Symbolic-Numeric Integration of the Dynamical Cosserat Equations

• Published in: Computer Algebra in Scientific Computing Vol. 10490; pp. 301 - 312
• Main Authors: Lyakhov, Dmitry A., Gerdt, Vladimir P., Weber, Andreas G., Michels, Dominik L.
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2017; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Analytical solution; Cosserat rods; Dynamic equations; Exponential integration; Generalized; Kinematic equations; method; Symbolic computation
• ISBN: 3319663194; 9783319663197
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-66320-3_22

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-method illustrating the computational efficiency of our approach for problems in structural mechanics.