The Analysis Of Magneto-Elastic Stress And Deformation In The Thin Current-Carrying Plate

Magneto-elasticity is a special subject, in which we investigate the inter- action between the strain and electromagnetic fields in a solid elastic body. The theory is essentially an extension of linear elasticity and linear electrodynamics of slowly moving media. If a elastic body placed in a strong initial magnetic field is moved by external loading, besides the strain field, there arises an electro- magnetic field. These two fields are coupled and interact with each other. The influence of the electromagnetic field on the strain occurs by means of Lorentz forces appearing in the equations of motion. The Ohm law contains a term descri- bing the increment of density of the electric field developing on the velocity of the material particles moving in the magnetic field.In this paper, based on the nonlinear magneto-elastic kinetic equation and the electrodynamics equation of the thin current-carrying plate, the normal Cauchy form nonlinear differential equations, which includes ten basic unknown functions in all, were obtained by means of variable replacement method. Using the differ- ence method and quasi-linearization method, the nonlinear magneto-elastic equa- tions were reduced to a sequence of quasi-linear differential equations, which can be solved by the method of discrete orthogonalization. Through specific examples, the numerical solution of the stress and deformation in the thin current-carrying strip-plate with different supported conditions were obtained and the relationship between the applied electro-magnetic fields and the stress of the thin current- carrying strip-plate, as well as the deformation of the thin strip-plate, were studied too. Considering the results that the stress and deformation of the thin current- carrying plate are altered with the variation of the applied electric current density and the applied magnetic field, the stress and the deformation of the thin current- carrying plate could be controlled. As a special case, the deflection of the thin current-carrying strip-plate were controlled by changing the applied electric current density.