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The purpose of this study is to explore the effect of the demagnetizing field in the Epstein characterization of grain-oriented electrical steels through a finite element method (FEM) simulations.

A 3D finite element simulation has been realized to represent the parallel and X-stacking configurations in the Epstein frame. The numerical results have been compared with experimental measures.

In a parallel configuration, the measured induction is actually the one in the material, whereas the resulting magnetic field differs from the applied one (in magnitude and angle) due to the shape anisotropy (demagnetizing field). In X-stacking configuration, the resulting magnetic field is close to the applied magnetic field (and then the supposed excitation field in the Epstein frame), whereas the magnetic induction has deviated from the axis of the strips.

Both stacking configurations (parallel and cross) of the Epstein frame are analyzed by three-dimensional finite element simulation.

The purpose of this paper is to propose a methodology to seek the optimal topology of electromagnetic devices using the density method while taking into account the non-linear behaviour of ferromagnetic materials. The tools and methods used are detailed and applied to a three-dimensional (3D) electromagnet for analysis and validation. Resulting topologies with and without the non-linear behaviour are investigated.

The polynomial mapping is used with the density method for material distribution in the optimisation domain. To consider the non-linear behaviour of the materials, an analytical approximation based on the Marrocco equation is used and combined with the polynomial mapping to solve the problem. Furthermore, to prevent the occurrence of intermediate materials, a weighted sum of objectives is used in the optimisation problem to eliminate these undesired materials.

Taking into account the non-linear materials behaviour and 3D model during topology optimisation (TO) is important, as it produces more physically feasible and coherent results. Moreover, the use of a weighted sum of objectives to eliminate intermediate materials increases the number of evaluations to reach the final solution, but it is efficient.

Considering non-linear materials behaviour yields results closer to reality, and physical feasibility of structures is more obvious in absence of intermediate materials.

This work tackles an obstacle of TO in electromagnetism which is often overlooked in literature, that is, non-linear behaviour of ferromagnetic materials by proposing a methodology.