A three-dimensional elasticity solution for two-directional FGM annular plates with non-uniform elastic foundations subjected to normal and shear tractions

In the present paper, bending and stress analyses of two-directional functionally graded (FG) annular plates resting on non-uniform two-parameter Winkler-Pasternak foundations and subjected to normal and in-plane-shear tractions is investigated using the exact three-dimensional theory of elasticity. Neither the in-plane shear loading nor the influence of the two-directional material heterogeneity has been investigated by the researchers before. The solution is obtained by employing the state space and differential quadrature methods. The material properties are assumed to vary in both transverse and radial directions. Three different types of variations of the stiffness of the foundation are considered in the radial direction: linear, parabolic, and sinusoidal. The convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the present approach. A parametric study consisting of evaluating effects of different parameters (e.g., exponents of the material properties laws, the thickness to radius ratio, trends of variations of the foundation stiffness, and different edge conditions) is carried out. The results are reported for the first time and are discussed in detail.