[Sur la théorie des méconnaissances en mécanique des structures]
La validation de modèles structuraux complexes – c'est-à-dire la vérification de leur qualité vis-à-vis d'une référence expérimentale – demeure un verrou scientifique fort. Le véritable problème de validation consiste à comparer la réponse du modèle numérique, qu'il soit déterministe ou pas, avec la réponse de toutes les structures réelles, dans tous les environnements possible. Un premier élément de réponse à ce problème a été introduit via la théorie des méconnaissances au LMT-Cachan. Afin de « modéliser l'inconnu », cette théorie prend en compte toutes les incertitudes, en incluant les erreurs de modèles, à travers le concept de méconnaissances de base. Dans le cet article, on introduit des méconnaissances de base sur les excitations (amplitude et direction). Ces méconnaissances de base sont ensuite propagées à travers le modèle mécanique afin de déterminer des intervalles dont les bornes sont probabilistes, contenant une quantité d'intérêt (contrainte ou déplacement). Ensuite une stratégie de réduction des méconnaissances de base par apport d'information expérimentale est présentée sur un exemple académique.
Today, the validation of complex structural models – i.e. the assessment of their quality compared to an experimental reference – remains a major issue. Strictly speaking, the validation problem consists in comparing the response of the numerical model (whether deterministic or stochastic) with complete reality. A first answer to this problem, using Lack-Of-Knowledge (LOK) theory, was introduced at LMT-Cachan. This theory is an attempt to “model the unknown” by taking all the sources of uncertainties, including modeling errors, into account through the concept of basic LOKs. In this article, we introduce basic LOKs associated with both the amplitudes and directions of excitations. These basic LOKs are propagated rigorously throughout the mechanical model in order to determine intervals (with stochastic bounds) within which lies a given quantity of interest (stress or displacement). Then, we introduce a strategy for the reduction of lack of knowledge, which we illustrate through an academic example.
Mot clés : Méconnaissances, Validation, Incertitudes, Problèmes inverses
@article{CRMECA_2010__338_7-8_424_0,
author = {Fran\c{c}ois Louf and Paul Enjalbert and Pierre Ladev\`eze and Thierry Romeuf},
title = {On lack-of-knowledge theory in structural mechanics},
journal = {Comptes Rendus. M\'ecanique},
pages = {424--433},
publisher = {Elsevier},
volume = {338},
number = {7-8},
year = {2010},
doi = {10.1016/j.crme.2010.07.012},
language = {en},
}
TY - JOUR AU - François Louf AU - Paul Enjalbert AU - Pierre Ladevèze AU - Thierry Romeuf TI - On lack-of-knowledge theory in structural mechanics JO - Comptes Rendus. Mécanique PY - 2010 SP - 424 EP - 433 VL - 338 IS - 7-8 PB - Elsevier DO - 10.1016/j.crme.2010.07.012 LA - en ID - CRMECA_2010__338_7-8_424_0 ER -
François Louf; Paul Enjalbert; Pierre Ladevèze; Thierry Romeuf. On lack-of-knowledge theory in structural mechanics. Comptes Rendus. Mécanique, Volume 338 (2010) no. 7-8, pp. 424-433. doi : 10.1016/j.crme.2010.07.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.07.012/
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