In this paper, we describe the quasi-static problem of magnetoelastic in solid deformed media caused by the eulerian and lagrangian coodinate and we discuss the electro-magnetic effect of the magneto-elasticity of conducting media.

According to the basic hypothesis of magneto-elasticity and Maxwell field equation, the expressions of electromagnetic force and torque in this equation are given.

This paper presents the research scopes, developing history, basic equations, theoretical studies and the applications of magnetoelasticity and thermal-magnetoelasticity.

Based on the magnetic-elasticity nonlinear kinetic equations,physical equations,electrical kinetic equations and the expression of Lorentz forces,the magnetic-elasticity kinetic buckling equation of a current-carrying plate applied mechanical load in a magnet field were derived.

The magnetic-elasticity stability problem of a current plate clamped at each edge,which is under the action of mechanical load in magnetic field,was studied by using the stability of Mathieu equation s solution in this paper.

The magnetic-elasticity kinetic stability problem of a current carrying plate under the action of mechanical load in a magnet field is studied by using the Mathieu equation.

The problemof buckling of a ferromagnetic elastic plate is investigated in a uniform magnetic field within theframework of linear magnetoelasticity.