Asymptotic analysis of plates in static and dynamic strain gradient elasticity

We study the steady-state and transient responses of a second-order elastic plate by implementing an asymptotic analysis of the three-dimensional equations with respect to two geometric characteristics seen as parameters: the thickness of the plate and an inner material length. Depending on their ra...

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Main Authors: Licht, Christian, Weller, Thibaut
Format: Article
Language:English
Published: Académie des sciences 2022-07-01
Series:Comptes Rendus. Mécanique
Subjects:
Online Access:https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.118/
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author Licht, Christian
Weller, Thibaut
author_facet Licht, Christian
Weller, Thibaut
author_sort Licht, Christian
collection DOAJ
description We study the steady-state and transient responses of a second-order elastic plate by implementing an asymptotic analysis of the three-dimensional equations with respect to two geometric characteristics seen as parameters: the thickness of the plate and an inner material length. Depending on their ratio, four different models arise. Conditions under which Reissner–Mindlin kinematics may appear are discussed while the influence of crystalline symmetries is studied. The transient situation is solved through Trotter’s theory of approximation of semi-groups of operators acting on variable spaces.
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spelling doaj.art-5b5f2d8aaac14a8489cc9fce216dc3282023-10-24T14:20:57ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342022-07-01350G232534210.5802/crmeca.11810.5802/crmeca.118Asymptotic analysis of plates in static and dynamic strain gradient elasticityLicht, Christian0Weller, Thibaut1Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand; LMGC, Université de Montpellier, CNRS, Montpellier, FranceLMGC, Université de Montpellier, CNRS, Montpellier, FranceWe study the steady-state and transient responses of a second-order elastic plate by implementing an asymptotic analysis of the three-dimensional equations with respect to two geometric characteristics seen as parameters: the thickness of the plate and an inner material length. Depending on their ratio, four different models arise. Conditions under which Reissner–Mindlin kinematics may appear are discussed while the influence of crystalline symmetries is studied. The transient situation is solved through Trotter’s theory of approximation of semi-groups of operators acting on variable spaces.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.118/Approximation of semi-groups in the sense of TrotterAsymptotic analysisStrain gradient elasticityPlate modelsTransient problems$m$-dissipative operatorsApproximation of semi-groups in the sense of Trotter
spellingShingle Licht, Christian
Weller, Thibaut
Asymptotic analysis of plates in static and dynamic strain gradient elasticity
Comptes Rendus. Mécanique
Approximation of semi-groups in the sense of Trotter
Asymptotic analysis
Strain gradient elasticity
Plate models
Transient problems
$m$-dissipative operators
Approximation of semi-groups in the sense of Trotter
title Asymptotic analysis of plates in static and dynamic strain gradient elasticity
title_full Asymptotic analysis of plates in static and dynamic strain gradient elasticity
title_fullStr Asymptotic analysis of plates in static and dynamic strain gradient elasticity
title_full_unstemmed Asymptotic analysis of plates in static and dynamic strain gradient elasticity
title_short Asymptotic analysis of plates in static and dynamic strain gradient elasticity
title_sort asymptotic analysis of plates in static and dynamic strain gradient elasticity
topic Approximation of semi-groups in the sense of Trotter
Asymptotic analysis
Strain gradient elasticity
Plate models
Transient problems
$m$-dissipative operators
Approximation of semi-groups in the sense of Trotter
url https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.118/
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AT wellerthibaut asymptoticanalysisofplatesinstaticanddynamicstraingradientelasticity