Open boundary finite element solution of eddy current shielding problems

The thesis describes (i) newly developed finite element open boundary techniques and (ii) the application of these techniques to the study of eddy current shielding. Together they represent the original contributions of this thesis.;The developed open boundary techniques for two- and three-dimensional (2D and 3D) eddy current problems subject to external field excitations are: (i) Hybrid finite element-Green's function method for 2D and 3D problems; (ii) 2D finite element method with scalar asymptotic boundary conditions (ABC) for circular and rectangular boundaries; (iii) 3D finite element method with vector ABC-s for brick-shaped boundaries.;The above techniques are validated by comparison with analytic solutions and published numerical results; Results are also verified by laboratory measurement of test models. They are then used for the study of eddy current shielding of structural steel beams in arc furnace installations. The objective of eddy current shielding is to reduce power losses in structural beams due to eddy currents induced by electrodes and bus bars nearby.;Due to memory requirements of the hybrid techniques, they are less effective for large engineering eddy current problems in comparison with finite element methods incorporating ABC-s. In fact, the limitations of the hybrid methods prompted the development of ABC-s. However, even ABC-s for circular boundaries are not efficient for engineering eddy current shielding problems due to high aspect ratios of the structural beams. Consequently, the scalar ABC-s are extended to rectangular outer boundaries. Such an extension makes it possible to perform finite element analysis of eddy current shielding of structural I-beams. In the 3D vector finite element formulation, the vector ABC-s are derived for brick-shaped outer boundaries. Such outer boundaries are also superior to conventional spherical boundaries for problems with non-spherical surfaces.