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MODELISATION MATHEMATIQUE ET SIMULATION NUMERIQUE DU DRAPE D'UN TEXTILE

Abstract : The purpose of this work is to study the
deformation of a fabric over a two- or three-dimensional obstacle and
submitted to its own weight.
In the first part, we establish the general equilibrium equations
and we introduce two mathematical models which describe the fabric drape.
The first model is a nonlinear membrane one, the mathematical analysis of
which leads to the computation of the quasi-convex envelope of the
associated energy density. The second model is a nonlinear membrane-flexion
model and is obtained when adding a regularising term to a non-coercive
energy functional. Using the techniques of the Calculus of Variations, we
prove the existence of at least one solution for this minimisation model.
Finally, we prove an existence result for the three-dimensional fabric drape
problem.
The second part is devoted to the numerical analysis of the
different models which have been built in the first part. We use a descent
iterative method coupled with a multigrid one in order to accelerate the
convergence of the algorithm. We prove that the discrete problem admits a
solution and prove the theoretical convergence of a subsequence of discrete
solutions to a solution of the continuous problem.
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Theses
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https://tel.archives-ouvertes.fr/tel-00001702
Contributor : Nadjombé Fare <>
Submitted on : Monday, September 16, 2002 - 4:32:03 PM
Last modification on : Tuesday, October 16, 2018 - 2:26:02 PM
Long-term archiving on: : Tuesday, September 11, 2012 - 6:00:09 PM

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  • HAL Id : tel-00001702, version 1

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Nadjombe Fare. MODELISATION MATHEMATIQUE ET SIMULATION NUMERIQUE DU DRAPE D'UN TEXTILE. Mathématiques [math]. Université de Haute Alsace - Mulhouse, 2002. Français. ⟨tel-00001702⟩

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