Stability Analysis of a Helical Rod Based on Exact Cosserat’s Model

LIU Yan-zhu; XUE Yun

doi:10.3879/j.issn.1000-0887.2011.05.007

Volume 32 Issue 5

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LIU Yan-zhu, XUE Yun. Stability Analysis of a Helical Rod Based on Exact Cosserat’s Model[J]. Applied Mathematics and Mechanics, 2011, 32(5): 570-578. doi: 10.3879/j.issn.1000-0887.2011.05.007

Citation:

LIU Yan-zhu, XUE Yun. Stability Analysis of a Helical Rod Based on Exact Cosserat’s Model[J]. Applied Mathematics and Mechanics, 2011, 32(5): 570-578. doi: 10.3879/j.issn.1000-0887.2011.05.007

Citation:

LIU Yan-zhu, XUE Yun. Stability Analysis of a Helical Rod Based on Exact Cosserat’s Model[J]. Applied Mathematics and Mechanics, 2011, 32(5): 570-578. doi: 10.3879/j.issn.1000-0887.2011.05.007

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Stability Analysis of a Helical Rod Based on Exact Cosserat’s Model

doi: 10.3879/j.issn.1000-0887.2011.05.007

LIU Yan-zhu¹,
XUE Yun²

1.
Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;

Received Date: 2011-02-21
Rev Recd Date: 2011-03-23
Publish Date: 2011-05-15

Abstract

Abstract

The helical equilibrium of a thin elastic rod has a practical background such as DNA, fiber, sub-ocean cable and oil-well dill string. The Kirchhoff's kinetic analogy is an effective approach in stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff's theory including no extension of the centerline and no shear deformation of the cross section are not adaptable to the real soft materials of biological fibers. The dynamic equations of a rod with circular cross section were established on the basis of exact Cosserat's model considering tension and shear deformations. The Euler's angles were applied as the attitude representation of the cross section. The deviation of the normal axis of cross section from the tangent of the centerline was considered as the result of shear deformation. The Liapunov's stability of helical equilibrium was discussed in static category and the Euler's critical values of axial force and torque were obtained. The Liapunov's and Euler's stability conditions in space domain are the necessary conditions of Liapunov's stability of the helical rod in time domain.
- exact Cosserat’s model,
- Kirchhoff’s rod,
- Liapunov’s stability,
- Euler’s load

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References(12)

References

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