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Asymptotic modeling of viscoelastic thin plates and slender beams, a unifying approach
Journal article   Open access   Peer reviewed

Asymptotic modeling of viscoelastic thin plates and slender beams, a unifying approach

Yotsawat Terapabkajornded, Somsak Orankitjaroen, Christian Licht and Thibaut Weller
Comptes Rendus. Mécanique, Vol.352(G1), pp.201-222
19/06/2024
DOI: https://doi.org/10.5802/crmeca.252

Abstract

Thin plates slender beams viscoelasticity of non-linear Kelvin-Voigt type Norton or Tresca friction transient problems asymptotic analysis dimension reduction maximal-monotone operators approximation of semi-groups in the sense of Trotter approximation 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
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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