Comptes Rendus
Mathematical Problems in Mechanics
The Reissner–Mindlin plate theory via Γ-convergence
Comptes Rendus. Mathématique, Volume 343 (2006) no. 6, pp. 437-440.

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.

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.

Published online:
DOI: 10.1016/j.crma.2006.08.006

Roberto Paroni 1; Paolo Podio-Guidugli 2; Giuseppe Tomassetti 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
     author = {Roberto Paroni and Paolo Podio-Guidugli and Giuseppe Tomassetti},
     title = {The {Reissner{\textendash}Mindlin} plate theory via {\protect\emph{\ensuremath{\Gamma}}-convergence}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {437--440},
     publisher = {Elsevier},
     volume = {343},
     number = {6},
     year = {2006},
     doi = {10.1016/j.crma.2006.08.006},
     language = {en},
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Roberto Paroni; Paolo Podio-Guidugli; Giuseppe Tomassetti. The Reissner–Mindlin plate theory via Γ-convergence. Comptes Rendus. Mathématique, Volume 343 (2006) no. 6, pp. 437-440. doi : 10.1016/j.crma.2006.08.006.

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

[2] H. Le Dret; A. Raoult 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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