Rigidity of square grids with holes

  • Zsolt Gáspár Technical University of Budapest
  • Norbert Radics Technical University of Budapest
  • Andras Recski Technical University of Budapest

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: 23 dec. 2024.
Citation Formats
Issue
Vol 6 No 3-4 (1999)
Section
Articles
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