Port-Hamiltonian formulation and symplectic discretization of plate models Part II: Kirchhoff model for thin plates

Authors

Andrea Brugnoli, Daniel Alazard, Valérie Pommier-Budinger, Denis Matignon

Abstract

The mechanical model of a thin plate with boundary control and observation is presented as a port-Hamiltonian system (PHs 1 1 PHs stands for port-Hamiltonian systems. ), both in vectorial and tensorial forms: the Kirchhoff-Love model of a plate is described by using a Stokes-Dirac structure and this represents a novelty with respect to the existing literature. This formulation is carried out both in vectorial and tensorial forms. Thanks to tensorial calculus, this model is found to mimic the interconnection structure of its one-dimensional counterpart, i.e. the Euler-Bernoulli beam. The Partitioned Finite Element Method (PFEM 2 2 PFEM stands for partitioned finite element method. ) is then extended to obtain a suitable, i.e. structure-preserving, weak form. The discretization procedure, performed on the vectorial formulation, leads to a finite-dimensional port-Hamiltonian system. This part II of the companion paper extends part I, dedicated to the Mindlin model for thick plates. The thin plate model comes along with additional difficulties, because of the higher order of the differential operator under consideration.

Keywords

Port-Hamiltonian systems; Kirchhoff plate; Partitioned Finite Element Method; Geometric spatial discretization; Boundary control

Citation

• Journal: Applied Mathematical Modelling
• Year: 2019
• Volume: 75
• Issue:
• Pages: 961–981
• Publisher: Elsevier BV
• DOI: 10.1016/j.apm.2019.04.036

BibTeX

@article{Brugnoli_2019,
  title={{Port-Hamiltonian formulation and symplectic discretization of plate models Part II: Kirchhoff model for thin plates}},
  volume={75},
  ISSN={0307-904X},
  DOI={10.1016/j.apm.2019.04.036},
  journal={Applied Mathematical Modelling},
  publisher={Elsevier BV},
  author={Brugnoli, Andrea and Alazard, Daniel and Pommier-Budinger, Valérie and Matignon, Denis},
  year={2019},
  pages={961--981}
}

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