On an Elastic Rod Inside a Slender Tube Under End Twisting Moment

Author:

Chen Jen-San,Li Hong-Chi1

Affiliation:

1. Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan

Abstract

In this paper, we study the deformation of a thin elastic rod constrained inside a cylindrical tube and under the action of an end twisting moment. The ends of the rod are clamped in the lateral direction. Unlike the previous works of others, in which only the fully developed line-contact spiral was considered, we present a complete analysis on the deformation when the dimensionless twisting moment Mx is increased from zero. It is found that the straight rod buckles into a spiral shape and touches the inner wall of the tube at the midpoint when Mx reaches 8.987. As Mx increases to 11.472, the contact point in the middle splits into two, leaving the midpoint floating in the air. As Mx increases to 13.022, the midpoint returns to touch the tube wall and the two-point-contact deformation evolves to a three-point-contact deformation. Starting from Mx=13.098, the point contact in the middle evolves to a line contact, and the deformation becomes a point-line-point contact configuration and remains so thereafter. In the case when the line-contact pattern is fully developed, it is possible to predict the spiral shape analytically. The numerical results are found to agree very well with those predicted analytically. Finally, an experimental setup is constructed to observe the deformation evolution of the constrained rod under end twist.

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference28 articles.

1. Spatially Complex Localization After One-Twist-Per-Wave Equilibria in Twisted Circular Rods With Initial Curvature;Champneys;Philos. Trans. R. Soc. London, Ser. A

2. Nonlinear Dynamics and Loop Formation in Kirchhoff Rods With Implications to the Mechanics of DNA and Cables;Goyal;J. Comput. Phys.

3. Helical Buckling of Tubing Sealed in Packers;Lubinski;J. Pet. Technol.

4. Buckling Behavior of Well Tubing: The Packer Effect;Mitchell;Soc. Pet. Eng. J.

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