Study on magneto–elastic–plastic deformation characteristics of ferromagnetic rectangular plate with simple supports

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.