A Parametric Study on the Centrifugal Force-Induced Stress and Displacements in Power-Law Graded Hyperbolic Discs

Abstract An extensive parametric study on the variation of the centrifugal-force-induced stress and displacements with the inhomogeneity indexes, profile parameters and boundary conditions is conducted based on the author’s recently published analytical formulas for radially functionally power-law graded rotating hyperbolic discs under axisymmetric conditions. The radial variation of the thickness of the disc is chosen to obey a hyperbolic function defined either convergent or divergent. In the present work, contrary to the published one, it is assumed that both Young’s modulus and density radially vary with the same inhomogeneity index to enable to conduct a parametric study. Under this additional assumption, for the values of the chosen power-law indexes β = − 5, 0, 5 for the material grading rule, and the chosen profile parameters m = − 1, − 0.75, − 0.5, − 0.25, 0, 0.25, 0.5, 0.75, 1 for a hyperbolic disc; the variations of the radial stress, the hoop stress and the radial displacement are all illustrated graphically for a rotating disc whose both surfaces are stress-free, for a rotating disc mounted a rigid shaft at its center and its outer surface is stress-free, and finally for a rotating disc attached a rigid shaft at its center and guided at its outer surface (a rigid casing exists at the outer surface).