Abstract
In this paper, the magnetic–elastic–plastic deformation behavior is studied for a ferromagnetic plate with simple supports. The perturbation formula of magnetic force is first derived based on the perturbation technique, and is then applied to the analysis of deformation characteristics with emphasis laid on the analyses of modes, symmetry of deformation and influences of incident angle of applied magnetic field on the plate deformation. The theoretical analyses offer explanations why the configuration of ferromagnetic rectangular plate with simple supports under an oblique magnetic field is in-wavy type along the x-direction, and why the largest deformation of the ferromagnetic plate occurs at the incident angle of 45° for the magnetic field. A numerical code based on the finite element method is developed to simulate quantitatively behaviors of the nonlinearly coupled multi-field problem. Some characteristic curves are plotted to illustrate the magneto–elastic–plastic deflections, and to reveal how the deflections can be influenced by the incident angle of applied magnetic field. The deformation characteristics obtained from the numerical simulations are found in good agreement with the theoretical analyses.
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References
Moon F.C., Pao Y.H.: Magnetoelastic buckling of a thin plate. ASME J. Appl. Mech. 35, 53–58 (1968)
Pao Y.H., Yeh C.S.: A linear theory for soft ferromagnetic elastic bodies. Int. J. Eng. Sci. 11, 415–436 (1973)
Eringen A.C.: Theory of electromagnetic elastic plates. Int. J. Eng. Sci. 27, 363–375 (1989)
Miya K., Hara K., Someya K.: Experimental and theoretical study on magneto-elastic buckling of a ferromagnetic beam-plate. ASME J. Appl. Mech. 45, 355–360 (1978)
Miya K., Tagaki T., Ando Y.: Finite-element analysis of magnetoelastic buckling of ferromagnetic beam-plate. ASME J. Appl. Mech. 47, 377–382 (1980)
Tagaki T., Tani J., Matsubara Y.M., Mogi T.: Dynamic behavior of fusion structural components under strong magnetic fields. Fusion Eng. Des. 27, 481–489 (1995)
Horiguchi K., Shindo Y.: Experimental and theoretical results for bending of ferromagnetic plate in a transverse magnetic field. Acta Mech. 162, 185–194 (2003)
Wu G.Y.: The analysis of dynamic instability and vibration motions of a pinned beam with transverse magnetic fields and thermal loads. J. Sound Vib. 284, 343–360 (2005)
Fang D.N., Wan Y.P., Soh A.K.: Magnetoelastic fracture of soft ferromagnetic materials. Theor. Appl. Fract. Mech. 42(3), 317–334 (2004)
Zhou Y.H., Zheng X.J.: A general expression of magnetic force for soft ferromagnetic plates in complex magnetic fields. Int. J.~Eng. Sci. 35, 1405–1417 (1997)
Zhou Y.H., Zheng X.J.: A generalized variational principle and theoretical model for magnetoelastic interaction of ferromagnetic bodies. Sci. China (Ser. A) 42, 618–626 (1999)
Zheng X.J., Liu X.E.: A nonlinear constitutive model for Terfenol-D rods. J. Appl. Phys. 97, 053901 (2005)
Zheng X.J., Sun L.: A nonlinear constitutive model of magneto-thermo-mechanical coupling for giant magnetostrictive materials. J. Appl. Phys. 100, 063906 (2006)
Zheng X.J., Gou X.F., Zhou Y.H.: Influence of flux creep on dynamic behavior of the magnetic levitation systems with a high-Tc superconductor. IEEE Appl. Supercond. 15(3), 3856–3863 (2005)
Littlefield D.L.: Magnetomechanical instability in elastic-plastic cylinders, Part II: plastic response. ASME J. Appl. Mech. 63, 742–749 (1996)
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 Struct. 40, 2875–2887 (2003)
Zhou Y.H., Gao Y.W., Zheng X.J.: Perturbation analysis for magneto-plastic instability of ferromagnetic beam-plate with geometric imperfection. Acta Mech. Solida Sin. 17, 297–306 (2004)
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 Eng. Mater. 276, 1131–1136 (2004)
Gao Y.W.: Analyses on the magneto-elastic-plastic buckling/ snapping of cantilever rectangular ferromagnetic plates. Acta Mech. Solida Sin. 20(2), 180–188 (2007)
Xu, Z.L.: Mechanics of Elasticity: Part II, 3rd edn. Publishing House of High Education, Beijing (1990) (in Chinese)
Kachanov L.M.: Foundations of the Theory of Plasticity. North-Holland, London (1971)
Owen D.R.J., Hinton E.: The Finite Element in Plasticity-Theories and Practice. Pineridge Press, Swansea (1980)
Wang X.Z., Zheng X.J.: Analyses on magnetoelastical initial postbuckling ans sensitivity to Imperfection for ferromagnetic beam-plate. Chin. J. Theor. Appl. Mech. 38(1), 34–40 (2006) (in Chinese)
Zhou Y.H., Zheng X.J.: The Electromagnetic Solid Structure Mechanics. Science Press, Beijing (1999) (in Chinese)
Gao Y.W., Zhou Y.H., Zheng X.J.: Analysis of chaotic motions of geometrically nonlinear ferromagnetic beam-plates excited by transverse magnetic fields. Acta Mech. Sin. 34(1), 101–106 (2002) (in Chinese)
Zhou Y.H., 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. 65, 121–126 (1998)
Zheng X.J., Zhou Y.H., Wang X.Z., Lee J.S.: Bending and buckling of ferroelastic plates. J. Eng. Mech. 125(2), 180–185 (1999)
Zhou Y.H., Gao Y.W., Zheng X.J., Jiang Q.: Buckling and post-buckling of a ferromagnetic beam-plate induced by magnetoelastic interaction. Int. J. Nonlinear Mech. 35, 1059–1065 (2000)
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The project supported by the National Natural Science Foundation of China (10672070, 10302009), the National Basic Research Program of China (2007CB607560), the Program for New Century Talented (NCET-06-0896), and the Natural Science Fund of Gansu Province.
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Gao, Y. Study on magneto–elastic–plastic deformation characteristics of ferromagnetic rectangular plate with simple supports. Acta Mech Sin 25, 139–147 (2009). https://doi.org/10.1007/s10409-008-0211-9
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DOI: https://doi.org/10.1007/s10409-008-0211-9