Free Access
Issue
ESAIM: M2AN
Volume 41, Number 3, May-June 2007
Page(s) 543 - 574
DOI https://doi.org/10.1051/m2an:2007026
Published online 02 August 2007
  1. G. Allaire, Shape Optimization by the Homogenization Method. Springer-Verlag (2002). [Google Scholar]
  2. G. Allaire and S. Gutiérrez, Optimal design in small amplitude homogenization (extended version). Preprint available at http://www.cmap.polytechnique.fr/preprint/repository/576.pdf (2005). [Google Scholar]
  3. G. Allaire and F. Jouve, Optimal design of micro-mechanisms by the homogenization method. Eur. J. Finite Elements 11 (2002) 405–416. [Google Scholar]
  4. G. Allaire, F. Jouve and H. Maillot, Topology optimization for minimum stress design with the homogenization method. Struct. Multidiscip. Optim. 28 (2004) 87–98. [Google Scholar]
  5. J.C. Bellido and P. Pedregal, Explicit quasiconvexification for some cost functionals depending on derivatives of the state in optimal designing. Discr. Contin. Dyn. Syst. 8 (2002) 967–982. [CrossRef] [Google Scholar]
  6. M.P. Bendsøe and O. Sigmund, Topology Optimization. Theory, Methods, and Applications. Springer-Verlag, New York (2003). [Google Scholar]
  7. A. Cherkaev, Variational Methods for Structural Optimization. Springer Verlag, New York (2000). [Google Scholar]
  8. A. Donoso and P. Pedregal, Optimal design of 2D conducting graded materials by minimizing quadratic functionals in the field. Struct. Multidiscip. Optim. 30 (2005) 360–367. [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Duysinx and M.P. Bendsøe, Topology optimization of continuum structures with local stress constraints. Int. J. Num. Meth. Engng. 43 (1998) 1453–1478. [Google Scholar]
  10. P. Gérard, Microlocal defect measures. Comm. Partial Diff. Equations 16 (1991) 1761–1794. [Google Scholar]
  11. Y. Grabovsky, Optimal design problems for two-phase conducting composites with weakly discontinuous objective functionals. Adv. Appl. Math. 27 (2001) 683–704. [CrossRef] [Google Scholar]
  12. F. Hecht, O. Pironneau and K. Ohtsuka, FreeFem++ Manual. Downloadable at http://www.freefem.org [Google Scholar]
  13. L. Hörmander, The analysis of linear partial differential operators III. Springer, Berlin (1985). [Google Scholar]
  14. R.V. Kohn, Relaxation of a double-well energy. Cont. Mech. Thermodyn. 3 (1991) 193–236. [Google Scholar]
  15. R. Lipton, Relaxation through homogenization for optimal design problems with gradient constraints. J. Optim. Theory Appl. 114 (2002) 27–53. [CrossRef] [MathSciNet] [Google Scholar]
  16. R. Lipton, Stress constrained G closure and relaxation of structural design problems. Quart. Appl. Math. 62 (2004) 295–321. [MathSciNet] [Google Scholar]
  17. R. Lipton and A. Velo, Optimal design of gradient fields with applications to electrostatics. Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. XIV, Stud. Math. Appl. 31 (2002) 509–532. [Google Scholar]
  18. G. Milton, The theory of composites. Cambridge University Press (2001). [Google Scholar]
  19. F. Murat and L. Tartar, Calcul des Variations et Homogénéisation, Les Méthodes de l'Homogénéisation Théorie et Applications en Physique, Coll. Dir. Études et Recherches EDF, 57, Eyrolles, Paris (1985) 319–369. English translation in Topics in the mathematical modelling of composite materials, A. Cherkaev and R. Kohn Eds., Progress in Nonlinear Differential Equations and their Applications 31, Birkhäuser, Boston (1997). [Google Scholar]
  20. U. Raitums, The extension of extremal problems connected with a linear elliptic equation. Soviet Math. 19 (1978) 1342–1345. [Google Scholar]
  21. L. Tartar, H-measures, a new approach for studying homogenization, oscillations and concentration effects in partial differential equations. Proc. Royal Soc. Edinburgh 115A (1990) 93–230. [Google Scholar]
  22. L. Tartar, Remarks on optimal design problems. Calculus of variations, homogenization and continuum mechanics (Marseille, 1993), World Sci. Publishing, River Edge, NJ, Ser. Adv. Math. Appl. Sci. 18 (1994) 279–296. [Google Scholar]
  23. L. Tartar, An introduction to the homogenization method in optimal design, in Optimal shape design (Tróia, 1998), A. Cellina and A. Ornelas Eds., Springer, Berlin, Lect. Notes Math. 1740 (2000) 47–156. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you