Port-Hamiltonian formulation and structure-preserving discretization of hyperelastic strings
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917614226243584 |
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| 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 |