Symbolic-Numeric Integration of the Dynamical Cosserat Equations

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}
}