Complementary finite element magnetodynamic formulations with enforced magnetic fluxes

Two complementary 3D finite element formulations, with either the magnetic field or the magnetic vector potential as unknowns, are developed to deal with the modeling of eddy currents in electrical steel laminations. The magnetic flux through the flux gates of the conducting region is imposed via the boundary terms of the weak formulations, in a natural way thanks to the use of edge finite elements. The two formulations are applied to a simple 1D eddy current problem with analytical solution. As a practical 3D application example, a T-joint region of an electrical steel lamination is considered.