Port-Hamiltonian formulation and structure-preserving discretization of hyperelastic strings

Fuente: arXiv
Enregistré dans:
Détails bibliographiques
Auteurs principaux: Kinon, Philipp L., Thoma, Tobias, Betsch, Peter, Kotyczka, Paul
Format: Preprint
Publié: 2023
Sujets:
Accès en ligne:
Tags: Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
_version_ 1866917614226243584
author Kinon, Philipp L.
Thoma, Tobias
Betsch, Peter
Kotyczka, Paul
author_facet Kinon, Philipp L.
Thoma, Tobias
Betsch, Peter
Kotyczka, Paul
contents Port-Hamiltonian (PH) systems provide a framework for modeling, analysis and control of complex dynamical systems, where the complexity might result from multi-physical couplings, non-trivial domains and diverse nonlinearities. A major benefit of the PH representation is the explicit formulation of power interfaces, so-called ports, which allow for a power-preserving interconnection of subsystems to compose flexible multibody systems in a modular way. In this work, we present a PH representation of geometrically exact strings with nonlinear material behaviour. Furthermore, using structure-preserving discretization techniques a corresponding finite-dimensional PH state space model is developed. Applying mixed finite elements, the semi-discrete model retains the PH structure and the ports (pairs of velocities and forces) on the discrete level. Moreover, discrete derivatives are used in order to obtain an energy-consistent time-stepping method. The numerical properties of the newly devised model are investigated in a representative example. The developed PH state space model can be used for structure-preserving simulation and model order reduction as well as feedforward and feedback control design.
format Preprint
id arxiv_https___arxiv_org_abs_2304_10957
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Port-Hamiltonian formulation and structure-preserving discretization of hyperelastic strings
Kinon, Philipp L.
Thoma, Tobias
Betsch, Peter
Kotyczka, Paul
Dynamical Systems
Computational Engineering, Finance, and Science
Systems and Control
Port-Hamiltonian (PH) systems provide a framework for modeling, analysis and control of complex dynamical systems, where the complexity might result from multi-physical couplings, non-trivial domains and diverse nonlinearities. A major benefit of the PH representation is the explicit formulation of power interfaces, so-called ports, which allow for a power-preserving interconnection of subsystems to compose flexible multibody systems in a modular way. In this work, we present a PH representation of geometrically exact strings with nonlinear material behaviour. Furthermore, using structure-preserving discretization techniques a corresponding finite-dimensional PH state space model is developed. Applying mixed finite elements, the semi-discrete model retains the PH structure and the ports (pairs of velocities and forces) on the discrete level. Moreover, discrete derivatives are used in order to obtain an energy-consistent time-stepping method. The numerical properties of the newly devised model are investigated in a representative example. The developed PH state space model can be used for structure-preserving simulation and model order reduction as well as feedforward and feedback control design.
title Port-Hamiltonian formulation and structure-preserving discretization of hyperelastic strings
topic Dynamical Systems
Computational Engineering, Finance, and Science
Systems and Control
url https://arxiv.org/abs/2304.10957