Frameworks symmetry and rigidity

International Journal of Computational Geometry and Applications

Volumn 20, Issue 6, 2010, Pages 723-750

  Owen, J C ^a   Power, S C ^b  

^a Park House   (United Kingdom)

^b LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Bar joint framework; rigidity; symmetry

Indexed keywords

EID: 78650899000     PISSN: 02181959     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218195910003505     Document Type: Article

References (24)

1. C. R. Calladine, Buckminster Fuller's ̀Tensegrity' structures and Clerk Maxwell's rules for the construction of sti frames, Int. J. Solids and Structures 14 (1978) 161.
2. P. W. Fowler and S. D. Guest, A symmetry extension of Maxwell's rule for rigidity of frames, Int. J. Solids and Structures 37 (2000) 1793-1804.
3. A. Ceulemans and P. W. Fowler, Extension of Euler's theorem to symmetry properties of polyhedra, Nature 353 (1991) 52-54.
4. R. D. Kangwai and S. D. Guest, Symmetry-adapted equilibrium matrices, Int. J. Solids and Structures 37 (2000) 1525-1548.
5. R. D. Kangwai, S. D. Guest and S. Pellegrino, An introduction to the analysis of symmetric structures, Comput. Structures 71 (1999) 671-688.
6. B. Schulze, Block-diagonalised rigidity matrices of symmetric frameworks and appli- cations, preprint 2009, arXiv:0906.3377.
7. R. Connelly, P. W. Fowler, S. D. Guest, B. Schulze and W. J. Whiteley, When is a pin-jointed framework isostatic? Int. J. Solids and Structures 46 (2009) 762-773.
8. G. Laman, On graphs and the rigidity of plane skeletal structures, J. Engin. Math. 4 (1970) 331-340.
9. B. Schulze, Symmetric versions of Laman's theorem, preprint, arXiv:0907.1958.
10. L. Asimow and B. Roth, The Rigidity of Graphs, Trans. Amer. Math. Soc., Vol. 245 (1978), pp. 279-289.
11. J. Graver, B. Servatius and H. Servatius, Combinatorial Rigidity, Graduate Texts in Mathematics, Vol. 2 (Amer. Math. Soc., 1993).
12. T. S. Tay and W. Whitely, Recent advances in the generic rigidity of structures, Struct. Topol. 9 (1984) 31-38.
13. B. Jackson and T. Jordan, The generic rank of body-bar-and-hinge frameworks, Eu- ropean J. Combinatorics 31 (2010) 574-588.
14. J. C. Owen, Algebraic solution for geometry from dimensional constraints, ACM Symp. Foundations in Solid Modeling (Austen, Texas, 1991), pp. 397-407.
15. J. C. Owen and S. C. Power, The non-solvability by radicals of generic 3-connected planar Laman graphs, Trans. Amer. Math. Soc., Vol. 359 (2007), pp. 2269-2303.
16. W. Whiteley, Rigidity and scene analysis, Handbook of Discrete and Computational Geometry, eds. J. E. Goodman and J. O'Rourke (CRC Press, 1997).
17. J. C. Owen and S. C. Power, Innite bar-joint frameworks, Proc. Symp. Applied Com- puting, SAC2009 (Honolulu, March 2009).
18. J. C. Owen and S. C. Power, Continuous curves from innite Kempe linkages, Bull. LMS 2009; doi: 10.1112/blms/bdp087.
19. J. C. Owen and S. C. Power, Innite bar-joint frameworks, crystals and operator theory, preprint 2010.
20. A. Donev and S. Torquato, Energy-effcient actuation in innite lattice structures, J. Mech. Phys. Solids 51 (2003) 1459-1475.
21. S. D. Guest and J. W. Hutchinson, On the determinacy of repetitive structures, J. Mech. Phys. Solids 51 (2003) 383-391.
22. A. Ceulemans, L. F. Chibotaru, P. W. Fowler and M. Szopa, Symmetry extensions of Euler's polyhedral theorem and the band theory of solids, J. Chem. Phys. 14 (1999) 6916-6926.
23. C. S. Borcea and I. Streinu, Periodic frameworks and exibility, Proc. R. Soc. A, doi:10.1098/rspa.2009.0676.
24. E. Ross, private communication.