacements in the radial direction and therefore only the distributions of the displacements in thickness direction are required to find. If the material properties vary in an exponential law, the exact solutions can be obtained for elastic simple support and rigid slipping support, which are satisfied on the every point of the boundaries. Moreover, the analytical solutions are also presented for simply supported and clamped conditions, which are satisfied using Saint Venant principle. Simultaneously, through the layerwise method a semi-analytical solution is proposed for the case of arbitrary variation of the material properties. Finally the numerical examples are presented to verify the proposed method.