Infinitesimal rigidity for non-Euclidean bar-joint frameworks

2014/04/08 by D. Kitson, S. C. Power · 3 citations
Engineering · Materials Science · #Structural Analysis and Optimization #Elasticity and Material Modeling #Nonlocal and gradient elasticity in micro/nano structures

paper · pdf · doi:10.1112/blms/bdu017

Abstract

The minimal infinitesimal rigidity of bar-joint frameworks in the non-Euclidean spaces ( R 2 , ∥ · ∥ q ) , for 1 ⩽ q ⩽ ∞ , q ≠ 2 , is characterized in terms of ( 2 , 2 ) -tight graphs. Specifically, a generically placed bar-joint framework ( G , p ) in the plane is minimally infinitesimally rigid with respect to a non-Euclidean ℓ q norm if and only if the underlying graph G = ( V , E ) contains 2 | V | - 2 edges and every subgraph H = ( V ( H ) , E ( H ) ) contains at most 2 | V ( H ) | - 2 edges.

Cited by

• Identifiability of Points and Rigidity of Hypergraphs under Algebraic Constraints
• Non-Euclidean Crystallographic Rigidity
• Which graphs are rigid in ℓ p d ? [europepmc]

Related

• Point-hyperplane frameworks, slider joints, and rigidity preserving transformations
• Rigidity of Frameworks Supported on Surfaces
• Finite and infinitesimal rigidity with polyhedral norms
• Double-distance frameworks and mixed sparsity graphs
• Infinitesimal Rigidity of Symmetric Frameworks