OATAO - Open Archive Toulouse Archive Ouverte Open Access Week

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

Brugnoli, Andrea and Alazard, Daniel and Pommier-Budinger, Valérie and Matignon, Denis Port-Hamiltonian formulation and symplectic discretization of plate models. Part II: Kirchhoff model for thin plates. ( In Press: 2019) Applied Mathematical Modelling. 1-21. ISSN 0307-904X

[img] (Document in English)

PDF (Publisher's version) - Depositor and staff only - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
1MB

Official URL: https://doi.org/10.1016/j.apm.2019.04.036

Abstract

The mechanical model of a thin plate with boundary control and observation is presented as a port-Hamiltonian system (pHs), 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) 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.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Laboratory name:
Statistics:download
Deposited By: Denis Matignon
Deposited On:07 Jun 2019 13:24

Repository Staff Only: item control page