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
Infinite bar-joint frameworks
John C. Owen,Stephen C. Power +1 more
- 08 Mar 2009
TL;DR: In this paper, some aspects of a mathematical theory of rigidity and flexibility are developed for general infinite frameworks and two main results are obtained: sufficient conditions, of a uniform local nature, are obtained for the existence of a proper flex of an infinite framework.
21
Generic Rigidity with Forced Symmetry and Sparse Colored Graphs
Justin Malestein,Louis Theran +1 more
TL;DR: In this article, the authors review some recent results in the generic rigidity theory of planar frameworks with forced symmetry, giving a uniform treatment to the topic and give new combinatorial characterizations of minimally rigid periodic frameworks with fixed-area fundamental domain and fixed-angle fundamental domain.
20
A characterisation of the generic rigidity of 2-dimensional point-line frameworks
Bill Jackson,J. C. Owen +1 more
TL;DR: In this article, the authors characterise when a generic point-line framework is rigid and give a polynomial algorithm for solving this decision problem, which can be obtained from the initial framework by a translation or a rotation.
Bi-stiffness property of motion structures transformed into square cells
TL;DR: In this paper, a bar-and-joint framework assembled with a basic unit of motion structure, which has eightfold rotational symmetry (MS-8), is proposed.
18
Symmetries and Dualities in the Theory of Elasticity.
Michel Fruchart,Vincenzo Vitelli +1 more
TL;DR: It is shown on general grounds how the existence of nonspatial symmetries further constrains the elastic tensor, reducing the number of independent moduli in systems exhibiting a duality transformation.
18
References
Foam topology bending versus stretching dominated architectures
TL;DR: In this paper, the authors investigated the topological criteria that dictate the deformation mechanism of a cellular solid by analysing the rigidity (or otherwise) of pin-jointed frameworks comprising inextensional struts.
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On graphs and rigidity of plane skeletal structures
TL;DR: In this paper, the combinatorial properties of rigid plane skeletal structures are investigated, and the properties are found to be adequately described by a class of graph-structured graphs.
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Matrix analysis of statically and kinematically indeterminate frameworks
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
TL;DR: In this article, it was shown that a single state of self-stress in the frame has the effect of imparting first-order stiffness to the frame, and it seems from experiments that such states can stiffen a large number of modes.
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