On weavings, grillages, tensegrities, and frameworks
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911741916479488 |
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| author | Millar, Cameron Schulze, Bernd Theran, Louis |
| author_facet | Millar, Cameron Schulze, Bernd Theran, Louis |
| contents | We investigate the stability of discrete structures comprising of woven elastic beams in a plane, exposing a connection between admissible over / under patterns and the first-order and static rigidity of an associated tensegrity that is related through a natural polarity transformation. The relationship between the Airy and Whiteley stress functions for the tensegrity and weaving structures is explored. Our results lead to an efficient method for finding such an over / under pattern. The method is illustrated through a worked example modelled on the complete bipartite graph $K_{4,4}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02397 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On weavings, grillages, tensegrities, and frameworks Millar, Cameron Schulze, Bernd Theran, Louis Metric Geometry 52C25 We investigate the stability of discrete structures comprising of woven elastic beams in a plane, exposing a connection between admissible over / under patterns and the first-order and static rigidity of an associated tensegrity that is related through a natural polarity transformation. The relationship between the Airy and Whiteley stress functions for the tensegrity and weaving structures is explored. Our results lead to an efficient method for finding such an over / under pattern. The method is illustrated through a worked example modelled on the complete bipartite graph $K_{4,4}$. |
| title | On weavings, grillages, tensegrities, and frameworks |
| topic | Metric Geometry 52C25 |
| url | https://arxiv.org/abs/2606.02397 |