Application de la différenciation automatique pour l'identification, l'optimisation et l'étude de sensibilité dans quelques problèmes mécaniques

Abstract : The finite element method allows for the determination of the states of the stress in a mechanical structure under solicitation. Manufacturing processes may be modeled. Nowadays, the reduction of computational costs allows to tackle inverse problems for the identification of some material or geometrical parameters of the structure that are optimal to a given problem. The inverse problem makes use of a mechanical model and an objective function measuring the discrepancies between the observed response and responses resulting from different sets of parameters. This thesis describes a gradient method and the automatic differentiation technique for the solution of two inverse problems in mechanics. The first one is concerned with the identification of a strain-hardening law from uniaxial tension test performed on two different steels and from the academical code \fl. The second one deals with the identification of a viscoelastic law for a sandwich material from experimental data measured on a simply supported sandwich beam and a complex eigenvalue solver developed at LPMM. These two models are differentiable. For each problem, the optimal parameter set is identified as a set for which the gradient of the objective function is zero. We use the automatic differentiation technique to generate codes for the computations of these gradients in a simplified manner. Results we obtained demonstrate the interest of such an approach
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Imen Elkhaldi-Mkaouar. Application de la différenciation automatique pour l'identification, l'optimisation et l'étude de sensibilité dans quelques problèmes mécaniques. Autre. Université de Lorraine, 2012. Français. ⟨NNT : 2012LORR0041⟩. ⟨tel-01749210⟩

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