Volume 41, Number 3, May-June 2007
|Page(s)||543 - 574|
|Published online||02 August 2007|
- G. Allaire, Shape Optimization by the Homogenization Method. Springer-Verlag (2002).
- 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).
- G. Allaire and F. Jouve, Optimal design of micro-mechanisms by the homogenization method. Eur. J. Finite Elements 11 (2002) 405–416.
- G. Allaire, F. Jouve and H. Maillot, Topology optimization for minimum stress design with the homogenization method. Struct. Multidiscip. Optim. 28 (2004) 87–98. [CrossRef] [MathSciNet]
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- A. Cherkaev, Variational Methods for Structural Optimization. Springer Verlag, New York (2000).
- 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]
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- F. Hecht, O. Pironneau and K. Ohtsuka, FreeFem++ Manual. Downloadable at http://www.freefem.org
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- R.V. Kohn, Relaxation of a double-well energy. Cont. Mech. Thermodyn. 3 (1991) 193–236. [CrossRef] [MathSciNet]
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- 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).
- U. Raitums, The extension of extremal problems connected with a linear elliptic equation. Soviet Math. 19 (1978) 1342–1345.
- 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.
- 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.
- 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.
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