Finite deformation of a pressurized magnetoelastic membrane in a stationary dipole field

A nonlinear boundary-value problem for the equilibrium of a pressurized magnetoelastic membrane acted upon by an applied magnetic field is derived from three-dimensional magnetoelasticity. The model is specified entirely by differential equations in the limit of weak material magnetization, these replacing the integro-differential equations of the general theory. The model is further specialized to axisymmetry, and several problems of technical interest are solved numerically.