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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 Dynamic relaxation ： ウィキペディア英語版 Dynamic relaxation Dynamic relaxation is a numerical method, which, among other things, can be used do "form-finding" for cable and fabric structures. The aim is to find a geometry where all forces are in equilibrium. In the past this was done by direct modelling, using hanging chains and weights (see Gaudi), or by using soap films, which have the property of adjusting to find a "minimal surface". The dynamic relaxation method is based on discretizing the continuum under consideration by lumping the mass at nodes and defining the relationship between nodes in terms of stiffness (see also the finite element method). The system oscillates about the equilibrium position under the influence of loads. An iterative process is followed by simulating a pseudo-dynamic process in time, with each iteration based on an update of the geometry,〔W J LEWIS, ''TENSION STRUCTURES: Form and behaviour'', London, Telford, 2003〕 similar to Leapfrog integration and related to Velocity Verlet integration. ==Main equations use== Considering Newton's second law of motion (force is mass multiplied by acceleration) in the $x$ direction at the $i$th node at time $t$: :$R\_(t)=M\_A\_(t)\backslash frac\backslash left(t+\; \backslash frac\; \backslash right)\; =\; V\_\; \backslash left(t-\; \backslash frac\; \backslash right)\; +\; \backslash fracR\_(t)$ :$X\_i(t+\; \backslash Delta\; t)=X\_i(t)+\backslash Delta\; t\; \backslash times\; V\_\; \backslash left(t+\; \backslash frac\; \backslash right)$ Where: :$\backslash Delta\; t$ is the time interval between two updates. By the principle of equilibrium of forces, the relationship between the residuals and the geometry can be obtained: :$R\_(t+\; \backslash Delta\; t)=P\_(t+\; \backslash Delta\; t)+\backslash sum\; \backslash frac\; \backslash times\; (X\_j(t+\; \backslash Delta\; t)-X\_i(t+\; \backslash Delta\; t))$ where: :$P$ is the applied load component :$T$ is the tension in link $m$ between nodes $i$ and $j$ :$l$ is the length of the link. The sum must cover the forces in all the connections between the node and other nodes. By repeating the use of the relationship between the residuals and the geometry, and the relationship between the geometry and the residual, the pseudo-dynamic process is simulated. 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「Dynamic relaxation」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.