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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 15
Efficient Graph Theoretical Methods for Examining the Rigidity of Planar Trusses A. Kaveh+ and F.N. Ehsani*
+Iran University of Science and Technology, Narmak, Tehran, Iran
Full Bibliographic Reference for this paper
A. Kaveh, F.N. Ehsani, "Efficient Graph Theoretical Methods for Examining the Rigidity of Planar Trusses", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 15, 2001. doi:10.4203/ccp.73.15
Keywords: rigidity, graph, truss, matching, decomposition, Henneberg sequence, generic independence.
Summary
Introduction
The first combinatorial approach to the study of rigidity is due to Laman [2] who found the necessary and sufficient conditions for a graph to be rigid, when its member and nodes correspond to rigid rods (bars) and rotatable pinned-joints of a planar truss. Two main types of methods are discussed for recognizing the generic independence of graphs, which use complete matching and decomposition approaches. The Edmonds' algorithm is studied in detail and a computer code is developed based on the modified version of the Edmonds' algorithm. A second algorithm is presented based on the Henneberg sequence. Methods for Examining the Rigidity of Trusses
Laman proved a basic theorem on rigidity as follows: The graph
This method is developed by Sugihara [3] and it is a polynomial bounded
algorithm. The method uses the following theorem for the recognition.
The graph model
Lovász and Yemini [4] proved a theorem that a graph References
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