A gradient-based, parameter-free approach to shape optimization

Chau Le, Tyler Bruns, Daniel Tortorelli

Research output: Contribution to journalArticlepeer-review


In shape optimization, the independent node movement approach, wherein finite element node coordinates are used directly as design variables, allows the most freedom for shape change and avoids the time-consuming parameterization preprocess. However, this approach lacks a length scale control that is necessary to ensure a well-posed shape optimization problem and avoid numerical instability. Motivated by the success of filtering techniques that impose minimum length scales in topology optimization, we propose a scheme with consistent filtering to introduce a length scale and thereby ensure smoothness in shape optimization while preserving the advantages of the independent node movement approach.

Original languageEnglish (US)
Pages (from-to)985-996
Number of pages12
JournalComputer Methods in Applied Mechanics and Engineering
Issue number9-12
StatePublished - Feb 1 2011


  • Consistent filtering
  • Length scale
  • Parameter-free
  • Shape optimization
  • Smoothing

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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