Stable configurations of the noncircular cross section elastic rod model with singularity theory

WANG Wei; LIN Zhi

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Stable configurations of the noncircular cross section elastic rod model with singularity theory

WANG Wei * #,LIN Zhi

Department of Mechanics, School of Engineering, Tianjin University, Tianjin 300072, China

*Correspondence author

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Funding: Project supported by the National Natural Science Foundation of China （No.Grant No. 11102127 and 11072168), the Specialized Research Fund for the Doctoral Program of Higher Education of China）

Opened online:15 January 2014

Accepted by: none

Citation: WANG Wei,LIN Zhi.Stable configurations of the noncircular cross section elastic rod model with singularity theory[OL]. [15 January 2014] http://en.paper.edu.cn/en_releasepaper/content/4580025

The stable configuration of elastic rod model under perturbation is researched by using the singularity theory. We consider the reduced Kirchhoff equations of the noncircular cross section elastic rod characterized by the inequality of the bending rigidities. For the possible buckling configurations belong to the minima along the elastic energy curve, it is analogue to the research of static bifurcation of the equilibrium and described as a 2-codimension unfolding. From that we realize the emergency of buckling configuration under perturbation is strongly connected with the correlations between different governing parameters. These correlations can be analytically detected with the variation in the transition set and bifurcation diagrams from the singularity theory. We also find the criterion of the localized buckling process. The process, following the buckling configuration, connects with the homoclinicity in the physical parameter regions and has been verified with numerical simulation in this article.

Keywords:elastic rod; static bifurcation; homoclinic bifurcation

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