Comptes Rendus
no. 12
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 Bouchitté1 ; Ilaria Fragalà2 ; Pierre Seppecher1
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.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.10.039
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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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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[3] G. Bouchitté; I. Fragalà 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] G. Bouchitté; I. Fragalà 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] D. Caillerie 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] P. Ciarlet Mathematical Elasticity, Vol. 2, Theory of Plates, Studies in Mathematics and Applications, vol. 27, North-Holland, Amsterdam, 1997

[7] T. Lewinski; J.J. Telega Michell-like grillages and structures with locking, Arch. Mech., Volume 53 (2001), pp. 457-485

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