On an Elastic Rod inside a Tube under End Twisting Moment
Date Issued
2010
Date
2010
Author(s)
Li, Hong-Chi
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 at the centers of the tube. 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 increases 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 set-up is constructed to observe the deformation evolution of the constrained rod under end twist.
Subjects
elastic rod
tube
buckle
torque
clamp
deformation
Type
thesis
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