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Homogénéisation de Structures Discrètes en Élasticité et en Incrémental - Applications aux modélisations continues linéaires et non-linéaires de treillis quasi-périodiques.

Abstract : The work presented in this paper forms the basis of the discrete homogenization method. The main objective is to propose for a quasi-periodic lattice with articulated nodes a continuous modeling. The study was done within the framework of elasticity, for statics in small and large displacements, for incremental loadings and results are stated for free vibrations. The method uses asymptotic expansions and a general variational approach which allows to study at the same time the lattice beams, the lattice plates and the lattices 3D. The equivalent continuous medium is then easily identifiable analytically. These developments have been integrated into a formal calculation software and examples are given which show the practical interest of the method. Boundary conditions on the lattice may not be taken into account by continuous modeling, so a study of these conditions is done to find boundary layers at the edges of the structure. Another method of making double-series developments has been developed. It makes it possible to find the exact analytical deformation of any periodic beam (lattice or not) within the framework of the linear statics. These two methods are complementary.
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Submitted on : Monday, April 9, 2018 - 6:02:05 PM
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Gabriel Moreau. Homogénéisation de Structures Discrètes en Élasticité et en Incrémental - Applications aux modélisations continues linéaires et non-linéaires de treillis quasi-périodiques.. Mécanique des structures [physics.class-ph]. Institut National Polytechnique de Grenoble, 1996. Français. ⟨tel-01762234⟩

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