Rigidity of square grids with holes
Keywords:
grids, rigidity, frameworks, graphsAbstract
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.
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.
[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
2023-04-18
Issue
pp. 329-335
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Gáspár, Z., Radics, N., & Recski, A. (2023). Rigidity of square grids with holes. Computer Assisted Methods in Engineering and Science, 6(3-4), 329-335. https://cames3.ippt.pan.pl/index.php/cames/article/view/1280
