On the optimization of non periodic homogenized microstructures
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 31 (1997) no. 5, p. 559-597
@article{M2AN_1997__31_5_559_0,
     author = {Chenais, D. and Mascarenhas, M. L. and Trabucho, L.},
     title = {On the optimization of non periodic homogenized microstructures},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {31},
     number = {5},
     year = {1997},
     pages = {559-597},
     zbl = {0882.65058},
     mrnumber = {1471179},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1997__31_5_559_0}
}
Chenais, D.; Mascarenhas, M. L.; Trabucho, L. On the optimization of non periodic homogenized microstructures. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 31 (1997) no. 5, pp. 559-597. http://www.numdam.org/item/M2AN_1997__31_5_559_0/

[1] G. Allaire, G. A. Francfort, 1993, A Numerical algorithm for topology and shape optimization, Topology Design of Structures, ed. by M. P. BendsØe and C. M. Soares, Kluwer, Serie E, 227, pp. 239-248. | MR 1250195

[2] G. Allaire, R. V. Kohn, 1993, Optimal design for minimum weight and compliance in plane stress using extremal microstructures, Eur. J. Mech. A Solids, 12, N° 4. | MR 1343090 | Zbl 0794.73044

[3] J. Cea, 1981, Optimization of distributed parameter structures, NATO Advanced Study Institutes series, 50, Sijthoff and Noordhoff. | Zbl 0511.00034

[4] D. Chenais, 1975, On the existence of a solution in a domain identification problem, J. Math. Anal and Appl., vol, 52, pp.189-289. | MR 385666 | Zbl 0317.49005

[5] D. Chenais, 1977, Sur une famille de variétés à bord lipschitziennes. Application à un problème d'identification de domaines, Annales de l'Institut Fourier de Grenoble, vol. 27(4), pp. 201-231. | Numdam | MR 473802 | Zbl 0333.46020

[6] D. Chenais, 1987, Optimal design of midsurface of shells : differentiability proof and sensitivity computation, Applied Math. and Optimization, vol. 16, pp. 93-133. | MR 894807 | Zbl 0626.73097

[7] D. Chenais, 1992, Optimisation de domaines, cours de 3e cycle.

[8] D. Cioranescu, J. S. J. Paulin, 1979, Homogenization in open sets with hole, J. Math. Anal. and Appl., vol. 71, pp. 590-607. | MR 548785 | Zbl 0427.35073

[9] P. Guillaume, 1994, Dérivées d'ordre supérieure en optimisation de forme, Thèse de l'Université de Toulouse, France.

[10] N. Kjkuchi, M. P. Bendsøe, 1988, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, vol. 71, pp. 197-224. | MR 969217 | Zbl 0671.73065

[11] R. V. Kohn, G. Strang, 1986, Optimal design and relaxation of variational problems, Comm. Pure Appl. Math. vol. 39, pp. 1-25 (Part I), pp. 139-182 (Part II), pp. 353-377 (Part III). | Zbl 0621.49008

[12] R. V. Kohn, G. Strang, 1986, Optimal design in elasticity and plasticity, Internat. J. Numer. Meths. Engrg., vol. 22, pp.183-188. | MR 831844 | Zbl 0593.73091

[13] M. L. Mascarenhas, D. Polisevski, 1994, The warping, the torsion and the Neumann problems in a quasi-periodically perforated domain, Mathematical Modeling and Numerical Analysis, vol. 28(1), pp. 37-57. | Numdam | MR 1259267 | Zbl 0819.73003

[14] M. Masmoudi, 1987, Outils pour la conception optimale de forme, Thesis of the University of Nice, France, 1987.

[15] F. Murat, J. Simon, 1976, Sur le contrôle par un domaine géométrique, publications du Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie.

[16] F. Murat, L. Tartar, 1985, Calcul des variations et homogénéisation. In : Les Méthodes de l'Homogénéisation : Théorie et Applications en Physique, Coll. de la Dir. des Etudes et Recherches de Electricité de France, Eyrolles, pp. 319-370, Paris. | MR 844873

[17] F. Murat, L. Tartar, Calculus of Variations and Homogenization, in : R. V. Kohn, ed. Topics in the mathematical modelling of composite materials, Birkäuser (to appear). | MR 844873 | Zbl 0939.35019

[18] D. Polisevski, 1992, Quasi-periodic structure optimization of the torsional rigidity, Preprint CMAF 15/92. | MR 1261603 | Zbl 0796.73047

[19] B. Rousselet, 1981, Optimization of distributed parameter structures, NATO Advanced Study Institutes series, 50, Sijthoff and Noordhoff.

[20] M. Zerner, 1994, Private communication.

[21] J. P. Zolesio, 1981, Optimization of distributed parameter structures, NATO Advanced Study Institutes series, 50, Sijthoff and Noordhoff.