On considère le problème de minimisation de la compliance d'un matériau élastique soumis à un chargement donné que l'on doit placer dans un domaine dont l'épaisseur tend vers zéro. Nous déterminons le problème limite ainsi que les conditions nécessaires et suffisantes d'optimalité associées.
We consider the variational problems which consist in minimizing the compliance of a prescribed amount of elastic material which is subject to a given load and is placed in a design region of infinitesimal height. We determine the limit problem, and we provide necessary and sufficient optimality conditions.
Accepté le :
Publié le :
@article{CRMATH_2007__345_12_713_0, author = {Bouchitt\'e, Guy and Fragal\`a, Ilaria and Seppecher, Pierre}, title = {3D{\textendash}2D analysis for the optimal elastic compliance problem}, journal = {Comptes Rendus. Math\'ematique}, pages = {713--718}, publisher = {Elsevier}, volume = {345}, number = {12}, year = {2007}, doi = {10.1016/j.crma.2007.10.039}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.10.039/} }
TY - JOUR AU - Bouchitté, Guy AU - Fragalà, Ilaria AU - Seppecher, Pierre TI - 3D–2D analysis for the optimal elastic compliance problem JO - Comptes Rendus. Mathématique PY - 2007 SP - 713 EP - 718 VL - 345 IS - 12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.10.039/ DO - 10.1016/j.crma.2007.10.039 LA - en ID - CRMATH_2007__345_12_713_0 ER -
%0 Journal Article %A Bouchitté, Guy %A Fragalà, Ilaria %A Seppecher, Pierre %T 3D–2D analysis for the optimal elastic compliance problem %J Comptes Rendus. Mathématique %D 2007 %P 713-718 %V 345 %N 12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.10.039/ %R 10.1016/j.crma.2007.10.039 %G en %F CRMATH_2007__345_12_713_0
Bouchitté, Guy; Fragalà, Ilaria; Seppecher, Pierre. 3D–2D analysis for the optimal elastic compliance problem. Comptes Rendus. Mathématique, Tome 345 (2007) no. 12, pp. 713-718. doi : 10.1016/j.crma.2007.10.039. http://archive.numdam.org/articles/10.1016/j.crma.2007.10.039/
[1] Shape Optimization by the Homogenization Method, Springer, Berlin, 2002
[2] Approximation of Young measures by functions and application to a problem of optimal design for plates with variable thickness, Proc. Roy. Soc. Edinburgh Sect. A, Volume 124 (1994) no. 3, pp. 399-422
[3] Optimality conditions for mass design problems and applications to thin plates, Arch. Ration. Mech. Anal., Volume 184 (2007) no. 2, pp. 257-284 (74)
[4] Optimal design of thin plates by a dimension reduction for linear constrained problems, SIAM J. Control Optim., Volume 46 (2007) no. 5, pp. 1664-1682
[5] Models of thin or thick plates and membranes derived from linear elasticity, Applications of Multiple Scaling in Mechanics, Masson, Paris, 1987, pp. 54-68
[6] Mathematical Elasticity, Vol. 2, Theory of Plates, Studies in Mathematics and Applications, vol. 27, North-Holland, Amsterdam, 1997
[7] Michell-like grillages and structures with locking, Arch. Mech., Volume 53 (2001), pp. 457-485
Cité par Sources :