Magnetoelastic bending and snapping of ferromagnetic plates in oblique magnetic fields

Ferritic stainless steel has been considered for structural components such as first walls and blankets of fusion power reactors because the material shows low rates of irradiation swelling. Since it is magnetizable, the magnetoelastic interaction between magnetic field and deformation of the structures in a fusion reactor is so strong that their safety is of concern due to the magnetoelastic bending, buckling and magnetic damping, etc. Basic research of the magnetoelastic characteristics of ferromagnetic plate has been paid special attention by researchers. In this paper, the magnetoelastic bending and snapping are studied for a ferromagnetic plate in an oblique magnetic field. The theoretical model is based on the variational principle where the functional is employed as real total energy in the system including external work. The obtained expression of magnetic force on the plate is the same as that derived from the dipole model when the total magnetic field in the ferromagnetic medium is considered. In order to effectively solve the nonlinearly coupled interaction problem between magnetic field and mechanical deformation, a numerical program combining the finite element method for analyzing the magnetic field with the finite difference technique for finding out the bending deformation of the plate is employed to obtain the solution of magnetoelastic bending of a soft ferromagnetic plate. The numerical calculations are carried out for the typical example of a ferromagnetic cantilevered beam-plate in an oblique magnetic field. From the bending curves, that is the tip deflection versus applied magnetic fields, the critical magnetic field for the magnetoelastic snapping is predicted by the Southwell plot. The theoretical predictions show that the critical magnetic field decreases with the increase in incident angle of the oblique magnetic field. By the effect of incident angle on the magnetic buckling, the discrepancy between theoretical and experimental data can be explained well.