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Importance and Effectiveness of Representing the Shapes of Cosserat Rods and Framed Curves as Paths in the Special Euclidean Algebra
https://oist.repo.nii.ac.jp/records/455
https://oist.repo.nii.ac.jp/records/4556a786f79-e98b-4a3f-979d-b125465c2509
名前 / ファイル | ライセンス | アクション |
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Giusteri-Fried2018_Article_ImportanceAndEffectivenessOfRe (2.6 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 | 2018-07-26 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Importance and Effectiveness of Representing the Shapes of Cosserat Rods and Framed Curves as Paths in the Special Euclidean Algebra | |||||
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) |
Giusteri, Giulio G.
× Giusteri, Giulio G.× Fried, Eliot |
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書誌情報 |
en : Journal of Elasticity 巻 132, 号 1, p. 43-65, 発行日 2017-09-05 |
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抄録 | ||||||
内容記述タイプ | Other | |||||
内容記述 | We discuss how the shape of a special Cosserat rod can be represented as a path in the special Euclidean algebra. By shape we mean all those geometric features that are invariant under isometries of the three-dimensional ambient space. The representation of the shape as a path in the special Euclidean algebra is intrinsic to the description of the mechanical properties of a rod, since it is given directly in terms of the strain fields that stimulate the elastic response of special Cosserat rods. Moreover, such a representation leads naturally to discretization schemes that avoid the need for the expensive reconstruction of the strains from the discretized placement and for interpolation procedures which introduce some arbitrariness in popular numerical schemes. Given the shape of a rod and the positioning of one of its cross sections, the full placement in the ambient space can be uniquely reconstructed and described by means of a base curve endowed with a material frame. By viewing a geometric curve as a rod with degenerate point-like cross sections, we highlight the essential difference between rods and framed curves, and clarify why the family of relatively parallel adapted frames is not suitable for describing the mechanics of rods but is the appropriate tool for dealing with the geometry of curves. | |||||
出版者 | ||||||
出版者 | Springer Netherlands | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0374-3535 | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 1573-2681 | |||||
DOI | ||||||
関連タイプ | isIdenticalTo | |||||
識別子タイプ | DOI | |||||
関連識別子 | info:doi/10.1007/s10659-017-9656-z | |||||
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%2Fs10659-017-9656-z | |||||
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 |