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- 1
- G. Allaire,
Relaxation of structural optimization problems by homogenization,
"Trends in Applications of Mathematics to Mechanics",
M.M.Marques and J.F.Rodrigues Eds., Pitman monographs and surveys in pure
and applied mathematics 77, pp.237-251, Longman, Harlow (1995).
- 2
- G. Allaire, Z. Belhachmi, F. Jouve,
The homogenization method for topology and shape optimization. Single
and multiple loads case,
Revue Européenne des Eléments Finis, 5, pp.649-672 (1996).
- 3
- G. Allaire, E. Bonnetier, G. Francfort, F. Jouve,
Shape optimization by the homogenization method,
Numerische Mathematik 76, pp.27-68 (1997).
- 4
- G. Allaire, R.V. Kohn,
Optimal design for minimum weight and compliance in plane stress
using extremal microstructures,
Europ. J. Mech. A/Solids 12, 6, 839-878 (1993).
- 5
- G. Allaire, R.V. Kohn,
Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materials,
Quat. Appl. Math. 51, 643-674 (1993).
- 6
- M. Avellaneda,
Optimal bounds and microgeometries for elastic two-phase composites,
SIAM J. Appl. Math., 47, 6, 1216-1228 (1987).
- 7
- M. Bendsoe,
Methods for optimization of structural topology, shape and material,
Springer Verlag (1995).
- 8
- M. Bendsoe, N. Kikuchi,
Generating Optimal Topologies in Structural Design Using a Homogenization Method,
Comp. Meth. Appl. Mech. Eng., 71, 197-224 (1988).
- 9
- M. Bendsoe, C. Mota Soares, Editors,
Topology optimization of structures,
Kluwer Academic Press, Dordrecht (1993).
- 10
- A. Bensoussan, J.L. Lions, G. Papanicolaou,
Asymptotic analysis for periodic structures,
North-Holland, Amsterdam (1978).
- 11
- J. Céa,
A numerical method for the computation of an optimal domain,
Lecture Notes in Computer Sciences 41, Springer, New York (1976).
- 12
- D. Chenais,
On the existence of a solution in a domain identification problem,
J. Math. Anal. Appl. 52, pp.189-289 (1975).
- 13
- G. Cheng, N. Olhoff,
An investigation concerning optimal design of solid elastic plates,
Int. J. Solids Struct. 16, pp.305-323 (1981).
- 14
- A. Cherkaev, R. Kohn, Editors,
Topics in the mathematical modelling of composite materials,
Progress in Nonlinear Differential Equations and their Applications,
31, Birkhaüser, Boston (1997).
- 15
- G. Francfort, F. Murat,
Homogenization and Optimal Bounds in Linear Elasticity,
Arch. Rat. Mech. Anal., 94, 307-334 (1986).
- 16
- L. Gibianski, A. Cherkaev,
Design of composite plates of extremal rigidity,
(1984),
Microstructures of composites of extremal rigidity and
exact bounds of the associated energy density,
Ioffe Physicotechnical Institute preprints (1987).
- 17
- Z. Hashin, S. Shtrikman,
A variational approach to the theory of the elastic behavior of
multiphase materials,
J. Mech. Phys. Solids, 11, 127-140 (1963).
- 18
- C. Jog, R. Haber, M. Bendsoe,
Topology design with optimized, self-adaptative materials,
Int. Journal for Numerical Methods in Engineering 37, 1323-1350 (1994).
- 19
- R. Kohn, G. Strang,
Optimal Design and Relaxation of Variational Problems I-II-III,
Comm. Pure Appl. Math., 39, 113-137, 139-182, 353-377 (1986).
- 20
- K. Lurie, A. Cherkaev, A. Fedorov,
Regularization of Optimal Design Problems for Bars and Plates I,II,
J. Optim. Th. Appl. 37, pp.499-521, 523-543 (1982).
- 21
- A. Michell,
The limits of economy of material in frame-structures,
Phil. Mag., 8, 589-597 (1904).
- 22
- G. Milton,
On characterizing the set of possible effective tensors of composites:
the variational method and the translation method,
Comm. Pure Appl. Math., XLIII, pp.63-125 (1990).
- 23
- F. Murat,
Contre-exemples pour divers problèmes où le contrôle intervient dans les coefficients,
Ann. Mat. Pura Appl., 112, 49-68 (1977).
- 24
- F. Murat, J. Simon,
Studies on optimal shape design problems,
Lecture Notes in Computer Science 41, Springer Verlag, Berlin (1976).
- 25
- F. Murat, L. Tartar,
Calcul des Variations et Homogénéisation,
Les Méthodes de l'Homogénéisation Théorie et Applications en Physique,
Coll. Dir. Etudes et Recherches EDF, Eyrolles, 319-369 (1985).
- 26
- O. Pironneau,
Optimal shape design for elliptic systems,
Springer-Verlag, New York (1984).
- 27
- G. Rozvany,
Structural design via optimality criteria,
Kluwer Academic Publishers, Dordrecht (1989).
- 28
- E. Sanchez-Palencia,
Non homogeneous media and vibration theory,
Lecture notes in physics 127, Springer Verlag (1980).
- 29
- O. Sigmund,
Design of material structures using topology optimization,
PhD thesis, report S 69, Dept. of Solid Mechanics, Technical
University of Denmark (1994).
- 30
- J. Sokolowski, J.-P. Zolezio,
Introduction to shape optimization. Shape sensitivity analysis,
Springer Verlag (1992).
- 31
- K. Suzuki, N. Kikuchi,
A homogenization method for shape and topology optimization,
Comp. Meth. Appl. Mech. Eng., 93, 291-318 (1991).
Gregoire Allaire
2005-06-06