Analytic Solutions To Power-Law Graded Hyperbolic Rotating Discs Subjected To Different Boundary Conditions

The exact elastic response of a convergent/divergent hyperbolic rotating disc made of a power-law graded material is studied under different boundary conditions. Soundness of the formulas derived is verified with the literature. A parametric study is performed to investigate elastic responses of those discs under four boundary conditions such as a stationary disc subjected to internal/external pressures, a rotating disc: both surfaces may expand freely, a rotating disc mounted a rigid shaft: outer surface either may freely expand or contains a rigid casing

___

  • Horgan C. and Chan A., The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials. Journal of Elasticity, 55, 43-59, 1999.
  • Horgan C. and Chan A., The stress response of functionally graded isotropic linearly elastic rotating disks. Journal of Elasticity, 55, 219-230, 1999.
  • Zenkour A.M., Analytical solutions for rotating exponentially-graded annular disks with various boundary conditions. International Journal of Structural Stability and Dynamics, 5, 557-577, 2005.
  • Eraslan A.N. and Akiş T., On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems, Acta Mechanica, 181 (1–2), 43–63, 2006.
  • Zenkour A.M., Elastic deformation of the rotating functionally graded annular disk with rigid casing, Journal of Materials Science, 42, 9717-9724, 2007.
  • Bayat M., Saleem M., Sahari B., Hamouda A. and Mahdi E., Analysis of functionally graded rotating disks with variable thickness, Mechanics Research Communications, 35, 283-309, 2008.
  • Peng X.L. and Li X.F., Thermoelastic analysis of a functionally graded annulus with an arbitrary gradient, Appl Math Mech, 30, 1211–1220, 2009.
  • Zenkour A.M. and Daoud S.M., Stress function of a rotating variable-thickness annular disk using exact and numerical methods, Engineering, 3, 422-430, 2011.
  • Saidi A., Naderi A. and Jomehzadeh E., A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 224, 1153-1163, 2010.
  • 0] Çallıoğlu H., Bektaş N.B. and Sayer M., Stress analysis of functionally graded rotating discs: analytical and numerical solutions, Acta Mechanica Sinica, 27, 950-955, 2011.
  • 1] Ghorbani M.T., A semi-analytical solution for time-variant thermoelastic creep analysis of functionally graded rotating disks with variable thickness and properties, International Journal of Advanced Design and Manufacturing Technology, 5, 41-50, 2012.
  • 2] Nejad M.Z., Abedi M., Lotfian M.H. and Ghannad M., Elastic analysis of exponential FGM disks subjected to internal and external pressure, Central European Journal of Engineering, 3, 459 465, 2013.
  • 3] Nejad M.Z., Rastgoo A. and Hadi A., Exact elasto-plastic analysis of rotating disks made of functionally graded materials, International Journal of Engineering Science, 85, 47-57, 2014.
  • 4] Khorshidv A.R. and Khalili S.M.R., A new analytical solution for deformation and stresses in functionally graded rotating cylinder subjected to thermal and mechanical loads, Continuum Mechanics, Fluids, Heat, ISSN: 1790-5095, ISBN: 978-960-474-158-8: 201-204, 2010.
  • 5] Jabbari, M., Sohrabpour, S. and Eslami, M.R., General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads, J. Appl. Mech., 70, 111–118, 2003.
  • 6] Vel S.S., Exact thermoelastic analysis of functionally graded anisotropic hollow cylinders with arbitrary material gradation, Mechanics of Advanced Materials and Structures,18, 14–31, 2011.
  • 7] Yıldırım V. and Boğa C., Closed-form elasticity solutions to uniform rotating discs made of a radially functionally graded material, IJIRSET International Journal of Innovative Research in Science, Engineering and Technology, 5/Special Issue 12, 80-91, 2016.
  • 8] Young W.C. and Budynas R.G., Roark’s Formulas for Stress and Strain, McGraw-Hill, Seventh Edition, New York, 2002.
  • 9] Bower A. F., Applied Mechanics of Solids. Taylor and Francis, 2012.