A level set based topology optimization method using the augmented lagrangian method

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper deals with a new topology optimization method based on the level set method that incorporates the augmented Lagrangian method. In previously proposed level set based structural optimization methods, dealing with multiple constraints has been problematic yet this is typically required for real-world design problems. Incorporating the augmented Lagrangian method in the structural optimization method proposed here enables the handling of multiple constraints. The level set function is discretized using finite elements and updated based on the design sensitivity of the augmented Lagrangian with respect to the discretized level set function. In this paper, the newly proposed structural optimization method is applied to the minimum compliance problem and a compliant mechanism design problem. In the formulations of these problems, a perimeter constraint is imposed to overcome the ill-posedness of the level set method-based structural optimization. Some numerical examples that include multiple constraints are provided to confirm the validity of the method, and we show that appropriate optimal structures are obtained.

Original languageEnglish
Pages (from-to)3192-3200
Number of pages9
JournalNihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
Issue number760
Publication statusPublished - 2009 Dec
Externally publishedYes


  • Finite element method
  • Optimum design
  • Sensitivity analysis
  • Structural analysis
  • Structural design

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering


Dive into the research topics of 'A level set based topology optimization method using the augmented lagrangian method'. Together they form a unique fingerprint.

Cite this