Finite element implementation of virtual work principle for magnetic or electric force and torque computation

In a recent paper [1], we described a methodology for the numerical evaluation of global magnetic or electric force and torque acting on a movable part of an electromagnetic device. The method is based on application of virtual work principle. Force and torque are obtained as the derivatives of the energy versus the displacement of the moving part. The paper [1] was essentially theoritical. In the present paper, we give more practical informations about the implementation of the method in a finite element context and illustrate it by a 3D application.