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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Format: | Article |
Language: | English |
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Académie des sciences
2022-07-01
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Series: | Comptes Rendus. Mécanique |
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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. |
first_indexed | 2024-03-11T16:15:09Z |
format | Article |
id | doaj.art-5b5f2d8aaac14a8489cc9fce216dc328 |
institution | Directory Open Access Journal |
issn | 1873-7234 |
language | English |
last_indexed | 2024-03-11T16:15:09Z |
publishDate | 2022-07-01 |
publisher | Académie des sciences |
record_format | Article |
series | Comptes Rendus. Mécanique |
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/ |
work_keys_str_mv | AT lichtchristian asymptoticanalysisofplatesinstaticanddynamicstraingradientelasticity AT wellerthibaut asymptoticanalysisofplatesinstaticanddynamicstraingradientelasticity |