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

Christian Licht; Thibaut Weller

doi:10.1016/j.crme.2019.07.001

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

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

Comptes Rendus. Mécanique, Volume 347 (2019) no. 8, pp. 555-560.

Résumé

We derive several models of thin plates equipped with a periodic distribution of stiffeners. Depending on the orders of magnitude of the different parameters involved, diverse situations arise, from classical Kirchhoff–Love behaviour with additional energy term to full rigidification.

Reçu le : 2019-06-13
Accepté le : 2019-07-19
Publié le : 2019-08-01

DOI : 10.1016/j.crme.2019.07.001

Mots clés : Hard abutting and rigidification of plates, Asymptotic modelling, Periodic homogenization, Reduction of dimension, Variational convergence

Affiliations des auteurs :

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

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     title = {Asymptotic analysis of a thin linearly elastic plate equipped with a periodic distribution of stiffeners},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {555--560},
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     volume = {347},
     number = {8},
     year = {2019},
     doi = {10.1016/j.crme.2019.07.001},
     language = {en},
}

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Christian Licht; Thibaut Weller. Asymptotic analysis of a thin linearly elastic plate equipped with a periodic distribution of stiffeners. Comptes Rendus. Mécanique, Volume 347 (2019) no. 8, pp. 555-560. doi : 10.1016/j.crme.2019.07.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.07.001/

Bibliographie
Cité par

[1] C. Licht; T. Weller An asymptotic Reissner–Mindlin plate model, C. R. Mecanique, Volume 346 (2018), pp. 432-438

[2] P. Villaggio Mathematical Models for Elastic Structures, Cambridge University Press, Cambridge, UK, 1997

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

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

[5] C. Licht; T. Weller Approximation of semi-groups in the sense of Trotter and asymptotic mathematical modeling in physics of continuous media, Discrete Contin. Dyn. Syst., Ser. S, Volume 12 (2019), pp. 1709-1741

[6] Y. Terapabkajornded; S. Orankitjaroen; C. Licht Asymptotic model of linearly visco-elastic Kelvin–Voigt type plates via Trotter theory, Adv. Differ. Equ., Volume 186 (2019) | DOI

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