Symbolic-Numeric Integration of the Dynamical Cosserat Equations

Dmitry A. Lyakhov, Vladimir P. Gerdt, Andreas Weber, and Dominik L. Michels
In proceedings of Computer Algebra in Scientific Computing (CASC 2017), Beijing, China, pages 301-312, Spring, 2017
 

Abstract

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear par- tial 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 sys- tem 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 general- ized α-method illustrating the computational efficiency of our approach for problems in structural mechanics.

Bibtex

@INPROCEEDINGS{LyakhovGerdtWeberMichels2017,
     author = {Lyakhov, Dmitry A. and Gerdt, Vladimir P. and Weber, Andreas and Michels, Dominik L.},
      pages = {301--312},
      title = {Symbolic-Numeric Integration of the Dynamical Cosserat Equations},
  booktitle = {Computer Algebra in Scientific Computing (CASC 2017)},
     series = {Lecture Notes in Computer Science},
     volume = {10490},
       year = {2017},
  publisher = {Spring},
   location = {Beijing, China},
   abstract = {We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat
               equations, a system of nonlinear par- tial 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 sys- tem 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
               general- ized α-method illustrating the computational efficiency of our approach for problems in
               structural mechanics.},
        url = {http://link.springer.com/10.1007/978-3-319-45641-6},
        doi = {10.1007/978-3-319-66320-3 22}
}