Finite elements solutions to magnetostriction. - I. Harmonic modelling

This work deals principally with linear finite element (FEM) modelling of highly magnetostrictive materials. This is accomplished by coupling the Maxwell's equations to the wave equation by using the linearised tensor equations governing magnetostriction. The model in this paper deals with harmonic oscillations and the resulting FE-model is verified against simplified analytical solutions and differences in results are discussed. The magnetic part of the model is based on the reduced scalar potential. This way only a part of the solutions are dependent on the FE-solutions, giving a model which is less sensitive to the placing of the far-field boundary. Further in this work, no interface condition between abruptly changing permeabilities has been performed since the relative permeability of the medium examined is about five and the so-called near cancellation errors, which some workers in the field accuse to be due to the reduced scalar potential occur in regions of a high relative permeability.