3D–2D analysis for the optimal elastic compliance problem

Guy Bouchitté; Ilaria Fragalà; Pierre Seppecher

doi:10.1016/j.crma.2007.10.039

Mathematical Problems in Mechanics/Partial Differential Equations

3D–2D analysis for the optimal elastic compliance problem
[Analyse limite 3D–2D du problème de compliance optimale]

Présenté par : Philippe G. Ciarlet

Guy Bouchitté ¹ ; Ilaria Fragalà ² ; Pierre Seppecher ¹

¹ Laboratoire ANAM, Université de Toulon et du Var, 83957 La Garde cedex, France
² Dipartimento di Matematica, Politecnico, Piazza L. da Vinci, 32, 20133 Milano, Italy

Comptes Rendus. Mathématique, Volume 345 (2007) no. 12, pp. 713-718.

Résumé
Abstract

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.

Reçu le : 2007-10-09
Accepté le : 2007-10-25
Publié le : 2007-11-26

DOI : 10.1016/j.crma.2007.10.039

Affiliations des auteurs :

Guy Bouchitté ¹ ; Ilaria Fragalà ² ; Pierre Seppecher ¹

¹ Laboratoire ANAM, Université de Toulon et du Var, 83957 La Garde cedex, France
² Dipartimento di Matematica, Politecnico, Piazza L. da Vinci, 32, 20133 Milano, Italy

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     title = {3D{\textendash}2D analysis for the optimal elastic compliance problem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {713--718},
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     year = {2007},
     doi = {10.1016/j.crma.2007.10.039},
     language = {en},
}

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Guy Bouchitté; Ilaria Fragalà; Pierre Seppecher. 3D–2D analysis for the optimal elastic compliance problem. Comptes Rendus. Mathématique, Volume 345 (2007) no. 12, pp. 713-718. doi : 10.1016/j.crma.2007.10.039. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.039/

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