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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Compatibility (mechanics) ： ウィキペディア英語版 Compatibility (mechanics) In continuum mechanics, a compatible deformation (or strain) tensor field in a body is that ''unique'' field that is obtained when the body is subjected to a continuous, single-valued, displacement field. Compatibility is the study of the conditions under which such a displacement field can be guaranteed. Compatibility conditions are particular cases of integrability conditions and were first derived for linear elasticity by Barré de Saint-Venant in 1864 and proved rigorously by Beltrami in 1886.〔C Amrouche, PG Ciarlet, L Gratie, S Kesavan, On Saint Venant's compatibility conditions and Poincaré's lemma, C. R. Acad. Sci. Paris, Ser. I, 342 (2006), 887-891. 〕 In the continuum description of a solid body we imagine the body to be composed of a set of infinitesimal volumes or material points. Each volume is assumed to be connected to its neighbors without any gaps or overlaps. Certain mathematical conditions have to be satisfied to ensure that gaps/overlaps do not develop when a continuum body is deformed. A body that deforms without developing any gaps/overlaps is called a compatible body. Compatibility conditions are mathematical conditions that determine whether a particular deformation will leave a body in a compatible state.〔Barber, J. R., 2002, Elasticity - 2nd Ed., Kluwer Academic Publications.〕 In the context of infinitesimal strain theory, these conditions are equivalent to stating that the displacements in a body can be obtained by integrating the strains. Such an integration is possible if the Saint-Venant's tensor (or incompatibility tensor) $\backslash boldsymbol(\backslash boldsymbol)$ vanishes in a simply-connected body〔N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity. Leyden: Noordhoff Intern. Publ., 1975.〕 where $\backslash boldsymbol$ is the infinitesimal strain tensor and :$$ \boldsymbol := \boldsymbol\times(\boldsymbol\times\boldsymbol) ~. For finite deformations the compatibility conditions take the form :$$ \boldsymbol :=\boldsymbol\times\boldsymbol = \boldsymbol where $\backslash boldsymbol$ is the deformation gradient. == Compatibility conditions for infinitesimal strains == The compatibility conditions in linear elasticity are obtained by observing that there are six strain-displacement relations that are functions of only three unknown displacements. This suggests that the three displacements may be removed from the system of equations without loss of information. The resulting expressions in terms of only the strains provide constraints on the possible forms of a strain field. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Compatibility (mechanics)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.