大変形を伴う梁のダイナミクスと変分的積分法による数値解析

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  • Dynamics of flexible beams undergoing large deformations and its numerical analysis based on variational integrators

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<p>In conjunction with analysis of flexible body dynamics such as a beam undergoing large deformation, it has been a crucial technical issue that such flexible body dynamics requires a long time stability in numerical integration, while the conventional scheme, for instance, Backward differential formula (BDF), which is known as a stiffly stable scheme, sometimes leads to serious numerical errors in a long-time energy computation. In this paper, we consider a flexible beam undergoing large deformations by employing Simo’s model and show how a variational integrator can be developed by discrete Hamilton’s principle (see Marsden and West), which is known as a structure-preserving scheme with a long-time energy stability. In particular, we examine the variational integrator to compare with BDF and Runge-Kutta method. Finally, we show the validity of the variational integrator in a long-time energy stability by comparing with other schemes.</p>

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