Year: 2025
Type: article
Abstract: For a bar-joint framework $$(G,\textbf{p})$$ ( G , p ) , a subgroup $$\Gamma $$ Γ of the automorphism group of G , and a subgroup of the orthogonal group isomorphic to $$\Gamma $$ Γ , we introduce a symmetric averaging map which produces a bar-joint framework on G with that symmetry. If the original configuration is “almost symmetric”, then the averaged one will be near the original configuration. With a view on structural engineering applications, we then introduce a hierarchy of definitions of “localised” and “non-localised” or “extensive” self-stresses of frameworks and investigate their behaviour under the symmetric averaging procedure. Finally, we present algorithms for finding non-degenerate symmetric frameworks with many states of self-stress, as well as non-symmetric and symmetric frameworks with extensive self-stresses. The latter uses the symmetric averaging map in combination with symmetric Maxwell-type character counts and a procedure based on the pure condition from algebraic geometry. These algorithms provide new theoretical and computational tools for the design of engineering structures such as gridshell roofs.
Authors: Cameron Millar, Bernd Schulze, Louis Theran
Institutions: Lancaster University, University of St Andrews
Language: English
Subfield: Civil and Structural Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,590
OpenAlex ID: W4416491587