Skip to main content
SpringerLink
Log in

General thermo-elastic solution of radially heterogeneous, spherically isotropic rotating sphere

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

A thick walled rotating spherical object made of transversely isotropic functionally graded materials (FGMs) with general types of thermo-mechanical boundary conditions is studied. The thermo-mechanical governing equations consisting of decoupled thermal and mechanical equations are represented. The centrifugal body forces of the rotation are considered in the modeling phase. The unsymmetrical thermo-mechanical boundary conditions and rotational body forces are expressed in terms of the Legendre series. The series method is also implemented in the solution of the resulting equations. The solutions are checked with the known literature and FEM based solutions of ABAQUS software. The effects of anisotropy and heterogeneity are studied through the case studies and the results are represented in different figures. The newly developed series form solution is applicable to the rotating FGM spherical transversely isotropic vessels having nonsymmetrical thermo-mechanical boundary condition.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. I. Gulyaev, P. Z. Lugovoi, I. L. Solov’ev and M. A. Belova, On the bifurcational states of rotating spherical shells, International Applied Mechanics, 38 (9) (2002) 1131–1137.

    Article  Google Scholar 

  2. J. Kadish, J. R. Barber, P. D. Washabaugh and D. J. Scheeres, Stresses in accreted planetary bodies, International J. of Solids and Structures, 45 (1) (2008) 540–550.

    Article  MATH  Google Scholar 

  3. M. Komijani, H. Mahbadi and M. R. Eslami, Thermal and mechanical cyclic loading of thick spherical vessels made of transversely isotropic materials, International J. of Pressure Vessels and Piping, 107 (2013) 1–11.

    Article  Google Scholar 

  4. S. G. Lekhnitshii, Theory of elasticity of an anisotropic body, Mir Publishers, Moscow, Russia (1981).

    Google Scholar 

  5. S. S. Lee, Elastic constants determination of cold-rolled stainless steels by dynamic elastic modulus measurements, J. of Material Science, 33 (1998) 687–692.

    Article  Google Scholar 

  6. W. T. Chen, On some problems in spherically isotropic elastic materials, Trans. ASME, J. of Applied Mechanics, 33 (3) (1966) 539–546.

    Article  MATH  Google Scholar 

  7. H. C. Hu, On the general theory of elasticity for a spherically isotropic medium, Acta Scientia Sinica, 3 (3) (1954) 247–260.

    Google Scholar 

  8. P. P. Raju, On shallow shells of transversely isotropic materials, Transactions of the ASME, J. of Pressure Vessel Technology, 97 (3) (1975) 185–91.

    Article  Google Scholar 

  9. A. E. Puro, Variable separation in elasticity-theory equations for spherically transversely isotropic inhomogeneous bodies, Soviet Applied Mechanics, 16 (2) (1980) 117–120.

    Article  MATH  Google Scholar 

  10. W. Q. Chen, Stress distribution in a rotating elastic functionally graded material hollow sphere with spherical isotropy, J. of Strain Analysis, 35 (1) (2000) 13–20.

    Article  Google Scholar 

  11. H. J. Ding and W. Q. Chen, Natural frequencies of an elastic spherically isotropic hollow sphere submerged in a compressible fluid medium, J. Sound Vibration, 192 (1) (1996) 173–198.

    Article  MathSciNet  Google Scholar 

  12. W. Q. Chen and H. J. Ding, Free vibration of multi-layered spherically isotropic hollow spheres, International J. of Mechanical Sciences, 43 (1) (2001) 667–680.

    Article  MATH  MathSciNet  Google Scholar 

  13. Q. C. He and Y. Benveniste, Exactly solvable spherically anisotropic thermo-elastic microstructures, J. of the Mechanics and Physics of Solids, 52 (1) (2004) 2661–2682.

    Article  MATH  MathSciNet  Google Scholar 

  14. D. Oliveira, Application of a transversely isotropic brittle rock mass model in roof support design, International J. of Mining Science and Technology, 22 (1) (2012) 639–643.

    Google Scholar 

  15. H. M. Shodja and A. Khorshidi, Tensor spherical harmonics theories on the exact nature of the elastic fields of a spherically anisotropic multi-inhomogeneous inclusion, J. of the Mechanics and Physics of Solids, 61 (1) (2013) 1124–1143.

    Article  MATH  MathSciNet  Google Scholar 

  16. M. Maiti, Stresses in anisotropic nonhomogeneous sphere, J. of Engineering Mechanics, 101 (1975) 101–108.

    Google Scholar 

  17. J. P. Montagner and D. L. Anderson, Constrained reference mantle model, Physics of the Earth and Planetary Interiors, 54 (1989) 205–227.

    Article  Google Scholar 

  18. Z. Y. Ding, D. Q. Zou and H. J. Ding, A study of effects of the Earth's radial anisotropy on the tidal stress field, Tectono Physics, 258 (1996) 103–14.

    Article  Google Scholar 

  19. M. R. Eslami, M. H. Babaei and R. Poultangari, Thermal and mechanical stresses in a FG thick walled sphere, International J. of Pressure Vessels and Piping, 82 (1) (2005) 522–527.

    Article  Google Scholar 

  20. R. Poultangari, M. Jabbari and M. R. Eslami, Functionally graded hollow spheres under non-axisymmetric thermomechanical loads, International J. of Pressure Vessels and Piping, 85 (1) (2008) 295–305.

    Article  Google Scholar 

  21. Y. Bayat, M. Ghannad and H. Torabi, Analytical and numerical analysis for the FGM thick walled sphere under combined pressure and temperature loading, Archive of Applied Mechanics, 82 (2012) 229–242.

    Article  MATH  Google Scholar 

  22. A. M. Mohazzab and M. Jabbari, Two-dimensional stresses in a hollow FG Sphere with heat source, Advanced Materials Research, 264–265 (1) (2011) 700–705.

    Article  Google Scholar 

  23. S. Karampour, Dimensional two steady state thermal and mechanical stresses of a Poro-FGM spherical vessel, Procedia-Social and Behavioral Sciences, 46 (1) (2012) 4880–4885.

    Article  Google Scholar 

  24. R. Zhiguo, Y. Ying, L. Jianfeng, Q. Zhongxing and Y. Lei, Determination of thermal expansion coefficients for unidirectional fiber-reinforced composites, Chinese J. of Aeronautics, 24 (1) (2014).

    Google Scholar 

  25. P. Maimi, J. A. Mayugo and P. P. Camanho, A threedimensional damage model for transversely isotropic composite laminates, J. of Composite Materials, 42 (25) (2008) 2717–2745.

    Article  Google Scholar 

  26. M. Koizumu, The concept of FGM, Ceramic Transactions, 34 (1993) 3–10.

    Google Scholar 

  27. B. Woodward and M. Kashtalyan, Three-dimensional elasticity solution for bending of transversely isotropic functionally graded plates, European J. of Mechanics A/Solids, 30 (1) (2011) 705–718.

    Article  MATH  MathSciNet  Google Scholar 

  28. R. B. Hetnarski and M. R. Eslami, Thermal stresse — Advanced theory and applications, Springer, New York, United States (2009).

    Google Scholar 

  29. G. A. Korn and T. M. Korn, Mathematical handbook for scientists and engineers, New York, McGraw-Hill (1968).

    Google Scholar 

  30. P. F. Hou, A. Y. T. Leung and C. P. Chen, Fundamental solution for transversely isotropic thermoelastic materials, International J. of Solids and Structures, 45 (1) (2008) 392–408.

    Article  MATH  MathSciNet  Google Scholar 

  31. H. Mahbadi and M. R. Eslami, Cyclic loading of thick vessels based on the Prager and Armstrong-Frederick kinematic hardening models, International J. of Pressure Vessels and Piping, 83 (2006) 409–419.

    Article  Google Scholar 

  32. O. Saeidi, V. Rasouli, R. G. Vaneghi, R. Gholami and S. R. Torabi, Modified failure criterion for transversely isotropic rocks, Geoscience Frontiers, 5 (1) (2014) 215–225.

    Article  Google Scholar 

  33. Z. Y. Ai and Z. X. Li, Time-harmonic response of transversely isotropic multilayered half-space in a cylindrical coordinate system, Soil Dynamics and Earthquake Engineering, 66 (1) (2014) 69–77.

    Article  Google Scholar 

  34. Y. C. Shiah and C. L. Tan, Boundary element method for thermo-elastic analysis of three-dimensional transversely isotropic solids, International J. of Solids and Structures, 49 (1) (2012) 2924–2933.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, 9177948944-11, Iran

    Yahya Bayat & Hamid EkhteraeiToussi

Authors
  1. Yahya Bayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamid EkhteraeiToussi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamid EkhteraeiToussi.

Additional information

Recommended by Associate Editor Heung Soo Kim

Yahya Bayat received a B.S. in Mechanical Engineering from University of Sistan and Baluchestan (Zahedan-Iran) in 2008, and M.Sc. in Mechanical Engineering from Shahrood University of Technology (Shahroud-Iran) in 2011. Currently he is a Ph.D. candidate of Solid Mechanics at Faculty of Engineering, Ferdowsi University of Mashhad (Mashhad-Iran). His research interests are the stress analysis of pressure vessels and the structural analyses of plates and shells made of hightech materials.

Hamid EkhteraeiToussi is an Associate Professor of Mechanical Engineering at Faculty of Engineering, Ferdowsi University of Mashhad (Mashhad-Iran). His main interests are the plasticity and fracture of materials. He started his career as a lecturer in 1993. After completing his Ph.D. in Mechanical Engineering at Sharif University of Technology (Tehran-Iran) he returned to work in 2003. The lists of his supervised graduate/undergraduate dissertations as well as my research papers are available at the following webpage: http://ekhteraee.profcms.um.ac.ir/index.php/.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bayat, Y., EkhteraeiToussi, H. General thermo-elastic solution of radially heterogeneous, spherically isotropic rotating sphere. J Mech Sci Technol 29, 2427–2438 (2015). https://doi.org/10.1007/s12206-015-0537-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-015-0537-8

Keywords

Search

Navigation