Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy

Abstract

Based on the basic equations for axisymmetric problems of transversely isotropic elastic materials, the displacement components are expressed in terms of polynomials of the radial coordinate with the five involved coefficients, named as displacement functions in this paper, being undetermined functions of the axial (thickness) coordinate. Five equations governing the displacement functions are then derived. It is shown that the displacement functions can be found through progressive integration by incorporating the boundary conditions. Thus a three-dimensional analytical solution is obtained for a transversely isotropic functionally graded disc rotating at a constant angular velocity. The solution can be degenerated into that for an isotropic functionally graded rotating disc. A prominent feature of this solution is that the material properties can be arbitrary functions of the axial coordinate. Thus, the solution for a homogeneous transversely isotropic rotating disc is just a special case that can be easily derived. An example is finally considered for a special functionally graded material, and numerical results shows that the material inhomogeneity has a remarkable effect on the elastic field.

Temperature and thickness effects on thermal and mechanical stresses of rotating FG-disks

“…In this study, elastic coefficient was considered to be a function of the disk's thickness. Chen et al [21] derived an analytical solution for rotating disks made of FGMs. In their investigation, all material properties were considered to vary in the thickness direction of the disk, and optimization was carried out according to the distribution of radial and hoop stresses.…”

“…In another paper, Bayat et al [24] performed a thermoelastic solution of a functionally graded, variable thickness rotating disk with bending based on the first-order shear deformation theory. Chen et al [25] considered a three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy.…”

Stress analysis in a functionally graded disc under mechanical loads and a steady state temperature distribution

“…Durodola & Attia (2000) have investigated deformation and stresses in functionally graded rotating discs by using finite element method and direct numerical integration of governing differential equations. Chen et al (2007) have presented three-dimensional analytical solution for a rotating disc made of transversely isotropic functionally graded materials. Mohammadi & Dryden (2008) have examined the role of non-homogeneous stiffness on the thermoelastic stress field.…”

Effect of material inhomogeneity on the rotating functionally of a graded orthotropic hollow cylinder

“…Zenkour [11] investigated stress distribution in rotating composite structures of functionally graded solid disks. Chen et al [12] obtained the threedimensional analytical solution of rotating functionally graded disks.…”