An immersed boundary element method for level-set based topology optimization

Shintaro Yamasaki*, Takayuki Yamada, Toshiro Matsumoto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)

Abstract

In this paper, we propose a new BEM for level-set based topology optimization. In the proposed BEM, the nodal coordinates of the boundary element are replaced with the nodal level-set function and the nodal coordinates of the Eulerian mesh that maintains the level-set function. Because this replacement causes the nodal coordinates of the boundary element to disappear, the boundary element mesh appears to be immersed in the Eulerian mesh. Therefore, we call the proposed BEM an immersed BEM. The relationship between the nodal coordinates of the boundary element and the nodal level-set function of the Eulerian mesh is clearly represented, and therefore, the sensitivities with respect to the nodal level-set function are strictly derived in the immersed BEM. Furthermore, the immersed BEM completely eliminates grayscale elements that are known to cause numerical difficulties in topology optimization. By using the immersed BEM, we construct a concrete topology optimization method for solving the minimum compliance problem. We provide some numerical examples and discuss the usefulness of the constructed optimization method on the basis of the obtained results.

Original languageEnglish
Pages (from-to)960-988
Number of pages29
JournalInternational Journal for Numerical Methods in Engineering
Volume93
Issue number9
DOIs
Publication statusPublished - 2013 Mar 2
Externally publishedYes

Keywords

  • Boundary element methods
  • Level sets
  • Topology design

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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