Shape and topology optimization based on the phase field method and sensitivity analysis

Akihiro Takezawa*, Shinji Nishiwaki, Mitsuru Kitamura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

275 Citations (Scopus)


This paper discusses a structural optimization method that optimizes shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions. The advantage of the method is the simplicity of computation, since extra operations such as re-initialization of functions are not required. Structural shapes are represented by the phase field function defined in the design domain, and optimization of this function is performed by solving a time-dependent reaction diffusion equation. The artificial double well potential function used in the equation is derived from sensitivity analysis. The proposed method is applied to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem. The numerical examples provided illustrate the convergence of the various objective functions and the effect that perimeter control has on the optimal configurations.

Original languageEnglish
Pages (from-to)2697-2718
Number of pages22
JournalJournal of Computational Physics
Issue number7
Publication statusPublished - 2010 Apr 1
Externally publishedYes


  • Level set method
  • Phase field method
  • Sensitivity analysis
  • Shape optimization
  • Topology optimization

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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