Symbolic-Numeric Integration of the Dynamical Cosserat Equations

Dmitry Lyakhov, Vladimir P. Gerdt, Andreas G. Weber, Dominik L. Michels

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.
Original languageEnglish (US)
Title of host publicationComputer Algebra in Scientific Computing
PublisherSpringer Nature
Pages301-312
Number of pages12
ISBN (Print)9783319663197
DOIs
StatePublished - Aug 30 2017

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