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

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 powerlaw indexes 5, 0, 5    for the material grading rule, and the chosen profile parameters 1, 0.75, 0.5, 0.25, 0, 0.25, 0.5, 0.75, 1 m      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).

[1]  Jan Melkebeek,et al.  Stability and Dynamics , 2018 .

[2]  V. Yıldırım Heat-Induced, Pressure-Induced and Centrifugal-Force-Induced Exact Axisymmetric Thermo-Mechanical Analyses in a Thick-Walled Spherical Vessel, an Infinite Cylindrical Vessel, and a Uniform Disk Made of an Isotropic and Homogeneous Material , 2017 .

[3]  V. Yıldırım Analytic Solutions To Power-Law Graded Hyperbolic Rotating Discs Subjected To Different Boundary Conditions , 2016 .

[4]  A. Eraslan,et al.  Analytical and numerical solutions to rotating variable thickness disks for a new thickness profile , 2015 .

[5]  A. Rastgoo,et al.  Exact elasto-plastic analysis of rotating disks made of functionally graded materials , 2014 .

[6]  F. Vivio,et al.  Theoretical Stress Analysis of Rotating Hyperbolic Disk without Singularities Subjected to Thermal Load , 2014 .

[7]  M. Z. Nejad,et al.  Elastic analysis of exponential FGM disks subjected to internal and external pressure , 2013 .

[8]  F. Vivio,et al.  Thermal Stresses of Rotating Hyperbolic Disks as Particular Case of Non-Linearly Variable Thickness Disks , 2012 .

[9]  Xian‐Fang Li,et al.  Effects of gradient on stress distribution in rotating functionally graded solid disks , 2012 .

[10]  H. Argeso Analytical Solutions to Variable Thickness and Variable Material Property Rotating Disks for a New Three-Parameter Variation Function , 2012 .

[11]  M. Sayer,et al.  Stress analysis of functionally graded rotating discs: analytical and numerical solutions , 2011 .

[12]  R. A. Alashti,et al.  Semi-exact elastic solutions for thermo-mechanical analysis of functionally graded rotating disks , 2011 .

[13]  D. Mashat,et al.  Stress Function of a Rotating Variable-Thickness Annular Disk Using Exact and Numerical Methods , 2011 .

[14]  Xian‐Fang Li,et al.  Thermoelastic analysis of functionally graded annulus with arbitrary gradient , 2009 .

[15]  Vincenzo Vullo,et al.  Elastic stress analysis of non-linear variable thickness rotating disks subjected to thermal load and having variable density along the radius , 2008 .

[16]  Abdel Magid Hamouda,et al.  ANALYSIS OF FUNCTIONALLY GRADED ROTATING DISKS WITH VARIABLE THICKNESS , 2008 .

[17]  Vincenzo Vullo,et al.  Elastic stress analysis of rotating converging conical disks subjected to thermal load and having variable density along the radius , 2007 .

[18]  Ashraf M. Zenkour,et al.  Elastic deformation of the rotating functionally graded annular disk with rigid casing , 2007 .

[19]  J. Zhang,et al.  On rotating circular disks with varying material properties , 2007 .

[20]  Ahmet N. Eraslan,et al.  On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems , 2006 .

[21]  A. Zenkour ANALYTICAL SOLUTIONS FOR ROTATING EXPONENTIALLY-GRADED ANNULAR DISKS WITH VARIOUS BOUNDARY CONDITIONS , 2005 .

[22]  Ahmet N. Eraslan,et al.  Elastoplastic deformations of rotating parabolic solid disks using Tresca's yield criterion , 2003 .

[23]  A. Eraslan Elastic–plastic deformations of rotating variable thickness annular disks with free, pressurized and radially constrained boundary conditions , 2003 .

[24]  C. Horgan,et al.  The Stress Response of Functionally Graded Isotropic Linearly Elastic Rotating Disks , 1999 .

[25]  Cornelius O. Horgan,et al.  The Pressurized Hollow Cylinder or Disk Problem for Functionally Graded Isotropic Linearly Elastic Materials , 1999 .

[26]  U. Güven Tresca's Yield Condition and the Linear Hardening Rotating Solid Disk of Variable Thickness , 1995 .

[27]  Fehmi Cirak,et al.  ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND MECHANIK , 1952, Über Stammfaktoren bei ternären quadratischen Formen.

[28]  M. Garg Stress Analysis of Variable Thickness Rotating FG Disc , 2022 .