A level set based topology optimization method using the discretized signed distance function as the design variables

Shintaro Yamasaki*, Tsuyoshi Nomura, Atsushi Kawamoto, Kazuo Sato, Kazuhiro Izui, Shinji Nishiwaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

This paper deals with a new topology optimization method based on the level set method. In the proposed method, the discretized signed distance function, a kind of level set function, is used as the design variables, and these are then updated using their sensitivities. The signed distance characteristic of the design variables are maintained by performing a re-initialization at every update during the iterated optimization procedure. In this paper, a minimum mean compliance problem and a compliant mechanism design problem are formulated based on the level set method. In the formulations of these design problems, a perimeter constraint is imposed to overcome the ill-posedness of the structural optimization problem. The sensitivity analysis for the above structural optimization problems is conducted based on the adjoint variable method. The augmented Lagrangian method is incorporated to deal with multiple constraints. Finally, several numerical examples that include multiple constraints are provided to confirm the validity of the method, and it is shown that appropriate optimal structures are obtained.

Original languageEnglish
Pages (from-to)685-698
Number of pages14
JournalStructural and Multidisciplinary Optimization
Volume41
Issue number5
DOIs
Publication statusPublished - 2010 May
Externally publishedYes

Keywords

  • Augmented Lagrangian method
  • Level set method
  • Perimeter constraint
  • Sensitivity analysis
  • Signed distance function
  • Topology optimization

ASJC Scopus subject areas

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

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