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Analyse modale des structures avec incertitudes par la méthode des éléments finis stochastiques spectrale

Abstract : We are interested in modelling structures with uncertain parameters. We focus on the characteristics of dynamic responses of such mechanical systems, especially the modal frequencies and shapes. Stochastic Finite Element Methods (SFEM) have been developed for thirty years to study uncertainty propagation in structural problems. The main issue aims at avoiding Monte-Carlo simulations, too expensive for many problems. This thesis is a contribution to the development of SFEM for modal analysis of structures. In the first part, we investigate the case of structures with uncertain parameters. We are particularly interested in the dynamic response, such as eigenfrequencies and eigenmodes. An innovative method is carried out, which uses the spectral stochastic finite element method in order to determine the main stochastic characteristics of the response. The material properties are modelled by a Karhunen-Loève series, whereas the eigenvalues and eigenvectors are developed on the basis of the polynomial chaos. The solution procedure is proposed for decoupling of the system of equations. This method, practical for linear problems, has the advantage of allowing the modelling of the uncertain input parameters as random variables and stochastic fields. Four numerical applications are considered to test the capabilities of the proposed method. Finally, we studied the extension of the MEFSS to deal with robust mechanical design. The proposed approach represent a powerful tool for the optimization of the dynamic performance of the mechanical systems, since it is possible to obtain, with lower computation effort, the mean and the standard deviation of the response, in order to evaluate the robust solution. The advantage of the presented method is illustrated by two examples dealing with car structures.
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  • HAL Id : tel-00725464, version 1

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Jalaa Ahmad. Analyse modale des structures avec incertitudes par la méthode des éléments finis stochastiques spectrale. Génie mécanique [physics.class-ph]. Université Blaise Pascal - Clermont-Ferrand II, 2009. Français. ⟨NNT : 2009CLF21936⟩. ⟨tel-00725464⟩

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