Skip to main content
SpringerLink
Log in

Magnetothermoelastic stress and perturbation of magnetic field vector in a functionally graded hollow sphere

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

In this article, a closed-form solution for one-dimensional magnetothermoelastic problem in a functionally graded material (FGM) hollow sphere placed in uniform magnetic and temperature fields subjected to an internal pressure is obtained using the infinitesimal theory of magnetothermoelasticity. Hyper-geometric functions are employed to solve the governing equation. The material properties through the graded direction are assumed to be nonlinear with an exponential distribution. The nonhomogeneity of the material in the radial direction is assumed to be exponential. The temperature, displacement and stress fields and the perturbation of magnetic field vector are determined and compared with those of the homogeneous case. Hence, the effect of inhomogeneity on the stresses and the perturbation of magnetic field vector distribution are demonstrated. The results of this study are applicable for designing optimum FGM hollow spheres.

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

Abbreviations

a:

Inner radius of sphere

b:

Outer radius of sphere

u :

Radial displacement (m)

\({\vec {U}}\) :

Displacement vector

λ, G :

Lame’ constants (N/m2)

α :

Thermal expansion coefficient (1/ °C)

α 0 :

Nominal thermal expansion coefficient (1/ °C)

K :

Thermal conductivity (W/mK)

K 0 :

Nominal thermal conductivity (W/mK)

σ r , σ θ :

Stress components (N/m2)

T :

Temperature (°C)

r :

Radial coordinate (m)

\({\vec {H}}\) :

Magnetic intensity vector

\({\vec {H}}\) :

Perturbation of magnetic field vector

\({\vec {J}}\) :

Electric current density vector

\({\vec {e}}\) :

Perturbation of electric field vector

μ :

Magnetic permeability (H/m)

μ 0 :

Nominal magnetic permeability (H/m)

\({f_\varphi }\) :

Lorentz’s force per unit volume (N/m3)

E :

Young’s Modulus

E 0 :

Nominal Young’s Modulus

ν :

Poisson’s ratio

References

  1. Lutz M.P., Zimmerman R.W.: Thermal stresses and effective thermal expansion coefficient of a functionally graded sphere. J. Therm. Stress 19, 39–54 (1996)

    Article  MathSciNet  Google Scholar 

  2. Zimmerman R.W., Lutz M.P.: Thermal stresses and effective thermal expansion in a uniformly heated functionally graded cylinder. J. Therm. Stress 22, 177–188 (1999)

    Article  Google Scholar 

  3. You L.H., Zhang J.J., You X.Y.: Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials. Int. J. Press. Vessel. Pip. 82, 347–354 (2005)

    Article  Google Scholar 

  4. Obata Y., Noda N.: Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material. J. Therm. Stress 17, 471–487 (1994)

    Article  Google Scholar 

  5. Eslami M.R., Babaei M.H., Poultangari R.: Thermal and mechanical stresses in a functionally graded thick sphere. Int. J. Press. Vessel. Pip. 82, 522–527 (2005)

    Article  Google Scholar 

  6. Nayebi A., El Abdi R.: Cyclic plastic and creep behaviour of pressure vessels under thermomechanical loading. Comput. Mater. Sci. 25, 285–296 (2002)

    Article  Google Scholar 

  7. Dai H.L., Fu Y.M., Dong Z.M.: Exact solution for functionally graded pressure vessels in a uniform magnetic field. Int. J. Solids Struct. 43, 5570–5580 (2006)

    Article  MATH  Google Scholar 

  8. Dai H.L., Fu Y.M.: Magnetothermoelastic interaction in hollow structures of functionally graded material subjected to mechanical loads. Int. J. Press. Vessel. Pip. 84, 132–138 (2007)

    Article  Google Scholar 

  9. Abd-Alla A.M., Fahmy M.A., El-Shahat T.M.: Magneto-thermo-elastic problem of a rotating nonhomogeneous anisotropic solid cylinder. J. Arch. Appl. Mech. 78(2), 135–148 (2008)

    Article  MATH  Google Scholar 

  10. Ghorbanpour, A., Salari, M., Khademizadeh. H., Arefmanesh, A.: Magnetothermoelastic transient response of a functionally graded thick hollow sphere subjected to magnetic and thermoelastic fields. J. Arch. Appl. Mech. 79, (2008) (online first)

  11. Kraus J.D.: Electromagnetic. McGraw-Hill, New York (1984)

    Google Scholar 

  12. Dai H.L., Wang X.: Dynamic responses of piezoelectric hollow cylinders in an axial magnetic field. Int. J. Solids. Struct 41, 5231–5246 (2004)

    Article  MATH  Google Scholar 

  13. Seaborn J.B.: Hypergeometric Functions and Their Applications. Springer, New York (1991)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, University of Kashan, Kashan, I.R. Iran

    Ghorbanpour Arani Ali & A. Arefmanesh

  2. Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111, Isfahan, I.R. Iran

    M. Salari & H. Khademizadeh

Authors
  1. Ghorbanpour Arani Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Salari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Khademizadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Arefmanesh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ghorbanpour Arani Ali.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ali, G.A., Salari, M., Khademizadeh, H. et al. Magnetothermoelastic stress and perturbation of magnetic field vector in a functionally graded hollow sphere. Arch Appl Mech 80, 189–200 (2010). https://doi.org/10.1007/s00419-009-0312-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-009-0312-3

Keywords

Search

Navigation