Magnetic Stability of Functionally Graded Soft Ferromagnetic Porous Rectangular Plate

Document Type: Research Paper


Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University


This study presents critical buckling of functionally graded soft ferromagnetic porous (FGFP) rectangular plates, under magnetic field with simply supported boundary condition. Equilibrium and stability equations of a porous rectangular plate in transverse magnetic field are derived. The geometrical nonlinearities are considered in the Love-Kirchhoff hypothesis sense. The formulations are compared to those of homogeneous isotropic plates were given in the literature. In this paper the effect of pore pressure on critical magnetic field of plate and the effect of important parameters of poroelastic material on buckling capacity are investigated. Also the compressibility of fluid and porosity on the buckling strength are studied.


[1] Moon F.C., Pao Y.H., 1968, Magnetoelastic buckling of a thin plate, Journal of Applied Mechanics 35: 53-58.
[2] Zhou Y.H., Zheng X.J, 1997, A general expression of magnetic force for soft ferromagnetic plates 278 in complex magnetic fields, International Journal of Engineering Science 35: 1405-1417.
[3] Wentao Y., Hao P., Dali Z., Qigong C., 1998, Buckling of a ferromagnetic thin plate in a transverse static magnetic field, Central Iron and Steel Research Institute 43(19):1666-1670.
[4] Zhou Y. H., Wang X., Zheng X., 1998, Magnetoelastic bending and stability of ferromagnetic rectangular plates, Applied Mathematics and Mechanics 19(7):669-676.
[5] Zheng X.J., Zhou Y.H., Wang X.Z., Lee J.S., 1999, Bending and buckling of ferroelastic plates, Journal of Engineering Mechanics 125(2):180-185.
[6] Zhou Y. H., Wang X., Zheng X., 2000, Buckling and post-buckling of a ferromagnetic beam-plate induced by magnetoelastic interactions, International Journal of Non-Linear Mechanics 35: 1059-1065.
[7] Zheng X.J., Wang X., 2001, Analysis of magnetoelastic interaction of rectangular ferromagnetic plates with nonlinear magnetization, International Journal of Solids and structures 38: 8641-8652.
[8] Wang X., Zhou Y.H., Zheng X., 2002, A generalized variational model of magneto-thermoelasticity for nonlinearly magnetized ferroelastic bodies, International Journal of Engineering Mechanics 40 (17): 1957-1973.
[9] Wang X., Lee J.S., Zheng X., 2003, Magneto-thermo-elastic instability of ferromagnetic plates in thermal and magnetic fields, Internatiuonal Journal of Solids and Structures 40 (22): 6125-6142.
[10] Zhou Y.H., Gao Y., Zheng X.J., 2003, Buckling and post-buckling analysis for magneto-elastic-plastic ferromagnetic beam-plates with unmovable simple supports, International Journal of Solids and Structures 40(11): 2875-2887.
[11] Zheng X., Wang X., 2003, A magneto elastic theoretical model for soft ferromagnetic shell in magnetic field, International Journal of Solids and Structures 40(24): 6897-6912.
[12] Er-gang X., She-liang W., Qian Z., Yi-jie D., 2006, Buckling of an elastic plate in a uniform magnetic field, Natural Science Edition , Article ID: 1006-7930(2006)04-0533-05.
[13] Wang X., Lee J.S., 2006, Dynamic stability of ferromagnetic plate under transverse magnetic field and in-plane periodic compression, International Journal of Mechanical Sciences 48(8): 889-898.
[14] Dai H.L., Fu Y.M., Dong Z.M., 2006, Exact solutions for functionally graded pressure vessels in a uniform magnetic field, International Journal of Solids and Structures 43: 5570-5580.
[15] Bhangale R.K., Ganesan N., 2006, Static analysis of simply supported functionally graded and layered magneto-electro-elastic plates, International Journal of Solids and Structures 43(10):3230-3253.
[16] Xing-zhe, Wang, 2008, Changes in the natural frequency of a ferromagnetic rod in a magnetic field due to magneto elastic interaction, Applied Mathematics and Mechanics 29(8):1023-1032.
[17] Raikher Yu L., Stolbov O.V., Stepanov G.V., 2008, Deformation of a Circular Ferroelastic Membrane in a Uniform Magnetic Field ,Technical Physics 78(9): 1169-1176.
[18] Kankanala S.V., Triantafyllidis N., 2008, Magnetoelastic buckling of a rectangular block in plane strain, Journal of the Mechanics and Physics of Solids 56(4): 1147-1169.
[19] Jin K., Kou Y., Zheng X., 2010, Magnetoelastic model of magnetizable media, Piers Proceedings, Xi'an, China.
[20] Biot M.A., 1964, Theory of buckling of a porous slab and its thermoelastic analogy, Journal of Applied Mechanics 31: 194-198.
[21] Jabbari M., Mojahedin A., Khorshidvand A.R., Eslami M.R., 2013, Buckling analysis of functionally graded thin circular plate made of saturated porous materials, Journal of Engineering Mechanics 140: 287-295.
[22] Jabbari M., Farzaneh Joubaneh E., Khorshidvand A.R., Eslami M.R., 2013, Buckling analysis of circular porous plate with piezoelectric actuator layers under uniform radial compressionInternational , Journal of Mechanical Sciences 70: 50-56.
[23] Magnucki K., Stasiewicz P., 2004, Elastic buckling of a porous beam, Journal of Theoretical and Applied Mechanics 42: 859-868.
[24] Magnucki K., Malinowski M., Kasprzak J., 2006, Bending and buckling of a rectangular porous plate, Steel & Composite Structures 6: 319-333.
[25] Magnucka-Blandzi E., 2008, Axi-symmetrical deflection and buckling of a circular porous-cellular plate, Thin-walled structures 46: 333-337.
[26] Javaheri R., Eslami M.R., 2002, Buckling of functionally graded plates under in plane compressive loading, ZAMM Journal of Applied Mathematics and Mechanics 82(4): 277-283.
[27] Jabbari M., Hashemitaheri M., Mojahedin A., 2014, Thermal buckling analysis of functionally graded thin circular plate made of saturated porous materials, Journal of Thermal Stresses 37: 202-220.
[28] Jabbari M. , Farzaneh Joubaneh E. , Mojahedin A., 2014, Thermal buckling analysis of a porous circularplate with piezoelectric actuators based on first order shear deformation theory, International Journal of Mechanical Sciences 83: 57-64.
[29] Khorshidvand A. R., Farzaneh Joubaneh E., Jabbari M., 2014, Buckling analysis of a porous circular plate with piezoelectric sensor-actuator layers under uniform radial compression, Acta Mechanica 225: 179-193.
[30] Magnuckia K., Jasion P., Magnucka-Blandzib E. , Wasilewicz P., 2014, Theoretical and experimental study of a sandwich circular plate under pure bending, Thin-Walled Structures 79: 1-7.
[31] Brush D.O., Almorth B.O., 1975, Buckling of Bars, Plates and Shells, McGraw-Hill, New York.