Journal
APPLIED MATHEMATICAL MODELLING
Volume 75, Issue -, Pages 940-960Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2019.04.035
Keywords
Port-Hamiltonian systems; Mindlin-Reissner plate; Partitioned Finite Element Method; Geometric spatial discretization; Boundary control
Funding
- French National Research Agency (ANR) [ANR-16-CE92-0028]
- Deutsche Forschungsgemeinschaft (DFG)
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The port-Hamiltonian formulation is a powerful method for modeling and interconnecting systems of different natures. In this paper, the port-Hamiltonian formulation in tensorial form of a thick plate described by the Mindlin-Reissner model is presented. Boundary control and observation are taken into account. Thanks to tensorial calculus, it can be seen that the Mindlin plate model mimics the interconnection structure of its one-dimensional counterpart, i.e. the Timoshenko beam. The Partitioned Finite Element Method (PFEM) is then extended to both the vectorial and tensorial formulations in order to obtain a suitable, i.e. structure-preserving, finite-dimensional port-Hamiltonian system (PHs), which preserves the structure and properties of the original distributed parameter system. Mixed boundary conditions are finally handled by introducing some algebraic constraints. Numerical examples are finally presented to validate this approach. (C) 2019 Elsevier Inc. All rights reserved.
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