Two dual formulations are proposed for the calculation of the electromagnetic forces in permanent magnets. The formulations are based on the virtual work principle with the use of nodal elements. Both methods allow the calculation of global force as well as local force densities. These densities depend on the expression of the magnetic energy or co-energy of the magnet. The energies of a permanent magnet are discussed on a physical basis.
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Medeiros et al. (1998) studied this question.
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