Topology Optimization for Magnetic Circuits Dedicated to Electric Propulsion

Sanogo, Satafa; Messine, Frédéric; Hénaux, Carole; Vilamot, R.

doi:10.1109/tmag.2014.2340374

Cited by 23 publications

(35 citation statements)

References 28 publications

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“…Indeed, the existence and the uniqueness of solution cannot be guaranteed. In general, these design problems could present many local minima (Sanogo et al, 2014;Sanogo and Messine, 2016;Sanogo, 2016). Moreover, for electromagnetic systems, the output responses are very sensitive with respect to small variations of input data.…”

Section: Introductionmentioning

confidence: 99%

“…This includes homogenization theory method (Murat and Tartar, 1985;Allaire, 2002), topological gradient analysis (Sokołowski and _ Zochowski, 2001), level-set method (Allaire, 2007), material density distribution approach (known as SIMP, solid isotropic material with penalization model: solid isotropic material with penalization of intermediate material densities) (Bendsøe and Sigmund, 2003). Here, we focus on the SIMP model, which is one of the most used methods for numerical structural optimization and was adapted to our framework (Sanogo et al, 2014). In structural optimization, typically in optimal design method based on material distribution concept, challenging problems are in general not well-posed, yielding some numerical stabilities and sensitivities (including convergence problems), and the interpretation of the optimal density distribution solution in terms of available/existent materials is difficult to do in some zones of the design domains (it occurs when the computed solution is non discrete, like it is the case in material layout designs).…”

Section: Introductionmentioning

confidence: 99%

“…Using these new MIS functions, an extension of ATOP TO is developed to provide better solution (in term of binary values: void or iron) than its first version. More information on ATOP TO architecture is given in Sanogo et al (2014). Note also that the approach presented in this paper and based on these general forms of MIS can be easily used on other electromagnetic design applications and on many structural optimization problems based on SIMP model: for example, the minimum compliance problem in mechanics Bendsøe and Sigmund (2003).…”

Section: Introductionmentioning

confidence: 99%

“…In Section 2, we review the principle of inverse problem in electromagnetism and present the considered design parameters. We recall also the optimization formulations and the sensitivity analysis about this inverse problem that we previously provided (Sanogo et al, 2014) to solve it with TO-based algorithms. In Section 3, the material density approach with SIMP model is discussed and a generalization of polynomial MIS is proposed for solution method.…”

Section: Introductionmentioning

confidence: 99%

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Topology optimization in electromagnetism using SIMP method

Sanogo¹,

Messine

2018

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Purpose In this work, the authors deal with topology optimization in electromagnetism using solid isotropic material with penalization (SIMP) method associated with a gradient-based algorithm. The purpose of this study is to propose and investigate the impact of new generalized material interpolation scheme (MIS) used in SIMP approaches. Design/methodology/approach The variable domains of this kind of electromagnetism design problem are decomposed into small squares which represent a material point (iron here) or void. A least square function where the magnetic ﬁeld in a target zone has to be as close as possible to a ﬁxed one is minimized. Then the binary optimization problem is relaxed to a continuous one. By using the adjoint variable method, the gradient is provided. By penalizing the objective function using MIS, gradient-based algorithms can then be directly applied to provide eﬃcient solutions close to the binary ones. Findings In this work, new general MISs are proposed. It is shown on numerous numerical instances that the so-obtained design solutions are more precise to define the zones with or without materials. Research limitations/implications Only the linearity of the materials is addressed because the associated adjoint method needs this assumption. However, the new penalization approaches are not dependent directly on this assumption. Originality/value The new MISs are efficiently applied to design of a hall effect thruster (HET) magnetic circuits. Furthermore, these schemes are generic and can then be applied to other topology optimization applications in electromagnetism as well as and in mechanism.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Topology optimization in electromagnetism using SIMP method

Sanogo¹,

Messine

2018

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“…This method has the particularity of generating topologies with unwanted intermediate materials at the end of the optimisation process. Many authors propose their solutions to this problem, such as in and (Sanogo et al, 2014), amongst others. In this paper, a different way of tackling the problem is presented to eliminate these intermediate materials.…”

Section: Introductionmentioning

confidence: 99%

Topology optimisation using nonlinear behaviour of ferromagnetic materials

Mohamodhosen

Gillon

Tounzi

et al. 2018

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Purpose 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. Design/methodology/approach 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. Findings 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. Practical implications Considering non-linear materials behaviour yields results closer to reality, and physical feasibility of structures is more obvious in absence of intermediate materials. Originality/value 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.

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