Three-dimensional stress field analysis of rotating thick bidirectional functionally graded axisymmetric annular plates with nonuniform loads and elastic foundations

Abstract

Based on the three-dimensional theory of elasticity, a comprehensive stress analysis is performed for the rotating bidirectional functionally graded thick axisymmetric circular/annular plates, for the first time. The plate may be subjected to arbitrary distributions of the transverse load and various mixed (Dirichlet-type and Neumann-type) edge conditions. Furthermore, the circular plate may be supported by a nonuniform elastic foundation or a rigid substrate. In contrast to the very limited works presented for the rotating functionally graded circular plates so far, the transverse flexibility and the transverse stress components are considered and studied in the present research. Since finite element and boundary element techniques, due to their integral natures, cannot adequately trace abrupt changes of the quantities, a second-order point collocation method with forward–backward schemes is adopted to solve the system of the governing and boundary conditions. Effects of the distributions of the various material properties (Poisson’s ratio, Young’s modulus, and mass density), angular velocity, foundation compliance, and edge conditions are evaluated. Results reveal that radially graded or transversely graded material properties significantly affect distribution and magnitude and location of the extrema of the stress components and the lateral deflections and orientation of the general neutral surface of the plate.