Topology optimisation using nonlinear behaviour of ferromagnetic materials

Abstract

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.

Citation

Mohamodhosen, B.B.S., Gillon, F., Tounzi, M. and Chevallier, L. (2018), "Topology optimisation using nonlinear behaviour of ferromagnetic materials", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 37 No. 6, pp. 2211-2223. https://doi.org/10.1108/COMPEL-12-2017-0522