A logarithmic complexity floating frame of reference formulation with interpolating splines for articulated multi-flexible-body dynamics |
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| Institution: | 1. Computational Dynamics Laboratory, Department of Mechanical Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA;2. The Center for Modeling, Simulation, and Imaging in Medicine, Department of Mechanical Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA;1. School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;2. The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;1. Instituto Nacional de Técnica Aeroespacial (INTA), Spain;2. GSMA, UMR 7331, CNRS, Université de Reims Champagne-Ardenne, Reims 51687, France;3. LATMOS, Université de Versailles-St-Quentin, Guyancourt, France;1. Berlin Joint EPR Laboratory, Freie Universität Berlin, Fachbereich Physik, Berlin, Germany;2. Charité - Universitätsmedizin Berlin, Department of Dermatology, Venerology and Allergology, Center of Experimental and Applied Cutaneous Physiology, Berlin, Germany;3. Freie Universität Berlin, Institut für Chemie und Biochemie, Berlin, Germany |
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| Abstract: | An interpolating spline-based approach is presented for modeling multi-flexible-body systems in the divide-and-conquer (DCA) scheme. This algorithm uses the floating frame of reference formulation and piecewise spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body system undergoing large rotations and translations. The new approach is compared with the flexible DCA (FDCA) that uses the assumed modes method 1]. The FDCA, in many cases, must resort to sub-structuring to accurately model the deformation of the system. We demonstrate, through numerical examples, that the interpolating spline-based approach is comparable in accuracy and superior in efficiency to the FDCA. The present approach is appropriate for modeling flexible mechanisms with thin 1D bodies undergoing large rotations and translations, including those with irregular shapes. As such, the present approach extends the current capability of the DCA to model deformable systems. The algorithm retains the theoretical logarithmic complexity inherent in the DCA when implemented in parallel. |
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| Keywords: | Multi-flexible-body systems Logarithmic complexity Divide-and-conquer algorithm Interpolating splines |
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