Acta Mechanica Solida Sinica

, Volume 22, Issue 3, pp 189–196 | Cite as

Analyses on nonlinear coupling of magneto-thermo-elasticity of ferromagnetic thin shell—I: Generalized variational theoretical modeling

  • Xingzhe Wang
  • Xiaojing Zheng


Based on the generalized variational principle of magneto-thermo-elasticity of the ferromagnetic elastic medium, a nonlinear coupling theoretical modeling for a ferromagnetic thin shell is developed. All governing equations and boundary conditions for the ferromagnetic shell are obtained from the variational manipulations on the magnetic scalar potential, temperature and the elastic displacement related to the total energy functional. The multi-field couplings and geometrical nonlinearity of the ferromagnetic thin shell are taken into account in the modeling. The general modeling can be further deduced to existing models of the magneto-elasticity and the thermo-elasticity of a ferromagnetic shell and magneto-thermo-elasticity of a ferromagnetic plate, which are coincident with the ones in literature.

Key words

ferromagnetic shell magneto-thermo-elasticity generalized variational principle multi-field coupling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Moon, F.C., Magneto-Solid Mechanics. New York: Jone Wiley and Sons, 1984.Google Scholar
  2. [2]
    Moon, F.C. and Pao, Y.H., Magnetoelastic buckling of a thin plate. ASME Journal of Applied Mechanics, 1968, 35(1): 53–58.CrossRefGoogle Scholar
  3. [3]
    Pao, Y.H. and Yeh, C.S., A linear theory for soft ferromagnetic elastic solids. International Journal of Engineering Sciences, 1973, 11(4): 415–436.CrossRefGoogle Scholar
  4. [4]
    Eringen, A.C., Mechanics of Continua, Second Edition. New York: Krieger, 1980.zbMATHGoogle Scholar
  5. [5]
    Maugin, G.A. and Goudjo, C., The equations of soft-ferromagnetic elastic plates. International Journal of Solids and Structures, 1982, 18(10): 889–912.CrossRefGoogle Scholar
  6. [6]
    van de Ven, A.A.F., A variational principle for magnetoelastic buckling. Journal of Engineering. Mathematics, 1987, 21: 227–252.CrossRefGoogle Scholar
  7. [7]
    Takagi, T., Tani, J., Matsubara, Y. and Mogi, I., Electromagneto-mechanics coupling effects for non-ferromagnetic and ferromagnetic structures. In: Proceeding of 2nd International Workshop on Electromagnetic Forces and Related Effects on Blankets and Other Structures Surrounding Fussion Plasma Torus. Edited Miya, Tokai, Japan, Sept., 1993: 81–90.Google Scholar
  8. [8]
    Misra, J.C., Samanta, S.C. and Chakrabarti, A.K., Magnetic-mechanical interaction in an aeolotropic solid cylinder subjected to a ramp-type heating. International Journal of Engineering Sciences, 1991, 29(9): 1065–1075.CrossRefGoogle Scholar
  9. [9]
    Abd-alla, A.N. and Maugin, G.A., Nonlinear equations for thermoelastic magnetizble conductors. International Journal of Engineering Sciences, 1990, 28(7): 589–603.CrossRefGoogle Scholar
  10. [10]
    Massalas, C.V., A note on magneto-thermo-elastic interactions. International Journal of Engineering Sciences. 1991, 29(10): 1217–1229.CrossRefGoogle Scholar
  11. [11]
    Zhou, Y.H. and Zheng, X.J., A general expression of magnetic force for soft ferromagnetic plates in complex magnetic fields. International Journal of Engineering Sciences, 1997, 35: 1405–1417.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Zhou, Y.H. and Zheng, X.J., A variational principle on magnetoelastic interaction of ferromagnetic thin plates. Acta Mechanica Solids Sinica, 1997, 10(1): 1–10.Google Scholar
  13. [13]
    Zhou, Y.H., and Miya, K., A theoretical prediction of natural frequency of a ferro-magnetic plates with low susceptibility in in-plane magnetic field. ASME Journal of Applied Mechanics, 1998, 65(1): 121–126.CrossRefGoogle Scholar
  14. [14]
    Zhou, Y.H. and Zheng, X.J., A generalized variational principle and theoretical model for magnetoelastic interaction of ferromagnetic bodies. Science in China (Series A), 1999, 42(6): 618–626.CrossRefGoogle Scholar
  15. [15]
    Xiaojing Zheng and Xingzhe Wang, A magnetoelastic theoretical model for soft ferromagnetic shell in magnetic field. International Journal of Solids and Structures, 2003, 40: 6897–6912.CrossRefGoogle Scholar
  16. [16]
    Xingzhe Wang, Jong, S. Lee and Xiaojing Zheng, Magneto-thermo-elastic instability of ferromagnetic plates in thermal and magnetic fields. International Journal of Solids and Structures, 2003, 40: 6125–6142.CrossRefGoogle Scholar
  17. [17]
    Chien, W.C., Variational Methods and the Finite Elements. Beijing: Science Press, 1980 (in Chinese).Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2009

Authors and Affiliations

  1. 1.Key Laboratory of Mechanics on Western Disasters and Environment, Ministry of Education of China, College of Civil Engineering and MechanicsLanzhou UniversityLanzhouChina

Personalised recommendations