Periodic Rigidity on a Variable Torus Using Inductive Constructions

2012/04/05 by Anthony Nixon, Nixon, Anthony, Elissa Ross +1 · 2 citations
Engineering · #Structural Analysis and Optimization #Advanced Materials and Mechanics #Dielectric materials and actuators

paper · pdf · doi:10.48550/arxiv.1204.1349

Abstract

In this paper we prove a recursive characterisation of generic rigidity for frameworks periodic with respect to a partially variable lattice. We follow the approach of modelling periodic frameworks as frameworks on a torus and use the language of gain graphs for the finite counterpart of a periodic graph. In this setting we employ variants of the Henneberg operations used frequently in rigidity theory.

Cited by

• Non-Euclidean Crystallographic Rigidity
• Inductive constructions for frameworks on a two-dimensional fixed torus
• A characterisation of generically rigid frameworks on surfaces of revolution

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• Inductive constructions for frameworks on a two-dimensional fixed torus
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