Comptes Rendus
no. 6
An asymptotic Reissner–Mindlin plate model
Christian Licht1, 2, 3  ; Thibaut Weller1
1 LMGC, Université de Montpellier, CNRS, Montpellier, France
2 Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
3 Centre of Excellence in Mathematics, CHE, Bangkok 10400, Thailand
Comptes Rendus. Mécanique, Volume 346 (2018) no. 6, pp. 432-438.

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner–Mindlin plate model.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2018.04.014
Mots clés : Reissner–Mindlin plate model, Periodic abutting of thin plates, Asymptotic modeling, Variational convergence, Space of bounded deformations
Christian Licht 1, 2, 3 ; Thibaut Weller 1

1 LMGC, Université de Montpellier, CNRS, Montpellier, France
2 Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
3 Centre of Excellence in Mathematics, CHE, Bangkok 10400, Thailand 
@article{CRMECA_2018__346_6_432_0,
     author = {Christian Licht and Thibaut Weller},
     title = {An asymptotic {Reissner{\textendash}Mindlin} plate model},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {432--438},
     publisher = {Elsevier},
     volume = {346},
     number = {6},
     year = {2018},
     doi = {10.1016/j.crme.2018.04.014},
     language = {en},
}
TY  - JOUR
AU  - Christian Licht
AU  - Thibaut Weller
TI  - An asymptotic Reissner–Mindlin plate model
JO  - Comptes Rendus. Mécanique
PY  - 2018
SP  - 432
EP  - 438
VL  - 346
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crme.2018.04.014
LA  - en
ID  - CRMECA_2018__346_6_432_0
ER  - 
%0 Journal Article
%A Christian Licht
%A Thibaut Weller
%T An asymptotic Reissner–Mindlin plate model
%J Comptes Rendus. Mécanique
%D 2018
%P 432-438
%V 346
%N 6
%I Elsevier
%R 10.1016/j.crme.2018.04.014
%G en
%F CRMECA_2018__346_6_432_0
Christian Licht; Thibaut Weller. An asymptotic Reissner–Mindlin plate model. Comptes Rendus. Mécanique, Volume 346 (2018) no. 6, pp. 432-438. doi : 10.1016/j.crme.2018.04.014. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.04.014/

[1] E. Reissner On the theory of bending of elastic plates, J. Math. Phys., Volume 23 (1945), pp. 184-191

[2] E. Reissner The effect of transverse shear deformations on the bending of elastic plates, J. Appl. Mech., Volume 12 (1945), p. A69-A77

[3] R.D. Mindlin Influence of rotary inertia and shear on flexural motions of isotropic elastic plate, J. Appl. Mech., Volume 18 (1951), pp. 31-38

[4] D.N. Arnold; A.L. Madureira; S. Zhang On the range of applicability of the Reissner–Mindlin and Kirchhoff–Love plate bending models, J. Elast., Volume 67 (2002), pp. 171-185

[5] P.G. Ciarlet Mathematical Elasticity, vol. II: Theory of Plates, North-Holland, Elsevier, 1997

[6] O. Iosifescu; C. Licht; G. Michaille Nonlinear boundary conditions in Kirchhoff–Love plate theory, J. Elast., Volume 96 (2009), pp. 57-79

[7] R. Paroni; P. Podio-Guidugli; G. Tomassetti A justification of the Reissner–Mindlin plate theory through variational convergence, Anal. Appl., Volume 5 (2007), pp. 165-182

[8] M. Serpilli; F. Krasucki; G. Geymonat An asymptotic strain gradient Reissner–Mindlin plate model, Meccanica, Volume 48 (2013), pp. 2007-2018

[9] P. Neff; K.-I. Hong; J. Jeong The Reissner–Mindlin plate is the Γ-limit of Cosserat elasticity, Math. Models Methods Appl. Sci., Volume 20 (2010), pp. 1553-1590

[10] C. Licht Asymptotic modeling of assemblies of thin linearly elastic plates, C. R. Mecanique, Volume 335 (2007), pp. 775-780

[11] R. Temam Problèmes Mathématiques en Plasticité, Gauthier-Villars, Paris, 1983

[12] H. Attouch; G. Buttazzo; G. Michaille Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization, MPS–SIAM Series on Optimization, vol. 6, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2005

[13] C. Licht; A. Léger; S. Orankitjaroen; A. Ould Khaoua Dynamics of elastic bodies connected by a thin soft viscoelastic layer, J. Math. Pures Appl., Volume 99 (2013), pp. 685-703

[14] C. Licht; G. Michaille A modelling of elastic adhesive bonded joints, Adv. Math. Sci. Appl., Volume 7 (1997), pp. 711-740

[15] A. Cecchi; K. Sab A homogenized Reissner–Mindlin model for orthotropic periodic plates: application to brickwork panels, Int. J. Solids Struct., Volume 44 (2007), pp. 6055-6079

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Asymptotic analysis of a thin linearly elastic plate equipped with a periodic distribution of stiffeners

Christian Licht; Thibaut Weller

C. R. Méca (2019)

Thin linearly viscoelastic Kelvin–Voigt plates

Christian Licht

C. R. Méca (2013)

About the atomic structures of icosahedral quasicrystals

Marianne Quiquandon; Denis Gratias

C. R. Phys (2014)