Thin layers in electrical engineering-example of shell models in analysing eddy-currents by boundary and finite element methods

Krähenbühl, Laurent; Müller, Dieter

doi:10.1109/20.250676

Cited by 129 publications

(59 citation statements)

References 4 publications

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“…It represents the ratio of the electric and magnetic field on the surface of the conducting material. In the case of this thin layer with symmetrical fields this boundary impedance is given to [6], [7], [8]…”

Section: B Impedance Boundary Conditionmentioning

confidence: 99%

Calculation of the transient temperature distribution in a TFIH device using the impedance boundary condition

Maï

Henneberger²

1998

IEEE Trans. Magn.

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This paper presents a method of alternately switched coils in transverse flux inductive heating devices (TFIH) and their finite element formulation in order to improve temperature distribution. In the present paper the application of the boundary impedance method in eddy-current computation in thin conducting sheets is combined with the transient calculation of the resulting temperature distribution. In this non-linear coupled electromagnetothermal problem the ?,a formulation is used to calculate the time-harmonic electromagnetic field. The Fourier's thermal conduction equation is extended by terms for conduction, convection and radiation. In addition a quasi steady state formulation for high switching frequencies is introduced.

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Section: B Impedance Boundary Conditionmentioning

confidence: 99%

Calculation of the transient temperature distribution in a TFIH device using the impedance boundary condition

Maï

Henneberger²

1998

IEEE Trans. Magn.

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“…The first difficulty is conveniently faced by the so-called thin-shell approach, which removes the three-dimensional screen by introducing suitable interface conditions between its surfaces [1,2]. The advantages of this technique have been extensively proved in several papers, evidencing its reliability in predicting the shielding efficiency of open and closed shields [3,4].…”

Section: Introductionmentioning

confidence: 99%

A multiscale approach to the analysis of magnetic grid shields and its validation

Bottauscio¹,

Chiampi²,

Manzin³

et al. 2007

Journal of Computational Physics

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“…The simplest approaches assume no variation in thickness direction, which leads to a surface quantity [5,22]. Using two functions in thickness direction Krähenbühl and Muller [18] derived a relation between the mean value of the tangential component of the electric or magnetic field on the interfaces of the sheet and the jump of the magnetic or electric field between the interfaces. This approach for time-harmonic Maxwell's equations is adopted by various authors [13,17,20] and is known as impedance boundary condition for thin layers.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic modelling of conductive thin sheets

Schmidt

Tordeux

2009

Z. Angew. Math. Phys.

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We derive and analyse models which reduce conducting sheets of a small thickness ε in two dimensions to an interface and approximate their shielding behaviour by conditions on this interface. For this we consider a model problem with a conductivity scaled reciprocal to the thickness ε, which leads to a nontrivial limit solution for ε → 0. The functions of the expansion are defined hierarchically, i.e. order by order. Our analysis shows that for smooth sheets the models are well defined for any order and have optimal convergence meaning that the H 1 -modelling error for an expansion with N terms is bounded by O(ε N +1 ) in the exterior of the sheet and by O(ε N +1/2 ) in its interior. We explicitly specify the models of order zero, one and two. Numerical experiments for sheets with varying curvature validate the theoretical results. Mathematics Subject Classification IntroductionMany electric devices contain very thin conducting parts either for electromagnetic shielding [13,16], or as casings, tank walls [9,25] or supply lines [5]. The large aspect ratio of these sheets of about few millimetres or centimetres to metres or hundreds of micrometres to centimetres and the high conductivity causes variations in thickness direction in much smaller scales than in the longitudinal directions. Their discretisation by the finite element method (FEM) is challenging when the thickness ε of the thin sheets is considerably smaller than the size of neighbouring parts for three reasons. First, domains with such thin sheets are difficult to mesh by most mesh generators. Secondly, a discretisation on meshes with cell sizes of different magnitudes can lead to ill-conditioned matrices, and thirdly, meshes of good quality may also contain cells around the sheet with sizes comparable to the sheet thickness which leads to a high number of additional degrees of freedom. By reducing the thin sheet to an interface and by approximating its effect by conditions on this interface, a highly accurate modelling with standard discretisation schemes like the FEM is possible.The so called impedance boundary conditions (IBCs), first proposed by Shchukin [29] and Leontovich [19], are traditionally used for replacing solid conductors, where the domain is artificially confined, by an approximate boundary condition [1][2][3]8,11,15,28]. This technique is proved to be accurate for smooth sheets and can be readily implemented.However, in the context of thin conducting sheets this technique of Shchukin and Leontovich has been seldom applied. Interface conditions for thin sheets are often based on a tensor product ansatz of a set of simple functions in thickness direction and functions defined on the interface. The simplest approaches assume no variation in thickness direction, which leads to a surface quantity [5,22]. Using two functions in thickness direction Krähenbühl and Muller [18] derived a relation between the mean value of the tangential component of the electric or magnetic field on the interfaces of the sheet and the jump of the magnetic or elec...

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Thin layers in electrical engineering-example of shell models in analysing eddy-currents by boundary and finite element methods

Cited by 129 publications

References 4 publications

Calculation of the transient temperature distribution in a TFIH device using the impedance boundary condition

Calculation of the transient temperature distribution in a TFIH device using the impedance boundary condition

A multiscale approach to the analysis of magnetic grid shields and its validation

Asymptotic modelling of conductive thin sheets

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