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Theses

Abaques virtuelle pour le génie parasismique incluant des parametres associes au chargement

Abstract : The complexity and the fineness of the numerical models used to predict the (often nonlinear) seismic behavior of reinforced concrete structures impose a calculation time of several days to solve the partial differential equations of the reference problem. Moreover, for margin assessment, safety analyses or model updating purposes, taking into account the uncertainties associated with constitutive parameters or the seismic loading itself generally impose to foresee this numerical effort, not for the simulation of a single model, but of a family of models submitted to a set of likely inputs defining the seismic scenario. To reduce computational times, certain techniques, called "model order reduction", must be considered. The Large Time Incremental (LATIN) method used in combination with the model order reduction technique called Proper Generalized Decomposition (PGD) has proven its efficiency for solving nonlinear problems in mechanics. Until now, the LATIN-PGD methodology has never been applied for solving nonlinear problems in dynamics. In this context, the LATIN-PGD framework is first adapted to the dynamic case, where the nonlinearities considered correspond to typical reinforced concrete materials, i.e. quasi-brittle isotropic damage for concrete and elasto-visco-plasticity for metals; additionally, dedicated strategies are developed to reduce computational costs when considering complex and large duration excitations, such as seismic inputs or fatigue loading. The contributions of this thesis work are the following: (i) an adaptation of the Time-Discontinuous Galerkin Method (TDGM) for solving incremental temporal problems in the LATIN-PGD framework, which allows to efficiently solve problems where the time interval is relatively large, (ii) a new signal approximation technique and a new multiscale strategy in time is developed to optimize the resolution of temporal PGD functions when dealing with long time excitations such as seismic inputs or fatigue loading, (iii) a hyper-reduction technique is proposed to accelerate the construction of the low-rank PGD approximation and finally, (iv) a parallel-time resolution strategy based on the use of TDGM is introduced, which aims at accelerating the temporal PGD resolution by taking advantage of the parallel architectures of recent computers. All the previous contributions allow a high optimization of the LATIN-PGD framework, which consequently allows a considerable reduction of the numerical cost to obtain the nonlinear response of a structure in dynamics.
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Submitted on : Wednesday, November 24, 2021 - 2:29:22 PM
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Sebastian Rodriguez Iturra. Abaques virtuelle pour le génie parasismique incluant des parametres associes au chargement. Civil Engineering. Université Paris-Saclay, 2021. English. ⟨NNT : 2021UPAST097⟩. ⟨tel-03446766⟩

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