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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 Flamant solution ： ウィキペディア英語版 Flamant solution The Flamant solution provides expressions for the stresses and displacements in a linear elastic wedge loaded by point forces at its sharp end. This solution was developed by A. Flamant 〔A. Flamant. (1892). ''Sur la répartition des pressions dans un solide rectangulaire chargé transversalement.'' Compte. Rendu. Acad. Sci. Paris, vol. 114, p. 1465.〕 in 1892 by modifying the three-dimensional solution of Boussinesq. The stresses predicted by the Flamant solution are (in polar coordinates) :$$ \begin \sigma_ & = \frac + \frac \\ \sigma_ & = 0 \\ \sigma_ & = 0 \end where $C\_1,\; C\_3$ are constants that are determined from the boundary conditions and the geometry of the wedge (i.e., the angles $\backslash alpha,\backslash beta$) and satisfy :$$ \begin F_1 & + 2\int_^ (C_1\cos\theta + C_3\sin\theta)\,\cos\theta\, d\theta = 0 \\ F_2 & + 2\int_^ (C_1\cos\theta + C_3\sin\theta)\,\sin\theta\, d\theta = 0 \end where $F\_1,F\_2$ are the applied forces. The wedge problem is ''self-similar'' and has no inherent length scale. Also, all quantities can be expressed in the separated-variable form $\backslash sigma\; =\; f(r)g(\backslash theta)$. The stresses vary as $(1/r)$. == Forces acting on a half-plane == For the special case where $\backslash alpha\; =\; -\backslash pi$, $\backslash beta\; =\; 0$, the wedge is converted into a half-plane with a normal force and a tangential force. In that case :$$ C_1 = - \frac,\quad C_3 = -\frac Therefore the stresses are :$$ \begin \sigma_ & = -\frac (F_1\cos\theta + F_2\sin\theta) \\ \sigma_ & = 0 \\ \sigma_ & = 0 \end and the displacements are (using Michell's solution) :$$ \begin u_r & = -\cfrac\left() \end The $\backslash ln\; r$ dependence of the displacements implies that the displacement grows the further one moves from the point of application of the force (and is unbounded at infinity). This feature of the Flamant solution is confusing and appears unphysical. For a discussion of the issue see (http://imechanica.org/node/319 ). 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「Flamant solution」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.