A structural optimization method based on the level set method using a new geometry-based re-initialization scheme

Shintaro Yamasaki*, Shinji Nishiwaki, Takayuki Yamada, Kazuhiro Izui, Masataka Yoshimura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

79 Citations (Scopus)

Abstract

Structural optimization methods based on the level set method are a new type of structural optimization method where the outlines of target structures can be implicitly represented using the level set function, and updated by solving the so-called Hamilton-Jacobi equation based on a Eulerian coordinate system. These new methods can allow topological alterations, such as the number of holes, during the optimization process whereas the boundaries of the target structure are clearly defined. However, the re-initialization scheme used when updating the level set function is a critical problem when seeking to obtain appropriately updated outlines of target structures. In this paper, we propose a new structural optimization method based on the level set method using a new geometry-based re-initialization scheme where both the numerical analysis used when solving the equilibrium equations and the updating process of the level set function are performed using the Finite Element Method. The stiffness maximization, eigenfrequency maximization, and eigenfrequency matching problems are considered as optimization problems. Several design examples are presented to confirm the usefulness of the proposed method.

Original languageEnglish
Pages (from-to)1580-1624
Number of pages45
JournalInternational Journal for Numerical Methods in Engineering
Volume83
Issue number12
DOIs
Publication statusPublished - 2010 Sep 17
Externally publishedYes

Keywords

  • Finite element method
  • Level set method
  • Re-initialization
  • Structural optimization

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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