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    Symbolic-Numeric Integration of the Dynamical Cosserat Equations

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    Type
    Conference Paper
    Authors
    Lyakhov, Dmitry cc
    Gerdt, Vladimir P.
    Weber, Andreas G.
    Michels, Dominik L.
    KAUST Department
    Visual Computing Center (VCC)
    Date
    2017-08-30
    Preprint Posting Date
    2017-04-05
    Online Publication Date
    2017-08-30
    Print Publication Date
    2017
    Permanent link to this record
    http://hdl.handle.net/10754/626006
    
    Metadata
    Show full item record
    Abstract
    We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.
    Citation
    Lyakhov DA, Gerdt VP, Weber AG, Michels DL (2017) Symbolic-Numeric Integration of the Dynamical Cosserat Equations. Lecture Notes in Computer Science: 301–312. Available: http://dx.doi.org/10.1007/978-3-319-66320-3_22.
    Sponsors
    The authors appreciate the insightful comments of the anonymous referees. This work has been partially supported by the King Abdullah University of Science and Technology (KAUST baseline funding), the Max Planck Center for Visual Computing and Communication (MPC-VCC) funded by Stanford University and the Federal Ministry of Education and Research of the Federal Republic of Germany (BMBF grants FKZ-01IMC01 and FKZ-01IM10001), the Russian Foundation for Basic Research (grant 16-01-00080) and the Ministry of Education and Science of the Russian Federation (agreement 02.a03.21.0008).
    Publisher
    Springer Nature
    Journal
    Computer Algebra in Scientific Computing
    Conference/Event name
    19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017
    DOI
    10.1007/978-3-319-66320-3_22
    arXiv
    1704.01309
    Additional Links
    https://link.springer.com/chapter/10.1007%2F978-3-319-66320-3_22
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-319-66320-3_22
    Scopus Count
    Collections
    Conference Papers; Visual Computing Center (VCC)

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