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Theses

Couplage éléments finis et méthode de transformation probaliste

Abstract : The modeling of mechanical systems can be defined as the mathematical idealization of the physical phenomena controlling it. This implies to define the input variables (geometrical parameters, loading conditions...) and the output variables (displacements, stresses...), allowing to understand the evolution of the system. The behavior models are more and more complex and the difficulty lies is the identification of the input parameters. As a matter of fact, we cannot admit to use the deterministic models where only the average parameters are considered, because it generally leads to wrong representation of the reality. Hence, it is interesting to introduce the uncertainties in the parameter evaluation and to consider their variability. The fundamental issue of probabilistic studies is therefore to take into account the uncertain character and the spatial variability of the parameters. The reliability methods have for main objective the determination of the structural safety level, based on some assumptions related to the uncertainties, and by defining the state of failure. Therefore, the failure probability can be evaluated along the structure life span and consequently, the design can be verified with respect to safety considerations. The application of probabilistic methods in design requires the use of efficient tools to evaluate the reliability of the considered structure. When the mechanical behavior is given by explicit models, the reliability analysis becomes easy, due to the large number of available methods which can be efficiently used. However, when the mechanical model is numerical (finite element method for example), a method allowing the combination of mechanical and probability models must be applied: it is the goal of mechanical-reliability coupling. The mechanical-reliability coupling is defined by the combination of finite element models and reliability algorithms, in such a way that the solution can be efficiently obtained. In this kind of approach, the reliability code drives the finite element analysis procedures and ensures the convergence. The objective of this thesis is therefore to analyze and to study the probabilistic response of mechanical systems with uncertain parameters. Contrary to other methods, the proposed technique couples the deterministic finite element method and the probabilistic transformation method, in order to evaluate the probability density function of the response, in a closed-form or in a semi-analytical form. To show the advantage of the proposed method, we have carried out different applications to cover several structural engineering fields: static, dynamic, reliability and optimization.
Mots-clés : mécanique matrice
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Submitted on : Friday, July 13, 2012 - 5:48:17 PM
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Seifedine Kadry. Couplage éléments finis et méthode de transformation probaliste. Mécanique [physics.med-ph]. Université Blaise Pascal - Clermont-Ferrand II, 2007. Français. ⟨NNT : 2007CLF21747⟩. ⟨tel-00717847⟩

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