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The purpose of this paper is to present a new approach to optimizing the design of 3D magnetic circuits. This approach is based on topology optimization, where derivative calculations are performed using the continuous adjoint method. Thus, the continuous adjoint method for magnetostatics has to be developed in 3D and has to be combined with penalization, filtering and homotopy approaches to provide an efficient optimization code.

To provide this new topology optimization code, this study starts from 2D magnetostatic results to perform the sensitivity analysis, and this approach is extended to 3D. From this sensitivity analysis, the continuous adjoint method is derived to compute the gradient of an objective function of a 3D topological optimization design problem. From this result, this design problem is discretized and can then be solved by finite element software. Thus, by adding the solid isotropic material with penalization (SIMP) penalization approach and developing a homotopy-based optimization algorithm, an interesting means for designing 3D magnetic circuits is provided.

In this paper, the 3D continuous adjoint method for magnetostatic problems involving an objective least-squares function is presented. Based on 2D results, new theoretical results for developing sensitivity analysis in 3D taking into account different parameters including the ferromagnetic material, the current density and the magnetization are provided. Then, by discretizing, filtering and penalizing using SIMP approaches, a topology optimization code has been derived to address only the ferromagnetic material parameters. Based on this efficient gradient computation method, a homotopy-based optimization algorithm for solving large-scale 3D design problems is developed.

In this paper, an approach based on topology optimization to solve 3D magnetostatic design problems when an objective least-squares function is involved is proposed. This approach is based on the continuous adjoint method derived for 3D magnetostatic design problems. The effectiveness of this topology optimization code is demonstrated by solving the design of a 3D magnetic circuit with up to 100,000 design variables.

Magnetic hysteresis holds significant technical and physical importance in the design of electromagnetic components. Despite extensive research in this area, modeling magnetic hysteresis remains a challenging task that is yet to be fully resolved. The purpose of this paper is to study vector hysteresis play models for anisotropic ferromagnetic materials in a physical, thermodynamical approach.

In this work, hysteresis play models are implemented to interpret magnetic properties, drawing upon classical rate-independent plasticity principles derived from continuum mechanics theory. By conducting qualitative and quantitative verification and validation, various aspects of ferromagnetic vector hysteresis were thoroughly examined. By directly incorporating the hysteresis play models into the primal formulations using fixed point method, the proposed model is validated with measurements in a finite element (FE) environments.

The proposed vector hysteresis play model is verified with fundamental properties of hysteresis effects. Numerical analysis is performed in an FE environment. Measured data from a rotational single sheet tester (RSST) are validated to the simulated results.

The results of this work demonstrates that the essential properties of the hysteresis effects by electrical steel sheets can be represented by the proposed vector hysteresis play models. By incorporation of hysteresis play models into the weak formulations of the magnetostatic problem in the h-based magnetic scalar potential form, magnetic properties of electrical steel sheets can be locally analyzed and represented.

This paper aims to apply the non-linear impedance boundary condition (IBC) for a linear piecewise B–H curve in frequency domain simulations to find the equivalent impedance of a simple induction heating system model.

An electromagnetic description of the inductor system is performed to substitute the effects of the induction load, for a mathematical condition, the so-called IBC. This is suitable to be used in electromagnetic systems involving high conductive materials at medium frequencies, as it occurs in an induction heating system.

A reduction of the computational cost of electromagnetic simulation through the application of the IBC. The model based on linear piecewise B–H curve simplifies the electromagnetic description, and it can facilitate the identification of the induction load characteristics from experimental measurements.

This work is performed to assess the feasibility of using the non-linear boundary impedance condition of materials with linear piecewise B–H curve to simulate in the frequency domain with a reduced computational cost compared to time domain simulations.

In this paper, the use of the non-linear boundary impedance condition to describe materials with B–H curve by segments, which can approximate any dependence without hysteresis, has been studied. The results are compared with computationally more expensive time domain simulations.