Authors

Tobias Thoma, Paul Kotyczka

Abstract

In this article, we present the port-Hamiltonian representation, the structure preserving discretization and the resulting finite-dimensional state space model of one-dimensional filaments based on a mixed finite element formulation. Due to the fact that the equations of motion of a filamentous body are based on the theory of geometrically nonlinear mechanical systems, the port-Hamiltonian formulation is expressed by means of its co-energy (effort) variables. The resulting port-Hamiltonian state space model features a quadratic Hamiltonian and the nonlinearity is reflected in the state dependence of its interconnection matrix. Numerical experiments generated with FEniCS illustrate the properties of the resulting finite element models.

Keywords

port-Hamiltonian systems; mixed finite elements; geometrically nonlinear mechanical systems; structure preserving discretization; filamentous bodies

Citation

  • Journal: IFAC-PapersOnLine
  • Year: 2022
  • Volume: 55
  • Issue: 30
  • Pages: 353–358
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.ifacol.2022.11.078
  • Note: 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022- Bayreuth, Germany, September 12-16, 2022

BibTeX

@article{Thoma_2022,
  title={{Port-Hamiltonian FE models for filaments}},
  volume={55},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2022.11.078},
  number={30},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Thoma, Tobias and Kotyczka, Paul},
  year={2022},
  pages={353--358}
}

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References