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

Shintaro Yamasaki*, Takayuki Yamada, Toshiro Matsumoto

*この研究の対応する著者

研究成果: Article査読

24 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)960-988
ページ数29
ジャーナルInternational Journal for Numerical Methods in Engineering
93
9
DOI
出版ステータスPublished - 2013 3月 2
外部発表はい

ASJC Scopus subject areas

  • 数値解析
  • 工学(全般)
  • 応用数学

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