Three-dimensional bending and stress analyses of the rotating two-directional functionally graded annular/circular plates or disks have not been accomplished so far. This task is performed in the present paper, employing a finite element formulation with a C 1 -continuity. Therefore, both transversely graded and radiallygraded plates may be analyzed as special cases of the present research. Distribution of the transverse loads as well as coefficients of the elastic foundation may be non-uniform. Mixed stress-based and displacement-based edge conditions are considered to cover many practical applications. Compatible Hermitian elements are employed to develop a consistent formulation and avoid jumps in the stress components at the elements interfaces. 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 also considered in the present research. Finally, influences of the material properties distribution, angular speed, geometric parameters, and the elastic foundation on distributions of the stress and displacement components are investigated for a variety of edge and boundary conditions and some design criteria are extracted.

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 secondorder 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.

No abstract

No abstract

In this paper, the dynamic stress and radial/lateral vibration of circular/annular discs made of fractional-order viscoelastic materials under nonuniform mechanical loads are investigated for the first time, utilizing the exact 3D theory of elasticity, rather than the plate theories. The governing equations of motion of the disc are derived based on the Kelvin–Voigt fractional viscoelastic model. To solve these equations, the spatial partial and the time ordinary derivatives are replaced by adequate central, backward or forward finite difference expressions. Then the resulting Caputo-type time-dependent system of the coupled integro-differential governing equations of the fractional-order is solved by a novel numerical procedure. Namely, a time-marching procedure is employed to extract the time histories of the responses, in the space-time domain for various time and spatial distributions. Finally, comprehensive sensitivity analyses and various 3D plots are presented and discussed. In this regard, effects of the fractional-order of the constitutive law, viscoelastic parameters, material rigidity, distribution and time variation patterns of the nonuniform distributed transverse loads, and boundary conditions on the distributions of the displacement and stress components are investigated.