TY - JOUR
T1 - Bifurcation hierarchy of symmetric structures
AU - Kiyohiro, Ikeda
AU - Kazuo, Murota
AU - Hiroshi, Fujii
N1 - Funding Information:
Acknowledgements-The authors are grateful for invaluable eomments offered by Professor Martin Golubitsky. The comments of the anonymous referees were helpful in revision. Shogo Matsushita and Shosaku Wada were of great assistance in the numerical analysis. This work was carried out while the second author stayed at the Institute of Operations Research, University of Bonn, supported by the Alexander von Humboldt Foundation.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1991
Y1 - 1991
N2 - A group-theoretic method for the analysis of bifurcation behavior of regular-polygonal symmetric structures is described. Possible bifurcation paths and points of these structures are categorized in terms of dihedral and cyclic groups, which express the symmetry. In particular, we offer a complete description of those double bifurcation points which occur due to group symmetry. The type, the number, and the stability of bifurcation paths branching at these points are determined by deriving bifurcation equations. The existence of a potential function plays a substantial role for the existence of bifurcation paths. As a result of these, all possible bifurcation process can be known a Priori as a natural consequence of bifurcation hierarchy before actual numerical analysis. An implementation of this method in numerical analysis shows its validity and usability.
AB - A group-theoretic method for the analysis of bifurcation behavior of regular-polygonal symmetric structures is described. Possible bifurcation paths and points of these structures are categorized in terms of dihedral and cyclic groups, which express the symmetry. In particular, we offer a complete description of those double bifurcation points which occur due to group symmetry. The type, the number, and the stability of bifurcation paths branching at these points are determined by deriving bifurcation equations. The existence of a potential function plays a substantial role for the existence of bifurcation paths. As a result of these, all possible bifurcation process can be known a Priori as a natural consequence of bifurcation hierarchy before actual numerical analysis. An implementation of this method in numerical analysis shows its validity and usability.
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U2 - 10.1016/0020-7683(91)90077-S
DO - 10.1016/0020-7683(91)90077-S
M3 - Article
AN - SCOPUS:0025791434
VL - 27
SP - 1551
EP - 1573
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
SN - 0020-7683
IS - 12
ER -