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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 Unit dummy force method ： ウィキペディア英語版 Unit dummy force method The Unit dummy force method provides a convenient means for computing displacements in structural systems. It is applicable for both linear and non-linear material behaviours as well as for systems subject to environmental effects, and hence more general than Castigliano's second theorem. ==Discrete systems== Consider a discrete system such as trusses, beams or frames having members interconnected at the nodes. Let the consistent set of members' deformations be given by $\backslash mathbf\_$, which can be computed using the member flexibility relation. These member deformations give rise to the nodal displacements $\backslash mathbf\_$, which we want to determine. We start by applying ''N'' virtual nodal forces $\backslash mathbf^$ *_ , one for each wanted ''r'', and find the virtual member forces $\backslash mathbf^$ *_ that are in equilibrium with $\backslash mathbf^$ *_ : :$\backslash mathbf^$ *_ = \mathbf_ \mathbf^ *_ \qquad \qquad \qquad \mathrm In the case of a statically indeterminate system, matrix B is not unique because the set of $\backslash mathbf^$ *_ that satisfies nodal equilibrium is infinite. It can be computed as the inverse of the nodal equilibrium matrix of any primary system derived from the original system. Imagine that internal and external virtual forces undergo, respectively, the real deformations and displacements; the virtual work done can be expressed as: * External virtual work: $\backslash mathbf^\; \backslash mathbf$ * Internal virtual work: $\backslash mathbf^\; \backslash mathbf$ According to the virtual work principle, the two work expressions are equal: :$\backslash mathbf^\; \backslash mathbf\; =\; \backslash mathbf^\; \backslash mathbf$ Substitution of (1) gives :$\backslash mathbf^\; \backslash mathbf\; =\; \backslash mathbf^\; \backslash mathbf^\; \backslash mathbf$ Since $\backslash mathbf^$ contains arbitrary virtual forces, the above equation gives :$\backslash mathbf\; =\; \backslash mathbf^\; \backslash mathbf\; \backslash qquad\; \backslash qquad\; \backslash qquad\; \backslash mathrm$ It is remarkable that the computation in (2) does not involve any integration regardless of the complexity of the systems, and that the result is unique irrespective of the choice of primary system for B. It is thus far more convenient and general than the classical form of the dummy unit load method, which varies with the type of system as well as with the imposed external effects. On the other hand, it is important to note that Eq.(2) is for computing displacements or rotations of the nodes only. This is not a restriction because we can make any point into a node when desired. Finally, the name unit load arises from the interepretation that the coefficients $B\_$ in matrix B are the member forces in equilibrium with the unit nodal force $R^$ *_j = 1 , by virtue of Eq.(1). 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「Unit dummy force method」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.