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

Abstract

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.

Received: 2019-06-13
Accepted: 2019-07-19
Published online: 2019-08-01

DOI: 10.1016/j.crme.2019.07.001

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

Author's affiliations:

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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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

References
Cited by

[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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