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Theses

Modélisation asymptotique et analyse numérique d'un problème de couplage fluide-structure

Abstract : How are the stresses and the deformations of an inflated structure when external forces are applied to it. This thesis answers that question when the structure is a long and thin shell composed of two congruent cylindrical orthotropical membranes which are glued together along rigid straight or curved axes and inflated by a perfect gas.
From a mechanical modelling in linearized elasticity, we established a 3D variatinnal problem well posed in classical Sobolev spaces. Then we let the thickness parameter tend to zero, in order to obtain a 2D asymptotic model, well posed as long as the external forces check special properties -they are then called admissible forces- in spaces obtained by completion. We proved that the mean value in the thickness of the 3D solution strongly tends to the solution of the 2D asymptotic problem. We also identified sufficient conditions of admissibility.
The numerical analysis showed that the error is a priori estimated in the energy norm. This, as confirmed by numerical simulations, creates problems as far as displacements are concerned, but is satisfying from the stresses point of view.
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https://tel.archives-ouvertes.fr/tel-00131977
Contributor : Cécile Poutous <>
Submitted on : Monday, February 19, 2007 - 6:08:24 PM
Last modification on : Tuesday, February 2, 2021 - 2:54:04 PM
Long-term archiving on: : Wednesday, April 7, 2010 - 2:48:37 AM

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  • HAL Id : tel-00131977, version 1

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Cécile Poutous. Modélisation asymptotique et analyse numérique d'un problème de couplage fluide-structure. Mathématiques [math]. Université de Pau et des Pays de l'Adour, 2006. Français. ⟨tel-00131977⟩

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