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Stratégies de contrôle d'erreur en calcul de structures industrielles. Mise en oeuvre d'estimation d'erreur en quantité d'intérêt et d'adaptation de maillage.

Abstract : For linear problems, various methods exist to estimate the quality of the finite element solution. They generally lead to estimate a norm of the global error. But the choice of a global precision founded on a norm of the displacement is often complex because there is no quantitative direct link with an error on local mechanical quantities (called quantities of interest) having an interest for the engineer. The objective of this work is to develop and implement in Code_Aster a method of error estimation in quantity of interest for the industrial structural analysis.

A bibliographical study was conducted to draw up the state of the art in global and local error estimation methods and mesh adaptation techniques. The most relevant methods for industrial structural analysis were then selected.

Then, a comparison was lead in order to determine the relevance of the error in quantity of interest in an adaptive process compared to the error in the energy norm, a uniform refinement or a local refinement in the zone of interest. This study pointed out that the use of the error in
quantities of interest provides the best precision for a given number of elements: this strategy is the most relevant in a context of industrial structural analysis.

Taking into account the previous results, a method of error estimation in quantity of interest was developed and implemented in Code_Aster. This method is based on the fundamental relation of the error in quantity of interest and on a global explicit residual based error estimator. This estimator does not provide bounds of the error but an approached value, thus it is an error indicator. To estimate the error in quantity of interest, the resolution of a dual problem is necessary. The loadings of this problem, different for each quantity of interest considered, are produced for many quantities of interest (in particular for the Von Mises stress). The final computation of the error in quantity of interest, from primal computation and of dual computation is automatic. A quantity of interest for the estimation of the error on the stress intensity factors was also developed in 2D and 3D. Numerical examples showed the good behavior of this indicator to guide a process of mesh adaptation with various quantities of interest.

Lastly, the developed error control strategy was used, with Code_Aster, within the framework of studies of industrial structures. Two studies carried out at department AMA, EDF R&D are presented. The first consists in studying the Von Mises stress in a HP rotor, the second is interested in the vertical stress in the pins of a bolted assembly.
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https://tel.archives-ouvertes.fr/tel-00311947
Contributor : Josselin Delmas <>
Submitted on : Friday, August 22, 2008 - 8:23:18 PM
Last modification on : Tuesday, March 6, 2018 - 5:28:17 PM
Document(s) archivé(s) le : Thursday, June 3, 2010 - 6:46:32 PM

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  • HAL Id : tel-00311947, version 1

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CNRS | CEA | EDF

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Josselin Delmas. Stratégies de contrôle d'erreur en calcul de structures industrielles. Mise en oeuvre d'estimation d'erreur en quantité d'intérêt et d'adaptation de maillage.. Mécanique [physics.med-ph]. Université de Picardie Jules Verne, 2008. Français. ⟨tel-00311947⟩

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