Rigidity of square grids with holes
Abstract
Bolker and Crapo gave a graph theoretical model of square grid frameworks with diagonal rods of certain squares. Using this model there are very fast methods for connected planar square grid frameworks to determine their (infinitesimal) rigidity when we can use diagonal rods, diagonal cables or struts, long rods, long cables or struts. But what about square grids containing some kind of holes? We will show that the model can be extended to the problem of holes too.
Keywords
grids, rigidity, frameworks, graphs,References
[1] J.A. Baglivo, J.E. Graver. Incidence and Symmetry in Design and Architecture. Cambridge University Press, Cambridge, 1983.[2] E.D. Bolker, H. Crapo. Bracing rectangular frameworks. SIAM J. Appl. Math., 36: 473-490, 1979.
[3] Zs. Gáspár, N. Radics, A. Recski. Square grids with long "diagonals". Optimization Methods and Software, 10: 217-231, 1998.
[4] A. Recski. Matroid Theory and its Applications in Electric Network Theory and in Statics. Springer, Berlin-Heidelberg-New York, and Akadémiai Kiadó, Budapest, 1989.
Published
Apr 18, 2023
How to Cite
GÁSPÁR, Zsolt; RADICS, Norbert; RECSKI, Andras.
Rigidity of square grids with holes.
Computer Assisted Methods in Engineering and Science, [S.l.], v. 6, n. 3-4, p. 329-335, apr. 2023.
ISSN 2956-5839.
Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1280>. Date accessed: 13 nov. 2024.
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This work is licensed under a Creative Commons Attribution 4.0 International License.