Topology optimization for three-dimensional design of segmented permanent magnet arrays

Jaejoon Lee, Jaewook Lee, Taehoon Jung, Jeonghoon Yoo

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


This paper proposes a topology optimization formulation for the three-dimensional (3-D) design of segmented permanent magnet (PM) arrays. Specifically, the proposed formulation aims to find an optimal 3-D structural topology of PM segments and their discrete magnetization directions. To achieve this, a design variable is defined in the vector form of a Cartesian coordinate system. The magnitude of the design variable vector determines a PM density, and the directional cosines of the vector determine PM magnetization directions. To acquire a segmented PM design with discrete magnetization directions, a PM strength penalization scheme is proposed. In this scheme, a PM strength is controlled using a minimum distance function between a magnetization direction and target discrete directions. Here, the minimum distance function is approximated using the p-norm for sensitivity calculation. To validate the effectiveness of the proposed formulation, three design examples are provided. In the first example, a two-dimensional (2-D) dipole Halbach cylinder is designed to confirm that the proposed formulation can be applied for a 2-D design problem. The second example aims to design 3-D dipole PM arrays with a cuboid cavity. In the third example, a 3-D PM arrays are designed for maximizing the magnetic force acting on a soft ferromagnetic material.

Original languageEnglish
Pages (from-to)3089-3104
Number of pages16
JournalStructural and Multidisciplinary Optimization
Issue number6
Publication statusPublished - 2020 Dec

Bibliographical note

Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) (NRF-2019R1A2C1002808), and GIST Research Institute(GRI) grant funded by the GIST in 2020.

Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


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