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Conception robuste de structures périodiques à non-linéarités fonctionnelles

Abstract : Dynamic analysis of large scale structures including several uncertain parameters and localized or distributed nonlinearities may be computationally unaffordable. In order to overcome this issue, approximation models can be developed to reproduce accurately the structural response at a low computational cost.The purpose of the first part of this thesis is to develop numerical models which must be robust against structural modifications (localized nonlinearities, parametric uncertainties or perturbations) and reduce the size of the initial problem. These models are created, according to the direct condensation and the component mode synthesis, by enriching truncated reduction modal bases and Craig-Bampton transformations, respectively, with static residual vectors accounting for the structural modifications. To propagate uncertainties through these first-level and second-level reduced order models, respectively, we focus particularly on the generalized polynomial chaos method. This methods combination allows creating first-level and second-level metamodels, respectively. The two proposed metamodels are compared to other metamodels based on the polynomial chaos method and Latin Hypercube method applied on reduced and full models. The proposed metamodels allow approximating the structural behavior at a low computational cost without a significant loss of accuracy.The second part of this thesis is devoted to the dynamic analysis of nonlinear periodic structures in presence of imperfections: parametric perturbations or uncertainties. Deterministic or stochastic analyses, respectively, are therefore carried out. For both configurations, a generic discrete analytical model is proposed. It consists in applying the multiple scales method and the perturbation theory to solve the equation of motion and then on projecting the resulting solution on standing wave modes. The proposed model leads to a set of coupled complex algebraic equations, depending on the number and positions of imperfections in the structure. Uncertainty propagation through the proposed model is finally done using the Latin Hypercube method and the generalized polynomial chaos expansion. The robustness the collective dynamics against imperfections is studied through statistical analysis of the frequency responses and the basins of attraction dispersions in the multistability domain. Numerical results show that the presence of imperfections in a periodic structure strengthens its nonlinearity, expands its multistability domain and generates a multiplicity of multimodal branches.
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Submitted on : Friday, June 8, 2018 - 9:42:08 AM
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Khaoula Chikhaoui. Conception robuste de structures périodiques à non-linéarités fonctionnelles. Mécanique des structures [physics.class-ph]. Université Bourgogne Franche-Comté; Université de Tunis, 2017. Français. ⟨NNT : 2017UBFCD029⟩. ⟨tel-01810643⟩



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