Topology optimization in electromagnetism using SIMP method: Issues of material interpolation schemes. Issue 6 (18th October 2018) - Sanogo, Satafa; Messine, Frédéric
Abstract : 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.