Abstract
We study eddy currents on a thin conductor surface in ℝ3. We suppose that these currents result from a periodic alternative time-varying excitation (such as a difference of potential or imposed currents).
In Section 1, we shall write the current equations by using the variable surface density of the current which is a tangential complex vector to Γ. We prove that these integro-differential equations admit a unique solution.
In Section 2, we introduce an approximate problem built by finite elements, and we prove some error estimates.
In Section 3, we present the numerical results obtained by our method. The studied problem was the case of some big conductors of an electric power station of Electricité de France. Finally, we have computed the resulting forces on the conductors.
Keywords
- Tangent Plane
- Eddy Current
- Current Line
- Approximate Problem
- Electric Power Station
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
DJAOUA, M., Méthodes d'éléments finis pour la résolution d'un problème intérieur dans ℝ3, Rapport Interne du Centre de Mathématiques Appliquées de l'Ecole Polytechnique, no 3, 1976.
LIONS, J.L., MAGENES, E., Problèmes aux limites non homogènes et applications, T.1, Dunod, Paris, 1968.
NEDELEC, J.C., Curved finite element methods for the solution of singular integral equations on surfaces in ℝ3, Comp. Meth. Appl. Mech. Eng., 8 (1976), 61–81.
NEDELEC, J.C., SABRIE, J.L., VERITE, J.C., Calculation of eddy currents in a conductor and its sheath by a finite element method, Proc., Conference on the Computation of Magnetic Fields, Oxford, april 1977.
NEDELEC, J.C., Computation of eddy currents on a surface in ℝ3 by finite element methods, to appear in SIAM J. on Numerical Analysis.
PLANCHARD, J., VERITE, J.C., Calcul des forces d'origine électro-magnétique sur des coques métalliques parcourues par des courants de Foucault — Etude Théorique, Rapport Interne HI 2434/02, E.D.F., mai 1977.
STOLL, R.L., The analysis of eddy currents, Clarendon Press, Oxford, 1974.
STROUD, H.A., Approximate calculation of multiple integrals, Prentice Hall, 1971.
VERITE, J.C., Calcul de la répartition des courants de Foucault dans les gaines coaxiales de sortie des alternateurs. I — Partie théorique — II — Application au cas d'un coude, Rapport Interne HI 2204/02, E.D.F., septembre 1976.
VERITE, J.C., Calcul de la répartition des courants de Foucault dans les gaines coaxiales de sortie des alternateurs. Résultats concernant un coude, Rapport Interne HI 2217/02, E.D.F., septembre 1976.
VERITE, J.C., Calcul de la répartition des courants de Foucault dans les gaines coaxiales de sortie des alternateurs. Résultats concernant un embranchement, Rapport Interne HI 2421/02, E.D.F., avril 1977.
VERITE, J.C., Calcul des forces d'origine électro-magnétique dans les gaines coaxiales de sortie des alternateurs. Résultats concernant un coude et un embranchement, Rapport Interne HI 2453/02, E.D.F., juin 1977.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
Nedelec, J.C., Verite, J.C. (1979). Computation of eddy currents on a surface in ℝ3 by finite element methods. In: Glowinski, R., Lions, J.L., Laboria, I. (eds) Computing Methods in Applied Sciences and Engineering, 1977, I. Lecture Notes in Mathematics, vol 704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063617
Download citation
DOI: https://doi.org/10.1007/BFb0063617
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09123-3
Online ISBN: 978-3-540-35411-6
eBook Packages: Springer Book Archive
