[Analyse asymptotique de plaques et de poutres viscoélastiques minces, une approche unitaire]
Nous nous penchons sur la modélisation mathématique asymptotique de structures minces viscoélastiques dans le cadre de la théorie de Trotter de convergence de semi-groupes d’opérateurs agissant sur des espaces variables [1, 2]. Nous montrons que dans ce contexte, il est possible d’effectuer d’une manière unitaire l’analyse asymptotique des plaques et des poutres minces. Nous mettons en évidence divers modèles de comportements dynamiques de telles structures en contact bilatéral avec frottement de type Norton ou Tresca le long d’une partie de leur surface latérale avec un corps rigide.
A dimension reduction problem is tackled using Trotter’s theory of convergence of semi-groups of operators acting on variable spaces [1, 2]. We show that this framework makes it possible to perform the asymptotic analysis for both viscoelastic thin plates and slender beams in a unifying manner. Several models are provided for the dynamic behavior of such structures in bilateral contact with a rigid body on a part of their boundaries with Norton or Tresca friction.
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Mot clés : Plaques minces, poutres élancées, viscoélasticité de type Kelvin-Voigt non linéaire, frottement de type Norton ou Tresca, problèmes d’évolution, analyse asymptotique, réduction de dimension, opérateurs maximaux-monotones, approximation de semi-groupes au sens de Trotter
Yotsawat Terapabkajornded 1, 2 ; Somsak Orankitjaroen 1, 3 ; Christian Licht 1, 2, 3 ; Thibaut Weller 2
CC-BY 4.0
@article{CRMECA_2024__352_G1_201_0,
author = {Yotsawat Terapabkajornded and Somsak Orankitjaroen and Christian Licht and Thibaut Weller},
title = {Asymptotic modeling of viscoelastic thin plates and slender beams, a unifying approach},
journal = {Comptes Rendus. M\'ecanique},
pages = {201--222},
publisher = {Acad\'emie des sciences, Paris},
volume = {352},
year = {2024},
doi = {10.5802/crmeca.252},
language = {en},
}
TY - JOUR AU - Yotsawat Terapabkajornded AU - Somsak Orankitjaroen AU - Christian Licht AU - Thibaut Weller TI - Asymptotic modeling of viscoelastic thin plates and slender beams, a unifying approach JO - Comptes Rendus. Mécanique PY - 2024 SP - 201 EP - 222 VL - 352 PB - Académie des sciences, Paris DO - 10.5802/crmeca.252 LA - en ID - CRMECA_2024__352_G1_201_0 ER -
%0 Journal Article %A Yotsawat Terapabkajornded %A Somsak Orankitjaroen %A Christian Licht %A Thibaut Weller %T Asymptotic modeling of viscoelastic thin plates and slender beams, a unifying approach %J Comptes Rendus. Mécanique %D 2024 %P 201-222 %V 352 %I Académie des sciences, Paris %R 10.5802/crmeca.252 %G en %F CRMECA_2024__352_G1_201_0
Yotsawat Terapabkajornded; Somsak Orankitjaroen; Christian Licht; Thibaut Weller. Asymptotic modeling of viscoelastic thin plates and slender beams, a unifying approach. Comptes Rendus. Mécanique, Volume 352 (2024), pp. 201-222. doi : 10.5802/crmeca.252. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.252/
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