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A port-Hamiltonian formulation of flexible structures. Modelling and structure-preserving finite element discretization

Brugnoli, Andrea. A port-Hamiltonian formulation of flexible structures. Modelling and structure-preserving finite element discretization. PhD, Automatique, ISAE-SUPAERO, 2020, 305 p.

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Official URL: http://www.theses.fr/2020ESAE0032

Abstract

Despite the large literature on port-Hamiltonian (pH) formalism, elasticity problems in higher geometrical dimensions have almost never been considered. This work establishes the connection between port-Hamiltonian distributed systems and elasticity problems. The originality resides in three major contributions. First, the novel pH formulation of plate models and coupled thermoelastic phenomena is presented. The use of tensor calculus is mandatory for continuum mechanical models and the inclusion of tensor variables is necessary to obtain an equivalent and intrinsic, i.e. coordinate free, pH description. Second, a finite element based discretization technique, capable of preserving the structure of the infinite-dimensional problem at a discrete level, is developed and validated. The discretization of elasticity problems requires the use of non-standard finite elements. Nevertheless, the numerical implementation is performed thanks to well-established open-source libraries, providing external users with an easy to use tool for simulating flexible systems in pH form. Third, flexible multibody systems are recast in pH form by making use of a floating frame description valid under small deformations assumptions. This reformulation include all kinds of linear elastic models and exploits the intrinsic modularity of pH systems.

Item Type:PhD Thesis
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Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
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Research Director:
Alazard, Daniel and Pommier-Budinger, Valérie
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Deposited On:17 Sep 2021 11:47

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