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Développement d'un modèle de calcul de la capacité ultime d'éléments de structure (3D) en béton armé, basé sur la théorie du calcul à la rupture

Abstract : To evaluate the load bearing capacity of structures, civil engineers often make use of empirical methods, which are often manuals, instead of nonlinear finite element methods available in existing civil engineering softwares, which are long to process and difficult to handle. Yield design (or limit analysis) approach, formalized by J. Salençon, is a rigorous method to evaluate the capacity of structures and can be used to answer the question of structural failure. It was, yet, not possible to take advantage of these theoretical methods due to the lack of efficient numerical methods. Recent progress in this field and notably in interior point algorithms allows one to rethink this opportunity. Therefore, the main objective of this thesis is to develop a numerical model, based on the yield design approach, to evaluate the ultimate capacity of massive (3D) reinforced concrete structural elements. Both static and kinematic approaches are implemented and expressed as an optimization problem that can be solved by a mathematical optimization solver in the framework of Semi-Definite Programming (SDP).A large part of this work is on modelling the resistance of the different components of the reinforced concrete composite material. The modelling assumptions taken to model the resistance of concrete are discussed. And the method used to model reinforcement is also questioned. The homogenization method is used to model periodic reinforcement and an adaptation of this technique is developed for isolated rebars. To conclude this work, a last part is dedicated to illustrate the power and potentialities of the numerical tool developed during this PhD thesis through various examples of massive structures
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Hugues Vincent. Développement d'un modèle de calcul de la capacité ultime d'éléments de structure (3D) en béton armé, basé sur la théorie du calcul à la rupture. Matériaux. Université Paris-Est, 2018. Français. ⟨NNT : 2018PESC1038⟩. ⟨tel-02053145v2⟩

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