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

Presented by: 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.

Abstract
Résumé

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.

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.

Received: 2005-10-25
Accepted: 2006-04-04
Published online: 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

Author's affiliations:

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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     author = {Pierre Ladev\`eze},
     title = {Upper error bounds on calculated outputs of interest for linear and nonlinear structural problems},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {399--407},
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     volume = {334},
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     year = {2006},
     doi = {10.1016/j.crme.2006.04.004},
     language = {en},
}

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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/

References
Cited by

[1] I. Babuška; T. Strouboulis The Finite Element Method and Its Reliability, Oxford Univ. Press, Oxford, UK, 2001

[2] P. Ladevèze; I.-P. Pelle Mastering Calculations in Linear and Nonlinear Mechanics, Springer-Verlag, New York, 2004

[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

[4] K. Washizu Bounds for solutions of boundary value problems in elasticity, J. Math. Phys., Volume 32 (1953), pp. 117-128

[5] P. Ladevèze, L. Chamoin, E. Florentin, Strict upper and lower bounds of outputs of interest for linear and nonlinear structural problems, Plenary lecture, ADMOS (Barcelona), 2005

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

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