Semi-Analytical Solution for the Static Analysis of 2D Functionally Graded Solid and Annular Circular Plates Resting on Elastic Foundation

The effects of two-parameter linear elastic foundations on axisymmetric response of two directionally functionally graded circular plates are investigated by using a differential quadrature method. The state equations are derived based on 3D theory of elasticity, and assuming the modulus of elasticity varies continuously throughout the thickness and radius directions in the form of an exponential function, and the Poisson's ratio is constant. The stresses and displacements distribution are obtained by solving these state equations. The influences of gradient indices, thickness to radius ratio, foundation stiffness, and edge supports on the static behavior of a plate are studied in the numerical examples.