Journal Article10.1016/S0022-5096(02)00107-2
On the determinacy of repetitive structures
TL;DR: In this paper, it was shown that repetitive, infinite structures cannot be simultaneously statically and kinematically determinate, and that infinite structures can not be statically determinate with respect to each other.
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Abstract: This paper shows that repetitive, infinite structures cannot be simultaneously statically, and kinematically, determinate.
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Citations
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Frameworks with crystallographic symmetry
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TL;DR: In this paper, a general deformation theory of periodic bar-and-joint structures in $R^d$ was investigated from the perspective of periodic frameworks with crystallographic symmetry, and upper bounds for the number of realizations of minimally rigid periodic graphs were derived.
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Directional mechanical response in the bulk of topological metamaterials
D. Zeb Rocklin,D. Zeb Rocklin +1 more
TL;DR: In this article, it was shown that applying force at a point in the bulk of these lattices generates a directional mechanical response, in which stress or strain is induced only on one side of the force.
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In-plane mechanical behaviors of 2D repetitive frameworks with four-coordinate flexible joints and elbowed beam members
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TL;DR: In this article, the relationship between joint flexibility and Poisson's ratio was clarified and two types of in-plane anisotropic structures made up of four-coordinate flexible joints and elbowed beam members were discussed.
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Phonons and elasticity in critically coordinated lattices
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Orthotropic elastic constants of 2D cellular structures with variously arranged square cells: The effect of filleted wall junctions
TL;DR: In this paper, the stiffness of 2D cellular structures with variously arranged square cells is evaluated. And the analytical model based on classical beam theory is proposed to identify the effect of stretching and bending actions on a single cell by applying the periodic boundary conditions.
21
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TL;DR: In this paper, the structural mechanics of assemblies of bars and pinjoints, particularly where they are simultaneously statically and kinematically indeterminate, are investigated, and an algorithm is set up which determines the rank of the matrix and the bases for the four subspaces.
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Buckminster Fuller's “Tensegrity” structures and Clerk Maxwell's rules for the construction of stiff frames
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