Equilibrium stresses and rigidity for infinite tensegrities and frameworks
Abstract
Asymptotic equilibrium stresses are defined for countably infinite tensegrities and generalisations of the Roth-Whiteley characterisation of first-order rigidity are obtained. Generalisations of prestress stability and second order rigidity are given for countably infinite bar-joint frameworks and are shown to give sufficient conditions for continuous rigidity relative to certain prescribed motions. The proofs are based on a new short proof for finite frameworks that prestress stability ensures continuous rigidity.
Keywords
Cite
@article{arxiv.2207.14369,
title = {Equilibrium stresses and rigidity for infinite tensegrities and frameworks},
author = {Stephen Power},
journal= {arXiv preprint arXiv:2207.14369},
year = {2023}
}
Comments
Journal accepted version, to appear in the Journal of Mathematical Analysis and Applications. 19 pages, 8 figures. More detail and examples given. The implication "BPS implies BSR (boundedly smoothly rigid)" has been strengthened to "BPS implies DCR (directedly continuously rigid)"