Topology optimization in electromagnetism using SIMP method

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.

Adjoint-based topology optimization to reduce the energy consumption of a Hall effect thruster

“…This method was introduced by Bendsøe et al in Sigmund, 2003, 1999) and it is based on the homogenization theory method. Moreover, a SIMP method is used here, because it owns some efficiency to solve our applications (Sanogo et al, 2014;Sanogo, 2016;Sanogo and Messine, 2016;Sanogo and Messine, 2018).…”

“…Thus, the fact that arctan is a non-convex function is not relevant. However, there are other convex penalization functions that was used and tested in (Bendsøe and Sigmund, 2003;Sanogo et al, 2014;Sanogo, 2016;Sanogo and Messine, 2018;Luk aš and Chalmovianský, 2007). But the numerical tests showed that the choice of a convex penalization function appears to be not necessary.…”

Multi-Material Topology Optimization with Continuous Magnetization Direction for Permanent Magnet Synchronous Reluctance Motors

“…However, it presents some symmetry issues and favors low ρ associated material in the final design. In [31], the authors compared this scheme to other schemes and concluded that the final design was not as good as many other proposed ones. To solve symmetry issues introduced by the classical polynomial interpolation, D. Lukàš introduced a new scheme in [21]:…”

Multi-material topology optimization of a flux switching machine

“…Indeed, gray materials do not necessarily have a proper physical interpretation or may represent, in the best case, a microstructure that is complex to manufacture [8]. A common solution for removing gray materials proposed by the literature involves penalizing the material interpolation, such as the Solid Isotropic Materials with Penalization (SIMP) scheme [8,9]. Yet topology optimization problems are generally ill-posed, and other numerical artifacts can occur, such as checkerboards that need regularization (e.g., numerical filtering [10]).…”