Level set-based topology optimization using an immersed boundary element method

Shintaro Yamasaki*, Takayuki Yamada, Toshiro Matsumoto

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this presentation, we propose a new immersed boundary element method (BEM) targeting level set-based topology optimization and construct a concrete topology optimization method using the immersed BEM. The key idea of the immersed BEM is replacing the nodal coordinates of the boundary element mesh with the nodal level set function values and the nodal coordinates of the Eulerian mesh maintaining the level set function. By this replacement, the boundary element mesh seems to be immersed in the Eulerian mesh. The relationship between the nodal coordinates of the boundary element mesh and the nodal level set function of the Eulerian mesh is clearly given in the immersed BEM, therefore, we can strictly derive the sensitivities of the nodal coordinates of the boundary element mesh with respect to the nodal level set function of the Eulerian mesh. That is, we can strictly derive the sensitivities of the objective function with respect to the nodal level set function, by using the immersed BEM. In the constructed topology optimization method, optimization is therefore performed using the strictly derived sensitivities while completely eliminating grayscale elements. The usefulness of the immersed BEM and the constructed topology optimization method is confirmed using a numerical example.

Original languageEnglish
Title of host publicationECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
Pages5182-5194
Number of pages13
Publication statusPublished - 2012
Externally publishedYes
Event6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 - Vienna, Austria
Duration: 2012 Sep 102012 Sep 14

Publication series

NameECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

Conference

Conference6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012
Country/TerritoryAustria
CityVienna
Period12/9/1012/9/14

Keywords

  • Boundary element method
  • Level set method
  • Topology optimization

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics

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