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When is a symmetric pin-jointed framework isostatic?

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When is a symmetric pin-jointed framework isostatic? / Connelly, Robert; Fowler, Patrick ; Guest, Simon et al.
In: International Journal of Solids and Structures, Vol. 46, No. 3-4, 02.2009, p. 762-773.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Connelly, R, Fowler, P, Guest, S, Schulze, B & Whiteley, W 2009, 'When is a symmetric pin-jointed framework isostatic?', International Journal of Solids and Structures, vol. 46, no. 3-4, pp. 762-773. https://doi.org/10.1016/j.ijsolstr.2008.09.023

APA

Connelly, R., Fowler, P., Guest, S., Schulze, B., & Whiteley, W. (2009). When is a symmetric pin-jointed framework isostatic? International Journal of Solids and Structures, 46(3-4), 762-773. https://doi.org/10.1016/j.ijsolstr.2008.09.023

Vancouver

Connelly R, Fowler P, Guest S, Schulze B, Whiteley W. When is a symmetric pin-jointed framework isostatic? International Journal of Solids and Structures. 2009 Feb;46(3-4):762-773. doi: 10.1016/j.ijsolstr.2008.09.023

Author

Connelly, Robert ; Fowler, Patrick ; Guest, Simon et al. / When is a symmetric pin-jointed framework isostatic?. In: International Journal of Solids and Structures. 2009 ; Vol. 46, No. 3-4. pp. 762-773.

Bibtex

@article{7aa58665e2644c809c2449ca43a7a440,
title = "When is a symmetric pin-jointed framework isostatic?",
abstract = "Maxwell{\textquoteright}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 conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. In particular, it turns out that an isostatic framework in 2D can belong to one of only six point groups. Some conjectures and initial results are presented that would give sufficient conditions (in both 2D and 3D) for a framework that is realized generically for a given symmetry group to be an isostatic framework.",
keywords = "Frameworks, Isostatic",
author = "Robert Connelly and Patrick Fowler and Simon Guest and Bernd Schulze and Walter Whiteley",
year = "2009",
month = feb,
doi = "10.1016/j.ijsolstr.2008.09.023",
language = "English",
volume = "46",
pages = "762--773",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Limited",
number = "3-4",

}

RIS

TY - JOUR

T1 - When is a symmetric pin-jointed framework isostatic?

AU - Connelly, Robert

AU - Fowler, Patrick

AU - Guest, Simon

AU - Schulze, Bernd

AU - Whiteley, Walter

PY - 2009/2

Y1 - 2009/2

N2 - 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 conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. In particular, it turns out that an isostatic framework in 2D can belong to one of only six point groups. Some conjectures and initial results are presented that would give sufficient conditions (in both 2D and 3D) for a framework that is realized generically for a given symmetry group to be an isostatic framework.

AB - 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 conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. In particular, it turns out that an isostatic framework in 2D can belong to one of only six point groups. Some conjectures and initial results are presented that would give sufficient conditions (in both 2D and 3D) for a framework that is realized generically for a given symmetry group to be an isostatic framework.

KW - Frameworks

KW - Isostatic

U2 - 10.1016/j.ijsolstr.2008.09.023

DO - 10.1016/j.ijsolstr.2008.09.023

M3 - Journal article

VL - 46

SP - 762

EP - 773

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

IS - 3-4

ER -