Equilibrium stressability of multidimensional frameworks
Oleg Karpenkov, Christian M\"uller, Gaiane Panina, Brigitte Servatius,, Herman Servatius, Dirk Siersma
TL;DR
This paper establishes a comprehensive criterion for equilibrium stressability in trivalent multidimensional tensegrities, connecting various mathematical frameworks such as stress monodromies, surgeries, discrete 1-forms, and Cayley algebra.
Contribution
It introduces a unified stressability criterion for multidimensional frameworks, linking multiple mathematical perspectives and extending understanding of tensegrity structures.
Findings
Provides a stressability criterion in terms of stress monodromies
Expresses the criterion through surgeries and exact discrete 1-forms
Relates the criterion to Cayley algebra representations
Abstract
We prove an equilibrium stressability criterium for trivalent multidimensional tensegrities. The criterium appears in different languages: (1) in terms of stress monodromies, (2) in terms of surgeries, (3) in terms of exact discrete 1-forms, and (4) in Cayley algebra terms.
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Taxonomy
TopicsStructural Analysis and Optimization · Advanced Materials and Mechanics · Dynamics and Control of Mechanical Systems