Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Moon F.C. and Pao P.H., Magnetoelastic buckling of a thin plate. ASME J. Appl. Mech., 1968, 35: 53–58.
Pao Y.H. and Yeh C.S., A linear theory for soft ferromagnetic elastic bodies. Int. J. Eng. Sci., 1973, 11: 415–436.
Eringen A.C., Theory of electromagnetic elastic plates. Int. J. Engng. Sci., 1989, 27: 363–375.
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.
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.
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.
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.
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.
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.
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.
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).
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.
Zheng X.J, Wang X., Large-deflection deformation of ferromagnetic plates in magnetic fields. J. Enging. Mech., 2003, 129: 245–248.
Horiguchi K., Shindo Y., Experimental and theoretical results for bending of ferromagnetic plate in a transverse magnetic field. Acta Mechanica, 2003, 162: 185–194.
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.
Littlefield D.L., Magnetomechanical instability in elastic-plastic cylinders — Part II: plastic response. ASME J. Appl. Mech., 1996, 63: 742–749.
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.
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.
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.
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).
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.
Xu Z.L., Mechanics of Elasticity: Part II (3rd Edition). Beijing: Publishing House of High Education, 1990 (in Chinese).
Kachanov L.M., Foundations of the Theory of Plasticity. London: North-Holland Publications, 1971.
Owen D.R.J. and Hinton E., The Finite Element in Plasticity — Theories and Practice. Swansea: Pineridge Press Limited, 1980.
Author information
Authors and Affiliations
Additional information
Project supported by the National Natural Sciences Fund of China (Nos.10302009 and 10672070), the Natural Sciences Fund of Gansu Province (3ZS051-A25-012) and the Excellent Doctors’ Fund of Lanzhou University.
Rights and permissions
About this article
Cite this article
Gao, Y. Analysis on the magneto-elastic-plastic buckling/snapping of cantilever rectangular ferromagnetic plates. Acta Mech. Solida Sin. 20, 180–188 (2007). https://doi.org/10.1007/s10338-007-0721-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10338-007-0721-1