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Representation of a Smooth Isometric Deformation of a Planar Material Region into a Curved Surface
https://oist.repo.nii.ac.jp/records/195
https://oist.repo.nii.ac.jp/records/195823955cb-9920-427c-9702-b6f99d54e705
名前 / ファイル | ライセンス | アクション |
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s10659-017-9637-2 (1.6 MB)
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Creative Commons Attribution 4.0 International
(http://creativecommons.org/licenses/by/4.0/) |
Item type | 学術雑誌論文 / Journal Article(1) | |||||
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公開日 | 2017-12-28 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Representation of a Smooth Isometric Deformation of a Planar Material Region into a Curved Surface | |||||
言語 | ||||||
言語 | eng | |||||
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) |
Chen, Y., Chao
× Chen, Y., Chao× Fosdick, Roger× Fried, Eliot |
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書誌情報 |
en : Journal of Elasticity 巻 130, 号 2, p. 145-195, 発行日 2017-04-10 |
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抄録 | ||||||
内容記述タイプ | Other | |||||
内容記述 | We consider the problem of characterizing the smooth, isometric deformations of a planar material region identified with an open, connected subset D of two-dimensional Euclidean point space E2 into a surface S in three-dimensional Euclidean point space E3. To be isometric, such a deformation must preserve the length of every possible arc of ma- terial points on D. Characterizing the curves of zero principal curvature of S is of major importance. After establishing this characterization, we introduce a special curvilinear co- ordinate system in E2, based upon an à priori chosen pre-image form of the curves of zero principal curvature in D, and use that coordinate system to construct the most general iso- metric deformation of D to a smooth surface S. A necessary and sufficient condition for the deformation to be isometric is noted and alternative representations are given. Expressions for the curvature tensor and potentially nonvanishing principal curvature of S are derived. A general cylindrical deformation is developed and two examples of circular cylindrical and spiral cylindrical form are constructed. A strategy for determining any smooth isometric deformation is outlined and that strategy is employed to determine the general isometric de- formation of a rectangular material strip to a ribbon on a conical surface. Finally, it is shown that the representation established here is equivalent to an alternative previously established by Chen, Fosdick and Fried (J. Elast. 119:335–350, 2015). | |||||
出版者 | ||||||
出版者 | Springer | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0374-3535 | |||||
DOI | ||||||
関連タイプ | isIdenticalTo | |||||
識別子タイプ | DOI | |||||
関連識別子 | info:doi/10.1007/s10659-017-9637-2 | |||||
権利 | ||||||
権利情報 | © 2017 The Author(s). | |||||
関連サイト | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://link.springer.com/article/10.1007%2Fs10659-017-9637-2 | |||||
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 |