no. 6
Mathematical Problems in Mechanics
The Reissner–Mindlin plate theory via Γ-convergence
[La théorie des plaques de Reissner–Mindlin via Γ-convergence]

Présenté par : Philippe G. Ciarlet

Paroni, Roberto1 ; Podio-Guidugli, Paolo2 ; Tomassetti, Giuseppe2
1 Dipartimento di Architettura e Pianificazione, Università degli Studi di Sassari, 07100 Sassari, Italy
2 Dipartimento di Ingegneria Civile, Università degli Studi di Roma TorVergata, Viale Politecnico 1, 00133 Roma, Italy
Comptes Rendus. Mathématique, Tome 343 (2006) no. 6, pp. 437-440.

Nous obtenons la fonctionnelle de l'énergie de plaques de Reissner–Mindlin comme la Γ-limite d'une famille de fonctionnelles d'énergie tri-dimensionnelles dans le cadre de l'élasticité linéaire du second ordre. Les choix de la famille de fonctionnelles et de la fonctionnelle limite sont suggérés par l'étude formelle des mises à l'échelle.

We obtain the energy functional of Reissner–Mindlin plates as the Γ-limit of a family of three-dimensional energy functionals within the framework of second-order linear elasticity. The choice of the family of functionals, as well as of the candidate limiting functional, is guided by a formal scaling argument.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2006.08.006
Paroni, Roberto 1 ; Podio-Guidugli, Paolo 2 ; Tomassetti, Giuseppe 2

1 Dipartimento di Architettura e Pianificazione, Università degli Studi di Sassari, 07100 Sassari, Italy
2 Dipartimento di Ingegneria Civile, Università degli Studi di Roma TorVergata, Viale Politecnico 1, 00133 Roma, Italy 
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Paroni, Roberto; Podio-Guidugli, Paolo; Tomassetti, Giuseppe. The Reissner–Mindlin plate theory via Γ-convergence. Comptes Rendus. Mathématique, Tome 343 (2006) no. 6, pp. 437-440. doi : 10.1016/j.crma.2006.08.006. http://www.numdam.org/articles/10.1016/j.crma.2006.08.006/

[1] Ciarlet, P.G. Mathematical Elasticity. Vol. II: Plates, North-Holland, 1997

[2] Le Dret, H.; Raoult, A. Variational convergence for nonlinear shell models with directors and related semicontinuity and relaxation results, Arch. Rational Mech. Anal., Volume 154 (2000), pp. 101-134

[3] B. Miara, P. Podio-Guidugli, Deduction by scaling: a unified approach to plate and rod theories (2006), submitted for publication

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