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Structural and Multidisciplinary Optimization

, Volume 32, Issue 3, pp 173–181 | Cite as

Structural optimization with \(\tt{FreeFem++}\)

  • G. AllaireEmail author
  • O. Pantz
Educational Article

Abstract

The aim of this paper is to show that relatively small, simple, and efficient shape optimization routines can be written using the free finite element software \(\tt{FreeFem++}\). This is illustrated by the implementation of two classical methods: the boundary variation method and the homogenization one. Even though these routines are simple enough so that their implementation can be assigned (partially or totally) as homework to graduate students, they yield results accurate enough to be useful tools for engineers or researchers.

Keywords

Shape and topology optimization Finite element software 

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References

  1. Allaire G (2001) Shape optimization by the homogenization method. Springer, Berlin Heidelberg New YorkGoogle Scholar
  2. Allaire G (2006) Conception optimale de structures. Collection Mathématiques et Applications. Springer.Google Scholar
  3. Allaire G, Jouve F, Toader A-M (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194/1:363–393CrossRefMathSciNetGoogle Scholar
  4. Bendsoe M, Sigmund O (2003) Topology optimization. Theory, methods, and applications. Springer, Berlin Heidelberg New YorkGoogle Scholar
  5. Hecht F, Pironneau O, Le Hyaric A, Ohtsuka K (2005) FreeFem++ Manual, downloadable at http://www.freefem.org
  6. Pironneau O (1984) Optimal shape design for elliptic systems. Springer, Berlin Heidelberg New YorkzbMATHGoogle Scholar
  7. Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidisc Optim 21:120–127CrossRefGoogle Scholar
  8. Sokołowski J, Zolesio JP (1992) Introduction to shape optimization: shape sensitivity analysis. Springer series in computational mathematics, vol 10. Springer, Berlin Heidelberg New YorkGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.CMAPEcole PolytechniquePalaiseauFrance

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