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When is a symmetric body-bar structure isostatic?

โœ Scribed by S.D. Guest; B. Schulze; W.J. Whiteley

Book ID
104018614
Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
414 KB
Volume
47
Category
Article
ISSN
0020-7683

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โœฆ Synopsis

Body-bar frameworks provide a special class of frameworks which are well understood generically, with a full combinatorial theory for rigidity. Given a symmetric body-bar framework, this paper exploits group representation theory to provide necessary conditions for rigidity in the form of very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. We give some initial results, and conjectures, for when these conditions are also sufficient for rigidity.

๐Ÿ“œ SIMILAR VOLUMES

When is a symmetric pin-jointed framewor
When is a symmetric pin-jointed framework isostatic?
โœ R. Connelly; P.W. Fowler; S.D. Guest; B. Schulze; W.J. Whiteley ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 292 KB

a b s t r a c t Maxwell's rule from 1864 gives a necessary condition for a framework to be isostatic in 2D or in 3D. Given a framework with point group symmetry, group representation theory is exploited to provide further necessary conditions. This paper shows how, for an isostatic framework, these