Finite motions from periodic frameworks with added symmetry

International Journal of Solids and Structures

Volumn 48, Issue 11-12, 2011, Pages 1711-1729

  Ross, Elissa ^a   Schulze, Bernd ^b   Whiteley, Walter ^a  

^a YORK UNIVERSITY   (Canada)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Crystal systems; Framework rigidity; Orbits; Periodic; Symmetry

Indexed keywords

CRYSTAL SYSTEM; FINITE MOTION; FRAMEWORK RIGIDITY; FURTHER DEVELOPMENT; INFINITE PERIODIC STRUCTURE; MATRIX; MOLECULAR FRAMEWORKS; PERIODIC; PERIODIC CELL; PERIODIC PATTERN; PHYSICAL AND CHEMICAL PROPERTIES; SYMMETRY; SYMMETRY OPERATIONS;

CHEMICAL PROPERTIES; MAXWELL EQUATIONS; PERIODIC STRUCTURES; RIGIDITY;

CRYSTAL SYMMETRY;

EID: 79953754850     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2011.02.018     Document Type: Article

References (31)

1. L. Asimov, and B. Roth The rigidity of graphs AMS 245 1978 279 289
2. D. Bishop Group Theory and Chemistry 1973 Clarendon Press Oxford
3. C. Borcea, and I. Streinu Periodic frameworks and flexibility Proc. R. Soc. A 466 2121 2010 2633 2649
4. Borcea, C., Streinu, I. 2010 b. Minimally rigid periodic graphs. Lecture presented at the LMS Workshop: Rigidity of Frameworks and Applications. Lancaster University, UK, July 12-15, 2010.
5. R. Bricard Mémoire sur la théorie de l'octadre articulé J. Math. Pures Appl. 5 3 1897 113 148
6. R. Connelly, P. Fowler, S. Guest, B. Schulze, and W. Whiteley When is a symmetric pin-jointed framework isostatic? Int J. Solids Struct. 46 2009 762 773
7. J.H. Conway, O.D. Friedrichs, D.H. Huson, and W.P. Thurston On three-dimensional space groups Beiträge Algebra Geom. 42 2001 475 507 (Pubitemid 33812709)
8. D.S. Dummit, and R.M. Foote Abstract Algebra 1991 Prentice Hall
9. P. Fowler, and S. Guest A symmetry extension of Maxwell's rule for rigidity of frames Int. J. Solids Struct. 37 2000 1793 1804 (Pubitemid 32213090)
10. J. Gross, and T. Tucker Topological Graph Theory 2001 Dover
11. S. Guest, and P. Fowler Symmetry conditions and finite mechanisms Mech. Mater. Struct. 2 6 2007
12. S. Guest, and R. Hutchinson On the determinacy of repetitive structures J. Mech. Phys. Solids 51 3 2003 383 391 (Pubitemid 35459652)
13. L. Hall Group Theory and Symmetry in Chemistry 1969 McGraw-Hill Inc
14. International Union of Crystallography, 2006. International Tables for Crystallography Volume A: Space-group Symmetry. first online edition. doi:10.1107/97809553602060000001.
15. R. Kangwai, and S. Guest Detection of finite mechanisms in symmetric structures Int. J. Solids Struct. 36 1999 5507 5527
16. R. Kangwai, and S. Guest Symmetry-adapted equilibrium matrices Int. J. Solids Struct. 37 2000 1525 1548 (Pubitemid 32213091)
17. V. Kapko, C. Dawson, M.J. Treacy, and M.F. Thorpe Flexibility of ideal zeolite frameworks Phys. Chem. Chem. Phys. 12 2010 8531 8541
18. G. Laman On graphs and rigidity of plane skeletal structures J. Eng. Math. 4 1970 331 340
19. Malestein, J., Theran, L. 2010. Generic combinatorial rigidity of periodic frameworks. preprint, arXiv:1008.1837.
20. Ross, E. 2011. Combinatorial and Geometric Rigidity of Periodic Structures. PhD thesis, York University, Toronto, Canada.
21. Schulze, B. 2009. Combinatorial and Geometric Rigidity with Symmetry Constraints. PhD thesis, York University, Toronto, Canada.
22. B. Schulze Block-diagonalized rigidity matrices of symmetric frameworks and applications Beiträge Algebra Geom. 51 2 2010 427 466
23. B. Schulze Injective and non-injective realizations with symmetry Contrib. Discrete Math. 5 1 2010 59 89
24. B. Schulze Symmetric versions of Laman's Theorem Discrete & Computational Geometry 44 4 2010 946 974
25. B. Schulze Symmetry as a sufficient condition for a finite flex SIAM J. Discrete Math. 24 4 2010 1291 1312
26. Schulze, B., Whiteley, W. 2010. The orbit rigidity matrix of a symmetric framework. Discrete & Computational Geometry, in press, doi:10.1007/s00454- 010-9317-50.
27. H. Stachel Zur einzigkeit der bricardschen oktaeder J. Geom. 28 41-56 1987
28. H. Stachel Flexible cross-polytopes in the Euclidean 4-space J. Geom. Graph. 4 2 2000 159 167
29. N. White, and W. Whiteley The algebraic geometry of stresses in frameworks SIAM J. Algebraic Discrete Methods 4 1983 481 511
30. W. Whiteley Some matroids from discrete applied geometry Contemporary Math. 197 1996 171 311
31. Wikipedia, 2010. Crystal systems. Retrieved October 11, 2010, from .