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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 Stress functions ： ウィキペディア英語版 Stress functions In linear elasticity, the equations describing the deformation of an elastic body subject only to surface forces on the boundary are (using index notation) the equilibrium equation: :$\backslash sigma\_=0\backslash ,$ where $\backslash sigma$ is the stress tensor, and the Beltrami-Michell compatibility equations: :$\backslash sigma\_+\backslash frac\backslash sigma\_=0$ A general solution of these equations may be expressed in terms the Beltrami stress tensor. Stress functions are derived as special cases of this Beltrami stress tensor which, although less general, sometimes will yield a more tractable method of solution for the elastic equations. == Beltrami stress functions == It can be shown that a complete solution to the equilibrium equations may be written as :$\backslash sigma=\backslash nabla\; \backslash times\; \backslash nabla\; \backslash times\; \backslash Phi$ Using index notation: :$\backslash sigma\_=\backslash varepsilon\_\backslash varepsilon\_\backslash Phi\_$ : + \frac -2\frac |                |$\backslash sigma\_$ =-\frac -\frac +\frac +\frac |- |$\backslash sigma\_y$ = \frac +\frac -2\frac |                |$\backslash sigma\_$ =-\frac -\frac +\frac +\frac |- |$\backslash sigma\_z$ = \frac +\frac -2\frac |                |$\backslash sigma\_$ =-\frac -\frac +\frac +\frac |} where $\backslash Phi\_$ is an arbitrary second-rank tensor field that is continuously differentiable at least four times, and is known as the ''Beltrami stress tensor''.〔 Its components are known as Beltrami stress functions. $\backslash varepsilon$ is the Levi-Civita pseudotensor, with all values equal to zero except those in which the indices are not repeated. For a set of non-repeating indices the component value will be +1 for even permutations of the indices, and -1 for odd permutations. And $\backslash nabla$ is the Nabla operator 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「Stress functions」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.