Simulation numérique du comportement mécanique non linéaire de gridshells composés de poutres élancées en matériaux composites et de sections quelconques

Abstract : The structures like gridshells are structures made of a plane regular grid which is elastically deformed and then stiffened in the wished configuration. The composite materials gridshells have been developed and studied for several years at Navier laboratory. The thesis offer a feedback, through a history of Navier realisations. It also precise the points to improve, in numerical simulation or about materials or technological aspects. Then, the thesis explains the new numerical developments that make possible the ultimate analysis of the structure, taking account the ruptures of beams (robustness), and that makes possible the consideration of the torsion in anisotropic beams, that is to say beams with any cross-section. In the first chapter the context of the work is presented. This chapter explains how the Navier laboratory designs and builds gridshells. In particular, the numerical method historically used - the dynamic relaxation method - is presented. The second chapter presents the gridshell realisations of the Navier laboratory. Several prototypes have been built during the past ten years. The two last ones, the Solidays gridshell and the Ephemeral Cathedral of Creteil, have been designed to shelter public. The important choices during design and fabrication are detailed with an accent on technological progresses and feedbacks. The third chapter deals with the behaviour of composite materials gridhsells. The approach was to investigate the behaviour of the gridshell to understand the processes of damage. It is shown that buckling is particularly dangerous for the gridshell. The results of the study shows that when the gridshell has been well designed and in particular if buckling is avoided, the gridshell behave in a robust manner, thanks to its redundancy. Finally the last chapter deals with a new beam model, able to take into account torsion, for beams with any section. In the previous chapters it was underlined that the consideration of torsion aspects was lacking and has various consequences – incorrect estimation of stress, ignorance of forces and moments in connections, imprecision in geometry. In this chapter, the model of beams used is a four degrees of freedom model, similar to the ones presented by Basile Audoly and Ethan Grinspun. The numerical simulation, performed once again thanks to a dynamic relaxation algorithm, is able to provide equilibrium configurations of highly reticulated structures as gridshells. One of the particularity of this work is the fact that the model is a continuous model, only discretized for numerical simulations. The external forces and moments can be implemented. For beams with rectangular cross-section, the results of the model are compared to finite element modelling simulations. The results are satisfying in term of accuracy and computational time. Finally the numerical method is applied to structures made of interconnected beams. The connections are modelled and the efforts through them are provided by the model. This provides important information about how to design the connections. Thanks to these work it become possible to use the large possibility of shapes offered by slender beams whose flexural inertias are different
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Frédéric Tayeb. Simulation numérique du comportement mécanique non linéaire de gridshells composés de poutres élancées en matériaux composites et de sections quelconques. Structures. Université Paris-Est, 2015. Français. ⟨NNT : 2015PESC1067⟩. ⟨tel-01260287⟩

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