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International audience; As an extension of safety factors, the Lack-Of-Knowledge theory is an answer to model validation problems in structural mechanics. We introduce a LOK operator for orthotropic elasticity problems. This refined model is illustrated on academic and industrial examples.; La théorie des méconnaissances répond au problème de la validation des modèles en mécanique des structures en étendant le concept de coefficient de sécurité. Dans cet article, nous introduisons une description par opérateur de méconnaissances pour traiter des problèmes d'élasticité anisotrope.

International audience; The validation of complex structural models - i.e. the assessment of their quality compared to an experimental reference - remains a major issue today. The true validation problem should be addressed through comparison of the model used classically - whether it is deterministic or not - with the complete reality. A tentative answer through the Lack-Of-Knowledge (LOK) theory was introduced in [1

International audience; This paper deals with the structural modeling of a family of similar, actual structures taking into account uncertainties and modeling errors. The concept of Lack Of Knowledge (LOK), first introduced in [1,2], consists in globalizing the various sources of errors on the substructure using internal variables, called the LOK variables, defined over an interval whose upper and lower bounds follow probabilistic laws. From these basic LOK, we can derive for the whole structure the effective LOK for a quantity of interest a, resulting in an interval with stochastic bounds that we can compare with experimental values. First, errors on the ”structural stiffness” have been considered [1,2,4]. Here we go further, extending the concept of LOK to modelize errors on applied forces, the mathematical framework being the same.

International audience; Concerning the quantification of the quality of a numerical model in comparison with an experimental reference, the theory of the Lack of Knowledge (LOK) consists in globalizing the various sources of errors on the substructure level using a scalar internal variable defined over an interval whose upper and lower bounds follow probabilistic laws. This paper is focused on the reduction of the LOKs of a actual structure from the aeronautical industry.; Dans le domaine de la quantification de la qualité d'un modèle numérique vis-à-vis d'une référence expérimentale, la théorie des méconnaissances permet de prendre en compte de façon globale les différentes sources d'erreur en associant à chaque sous-structure une variable interne scalaire contenue dans un intervalle dont les bornes sont des variables aléatoires. Nous présentons ici plus précisément la réduction des méconnaissances d'une structure réelle issue de l'industrie aérospatiale.

International audience; The concept of Lack Of Knowledge (LOK), first introduced in [1,2], combines probabilities with interval analysis [3]. The basic principle consists in globalizing the various sources of errors on the substructure level using a scalar internal variable, called the LOK variable, defined over an interval whose upper and lower bounds follow probabilistic laws. From these basic LOKs, we can derive for the whole structure the effective LOK for a quantity of interest a, resulting in an interval with stochastic bounds that we can compare with experimental values. In [4], we presented the first results of a strategy of using additional experimental information to reduce the LOKs, starting from an initial overestimated LOK level, given by experience or a priori knowledge. This paper is focused on the reduction of the LOKs of a actual, industrial structure from the European Aeronautic Defence and Space company; this real-case study shows the effectiveness of the strategy of reduction used.

International audience; The concept of Lack Of Knowledge (LOK) was first introduced in [1, 2]. The basic principle consists in globalizing the various sources of errors on the substructure level using a scalar internal variable, called the LOK variable, defined over an interval whose upper and lower bounds follow probabilistic laws. The question of the impact of the structural model with LOKs on the prediction of the structural response can then be addressed. By a rigorous propagation of the intervals and the probability laws associated to the bounds, the envelope of the possible actual responses is defined, resulting in an interval with stochastic bounds including the structural response of interest. The comparison between these intervals and the experimental values available results in a reduction process of the basic LOKs, which considers the experimental data as additional information. In [3], we presented the first results of this strategy of reduction, starting from an initial overestimated LOK level, given by experience or a priori knowledge. This paper is focused on the reduction of the LOKs of a actual, industrial structure from the EADS Space Transportation division; this real-case study shows the effectiveness of the strategy of reduction used.

International audience; The quantification of the quality of a structural mechanical model remains a major issue today, with the use of an increasing number of methods in order to validate a model in comparison with an experimental reference. This paper presents a new theory based on the concept of Lack of Knowledge combining convex uncertainty models with probabilistic features by introducing for each substructure two bounds of the strain energy as stochastic variables. A general strategy of reduction of the lack of knowledge is discussed and applied to academic as well as industrial cases.

International audience; The concept of Lack Of Knowledge (LOK) was introduced in a previous paper in order to describe uncertainties caused by phenomena which often cannot be described, even by a properly updated model. This new theory combines convex uncertainty models with probabilistic features by introducing for each substructure two bounds of the strain energy as stochastic variables. In this paper, we discuss a general strategy of reduction of the lacks of knowledge, which consists in selecting the most relevant tests to achieve this reduction.

International audience