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Optimisation en présence d'incertitudes de la répartition de la charge dans les problèmes elliptiques : Application à la mécanique des structures.

Abstract : This thesis concerns the application of a direct method of optimization of the distribution of mechanical loads on a structure.The goal is to bring the structure to a prescribed deformation.We show how to take advantage of the presence of linearity between the optimization variables and the solution of the equation of state to declineexplicitly the optimal solution in the sense of the least squares, and this without any iterative method of type gradient. We show, moreover, how this method allows an analysis of the sensitivity of the solution with respect to small disturbances on the one hand of the loads, and on the other hand, of the target strain.These sensitivity analyzes use low complexity strategiesof direct and retrograde propagation of uncertainties, and we show that here too the operations can be explicitly declined.
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https://theses.hal.science/tel-03391079
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Submitted on : Thursday, October 21, 2021 - 3:30:10 PM
Last modification on : Friday, August 5, 2022 - 10:51:48 AM
Long-term archiving on: : Saturday, January 22, 2022 - 7:29:04 PM

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  • HAL Id : tel-03391079, version 1

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Radia Bouabdallah. Optimisation en présence d'incertitudes de la répartition de la charge dans les problèmes elliptiques : Application à la mécanique des structures.. Probabilités [math.PR]. Université Montpellier, 2021. Français. ⟨NNT : 2021MONTS028⟩. ⟨tel-03391079⟩

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