Différentiation automatique de codes mécaniques : application à l'analyse de sensibilité des tôles sandwich aux paramètres de modélisation

Abstract : In engineering, for a better understanding of the mechanical behavior of a structure submitted to some perturbation of the modeling parameters, one often proceed to a sensitivity analysis. This provides quantitative and qualitative information on the behavior of the model under study and gives access to gradients that may be used in identification and optimization methods. In this thesis, we demonstrate that this information may be obtained at a low development effort by applying an Automatic Differentiation (AD) tool to the computer code that implements the model. We adapt the AD techniques to the Asymptotic Numerical Method (ANM), in its Diamant version for sensitivity computations of numerical solutions of nonlinear problems discretized through a finite element method. We discuss in a generic manner both the theoretical aspects and the implementation of several algorithms written in Matlab. Applications are concerned with sandwich beams and sandwich plates in both the static and dynamic (free vibration) cases. Sensitivities are computed with respect to geometric and mechanical parameters, and with respect to elementary stiffness matrix. The generality of our developments allows to take into account several viscoelastic laws with no additional effort. Three kinds of viscoelastic models are studied: constant complex modulus, low damping and higher damping. In comparison with the finite difference approximation often used in mechanics, our approach provides more accurate results for the sensitivity of the structure response to a perturbation of the modeling parameters. It also allows a reduction of the computation effort
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Komlanvi Lampoh. Différentiation automatique de codes mécaniques : application à l'analyse de sensibilité des tôles sandwich aux paramètres de modélisation. Autre. Université de Lorraine, 2012. Français. ⟨NNT : 2012LORR0220⟩. ⟨tel-01749313⟩

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