Bracing rhombic structure by one-dimensional tensegrities
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Certain behaviors of some material are characterized by the periodic bar and joint elements. We present a kinematic, geometric and graph theoretic connected model that describes the stability, rigidity property of these rhombic tiling materials in two dimensions. Cables, struts or rods are placed as bracing elements between opposite pairs of diagonal joints, to prevent the rhombic tiling from the rotation of the bars around their common joint. We characterize the rigidity of the finite parts of the rhombic bracing structure in the plane. The results of this paper are based on the theorem of the rigidity of one-dimensional tensegrity framework from Recski and Shai. We have applied our results to describe some auxetic type structures that were mentioned earlier in the scientific literature. We also introduce the model as a possible candidate for the mechanical information processing system in a repetitive bar and joint structure.
KeywordsTensegrity Auxetic mechanism Infinitesimal rigidity Tiling Tessellations
I would like to thank András Recski for many productive discussions. I thank the editors and anonymous reviewers for their careful reading of the manuscript and their many Insightful comments and suggestions. This research was supported by the Hungarian National Science Foundation (Grant Number: 108947).
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