Equilibrium stresses and rigidity for infinite tensegrities and frameworks

Power, Stephen (2024) Equilibrium stresses and rigidity for infinite tensegrities and frameworks. Journal of Mathematical Analysis and Applications, 529 (1). ISSN 0022-247X

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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.