A finite element method for analysing skin effect in conductors with unknown values of surface boundary conditions

✍ Scribed by A. K. Gasiorski

• Publisher: John Wiley and Sons
• Year: 1985
• Tongue: English
• Weight: 840 KB
• Volume: 21
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620210907

✦ Synopsis

This paper presents a method of analysing the distribution of a two-dimensional electromagnetic field in a conducting medium of known cross-section carrying sinusoidal current and of unknown numerical values of boundary conditions on conductors surfaces. The method combines the finite element and separation of variables methods. An example is given of application of the method to calculation of impedance and electrodynamic forces of two thick, full and round conductors carrying oppositely directed sinusoidal currents. On the basis of numerical computation, graphs of resistance, reactance and electrodynamic forces are plotted.

1. TNTRODUCTION

Conducting elements carrying electric currents are characterized by the basic parameters of impedance and electrodynamic forces acting upon them. The parameters were calculated either by classical methods (e.g. the separation of variables method,49s the conformal transformation method24) or by other methods, e.g. the substitute rod m e t h ~d . ~

In those references the boundary conditions were known. However, in papers analysing fields of the unknown numerical values of boundary conditions on the conductor surfaces, three kinds of procedures have been applied. Two of them are connected with the variational approach and the finite element method.

The first procedure consists in surrounding the considered region with another, sufficiently wide, region. Both regions are then divided into finite elements. At the external boundary of the limiting region, the conditions valid for infinity are assumed; i.e. the disappearance of the field is assumed. Such a procedure is widely used. The authors of Reference 22 considered a conductor described by Laplace's equation with Dirichlet's boundary condition where, as in Reference 20 Laplace's and Poisson's equations were applied in order to describe the electrostatic and thermal fields. In order to obtain an accurate solution, it is necessary to assume the bounding region to be as big as possible. This results in a greater number of elements and consequently in longer and more expensive calculations.

The above drawbacks are eliminated by use of the second procedure, which consists of surrounding the considered region with a surface and applying the finite element method in the region between them. The solution is approximated on the surrounding surface by using either Green's function or an approximate analytical solution for the external region. This approach is frequently referred to as the boundary condition procedure and is often encountered in the literature on the subject.