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Coordinate-free compatibility conditions for deformations of material surfaces
https://oist.repo.nii.ac.jp/records/2600
https://oist.repo.nii.ac.jp/records/26004b8855ca-f70b-4821-b76c-dfc470106c59
名前 / ファイル | ライセンス | アクション |
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1-s2.0-S0167663621004038-main (664.9 kB)
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (https://creativecommons.org/licenses/by-nc-nd/4.0/)
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Item type | 学術雑誌論文 / Journal Article(1) | |||||
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公開日 | 2022-03-22 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Coordinate-free compatibility conditions for deformations of material surfaces | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | Covariant gradient | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | Deformable surfaces | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | Material interfaces | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | Shells | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | Plates Kinematical constraints | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | journal article | |||||
著者(英) |
Seguin, Brian
× Seguin, Brian× Fried, Eliot |
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書誌情報 |
en : Mechanics of Materials 巻 166, p. 104193, 発行日 2022-01-10 |
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抄録 | ||||||
内容記述タイプ | Other | |||||
内容記述 | The study of material surfaces uses notions from classical differential geometry, such as the covariant gradient, the mean and Gaussian curvatures, and the Peterson–Mainardi–Codazzi and Gauss equations. These notions are traditionally introduced relative to local surface coordinates and involve Christoffel symbols. We proceed instead without recourse to coordinates using direct notation. After developing the formula for the covariant gradient relative to a surface metric, we derive versions of the Peterson–Mainardi–Codazzi and Gauss equations and Gauss’ Theorema Egregium relevant to a deformed material surface. We then apply our framework to kinematically constrained material surfaces. For material surfaces that can sustain only deformations that preserve either angles or lengths, we obtain explicit representations for the covariant gradient relative to the surface metric in terms of the surface gradient. We show also that a deformation of a material surface that preserves angles and areas must be length preserving and vice versa. Finally, we present an alternative derivation of the Peterson–Mainardi–Codazzi and Gauss equations for a deformed material surface subject to the provision that the surface metric derives from the metric for the ambient Euclidean space within which the surface is embedded. An Appendix involving coordinates is included to ease comparisons between our approach to covariant differentiation and associated derivations of the Peterson–Mainardi–Codazzi and Gauss equations and standard coordinate-based approaches. | |||||
出版者 | ||||||
出版者 | Elsevier Ltd. | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0167-6636 | |||||
DOI | ||||||
関連タイプ | isIdenticalTo | |||||
識別子タイプ | DOI | |||||
関連識別子 | info:doi/10.1016/j.mechmat.2021.104193 | |||||
権利 | ||||||
権利情報 | © 2022 The Author(s). | |||||
関連サイト | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://www.sciencedirect.com/science/article/pii/S0167663621004038 | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 |