Acta Mechanica Solida Sinica

, Volume 20, Issue 2, pp 180–188 | Cite as

Analysis on the magneto-elastic-plastic buckling/snapping of cantilever rectangular ferromagnetic plates

  • Yuanwen Gao


An analysis of buckling/snapping and bending behaviors of magneto-elastic-plastic interaction and coupling for cantilever rectangular soft ferromagnetic plates is presented. Based on the expression of magnetic force from the variational principle of ferromagnetic plates, the buckling and bending theory of thin plates, the Mises yield criterion and the increment theory for plastic deformation, we establish a numerical code to quantitatively simulate the behaviors of the nonlinearly multi-fields coupling problems by the finite element method. Along with the phenomena of buckling/snapping and bending, or the characteristic curve of deflection versus magnitude of applied magnetic fields being numerically displayed, the critical loads of buckling/snapping, and the influences of plastic deformation and the width of plate on these critical loads, the plastic regions expanding with the magnitude of applied magnetic field, as well as the evolvement of deflection configuration of the plate are numerically obtained in a case study.

Key words

buckling/snapping and bending cantilever rectangular ferromagnetic plate plastic yield 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Moon F.C. and Pao P.H., Magnetoelastic buckling of a thin plate. ASME J. Appl. Mech., 1968, 35: 53–58.CrossRefGoogle Scholar
  2. [2]
    Pao Y.H. and Yeh C.S., A linear theory for soft ferromagnetic elastic bodies. Int. J. Eng. Sci., 1973, 11: 415–436.CrossRefGoogle Scholar
  3. [3]
    Eringen A.C., Theory of electromagnetic elastic plates. Int. J. Engng. Sci., 1989, 27: 363–375.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Miya K., Hara K. and Someya K., Experimental and theoretical study on magneto-elastic buckling of a ferromagnetic beam-plate. ASME J. Appl. Mech., 1978, 45: 355–360.CrossRefGoogle Scholar
  5. [5]
    Miya K., Tagaki T. and Ando Y., Finite-element analysis of magnetoelastic buckling of Ferromagnetic beam-plate. ASME J. Appl. Mech., 1980, 47: 377–382.CrossRefGoogle Scholar
  6. [6]
    Tagaki T., Tani J., Matsubara Y.M. and Mogi T., Dynamic behavior field of fusion structural components under strong magnetic fields. Fusion Eng. Des., 1995, 27: 481–489.CrossRefGoogle Scholar
  7. [7]
    Zhou Y.H., Zheng X.J. and Miya K., Magnetoelastic bending and snapping of ferromagnetic plates in oblique magnetic fields. Fusion Eng. and Des., 1995, 30: 325–337.CrossRefGoogle Scholar
  8. [8]
    Zhou Y.H. and Zheng X.J., A general expression of magnetic force for soft ferromagnetic plates in complex magnetic fields. Int. J. Eng. Sci., 1997, 35: 1405–1417.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Zhou Y.H. and Zheng X.J., A generalized variational principle and theoretical model for magnetoelastic interaction of ferromagnetic bodies. Science in China (serial A), 1999, 42: 618–626.CrossRefGoogle Scholar
  10. [10]
    Zhou Y.H. and Miya K., A theoretical prediction of natural frequency of Ferromagnetic beam plate with low susceptibility in an in-plane magnetic field. ASME J. Appl. Mech., 1998, 65: 121–126.CrossRefGoogle Scholar
  11. [11]
    Zheng X.J. and Liu X.E., Analysis on dynamic characteristics for ferromagnetic conducting plates in a transverse uniform magnetic field. Acta Mechanica Solida Sinica, 2000, 21: 243–250 (in Chinese).Google Scholar
  12. [12]
    Zheng X.J. and Wang X., Analysis of magnetoelastic interaction of rectangular plates with nonlinear magnetization. Int. J. of Solids and Struct., 2001, 38: 8641–8652.CrossRefGoogle Scholar
  13. [13]
    Zheng X.J, Wang X., Large-deflection deformation of ferromagnetic plates in magnetic fields. J. Enging. Mech., 2003, 129: 245–248.CrossRefGoogle Scholar
  14. [14]
    Horiguchi K., Shindo Y., Experimental and theoretical results for bending of ferromagnetic plate in a transverse magnetic field. Acta Mechanica, 2003, 162: 185–194.CrossRefGoogle Scholar
  15. [15]
    Wu G.Y., The analysis of dynamic instability and vibration motions of a pinned beam with transverse magnetic fields and thermal loads. J. of Sound and Vibration, 2005, 284: 343–360.CrossRefGoogle Scholar
  16. [16]
    Littlefield D.L., Magnetomechanical instability in elastic-plastic cylinders — Part II: plastic response. ASME J. Appl. Mech., 1996, 63: 742–749.CrossRefGoogle Scholar
  17. [17]
    Zhou Y.H., Gao Y.W., Zheng X.J., Buckling and post-buckling analysis for magneto-elastic-plastic ferromagnetic beam-plates with unmovable simple supports. Int. J. Solids and struc., 2003, 40: 2875–2887.CrossRefGoogle Scholar
  18. [18]
    Zhou Y.H., Gao Y.W., Zheng X.J., Perturbation analysis for magneto-plastic instability of ferromagnetic beam-plate with geometric imperfection. Acta Mechanica Solida Sinica, 2004, 17: 297–306.Google Scholar
  19. [19]
    Gao Y.W., Zhou Y.H., Zheng X.J., Magneto-elastic-plastic dynamic characteristic analysis of ferromagnetic beam-plate under the pulse magnetic field. Key Engineering Materials, 2004, 274–276: 1131–1136.CrossRefGoogle Scholar
  20. [20]
    Gao Y.W., Zhou Y.H., Perturbation analyses for magneto-elastic bending of flat ferromagnetic beam-plate under an oblique magnetic fields. Acta Mechanica Solida Sinica, 2006, 27: 283–287 (in Chinese).Google Scholar
  21. [21]
    Zhou Y.H., Gao Y., Zheng X.J., and Jiang Q., Buckling and post-buckling of a ferromagnetic beam-plate induced by magnetoelastic interaction. Int. J. Non-Linear Mech., 2000, 35: 1059–1065.CrossRefGoogle Scholar
  22. [22]
    Xu Z.L., Mechanics of Elasticity: Part II (3rd Edition). Beijing: Publishing House of High Education, 1990 (in Chinese).Google Scholar
  23. [23]
    Kachanov L.M., Foundations of the Theory of Plasticity. London: North-Holland Publications, 1971.zbMATHGoogle Scholar
  24. [24]
    Owen D.R.J. and Hinton E., The Finite Element in Plasticity — Theories and Practice. Swansea: Pineridge Press Limited, 1980.zbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2007

Authors and Affiliations

  • Yuanwen Gao
    • 1
  1. 1.Key Laboratory of Mechanics on Western Disaster and Environment, College of Civil Engineering and MechanicsLanzhou UniversityLanzhouChina

Personalised recommendations