Upper error bounds on calculated outputs of interest for linear and nonlinear structural problems

Pierre Ladevèze

doi:10.1016/j.crme.2006.04.004

Upper error bounds on calculated outputs of interest for linear and nonlinear structural problems

Présenté par : Évariste Sanchez-Palencia

Pierre Ladevèze ^1,²

¹ LMT-Cachan, ENS-Cachan/CNRS/Paris 6 University, 61, avenue du Président Wilson, 94235 Cachan cedex, France
² EADS Foundation Chair Advanced Computational Structural Mechanics, France

Comptes Rendus. Mécanique, Volume 334 (2006) no. 7, pp. 399-407.

Résumé
Abstract

Bornes supérieures de l'erreur sur une quantité d'intérêt calculée par éléments finis en mécanique linéaire et non-linéaire des structures. La Note introduit de nouvelles bornes supérieures de l'erreur relative à une quantité d'intérêt calculée par éléments finis en mécanique linéaire et non-linéaire des structures. Sont considérés les problèmes en petites perturbations du type (visco)plastique sans adoucissement dans le cadre de la thermodynamique classique avec variables internes.

This Note introduces new strict upper error bounds on outputs of interest for linear as well as time-dependent nonlinear structural problems calculated by the finite element method. Small-displacement problems without softening, such as (visco)plasticity problems, are included through the standard thermodynamics framework involving internal state variables.

Reçu le : 2005-10-25
Accepté le : 2006-04-04
Publié le : 2006-06-22

DOI : 10.1016/j.crme.2006.04.004

Keywords: Computational solid mechanics, Verification, Output of interest, Constitutive relation error, Finite elements, Nonlinear mechanics
Mots-clés : Mécanique des solides numérique, Vérification, Quantité d'intérêt, Erreur en relation de comportement, Eléments finis, Non-linéaire

Affiliations des auteurs :

Pierre Ladevèze ^{1, 2}

¹ LMT-Cachan, ENS-Cachan/CNRS/Paris 6 University, 61, avenue du Président Wilson, 94235 Cachan cedex, France
² EADS Foundation Chair Advanced Computational Structural Mechanics, France

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Pierre Ladevèze. Upper error bounds on calculated outputs of interest for linear and nonlinear structural problems. Comptes Rendus. Mécanique, Volume 334 (2006) no. 7, pp. 399-407. doi : 10.1016/j.crme.2006.04.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.04.004/

Bibliographie
Cité par

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[3] H.J. Greenberg The determination of upper and lower bounds for the solution of Dirichlet problem, J. Math. Phys., Volume 27 (1948), pp. 161-182

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[6] P. Ladevèze Nonlinear Structural Mechanics—New Approaches and Non-Incremental Methods of Calculation, Springer-Verlag, New York, 1998

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Ludovic Chamoin; Pierre Ladevèze A non-intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems, Computer Methods in Applied Mechanics and Engineering, Volume 197 (2008) no. 9-12, pp. 994-1014 | DOI:10.1016/j.cma.2007.09.021 | Zbl:1169.74357
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Cité par 28 documents. Sources : Crossref, zbMATH

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