next up previous
Next: About this document ... Up: matap2 Previous: Algorithme numérique d'optimisation de

Bibliography

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