Post-buckling Behaviour Of A Slender Beam In A
Circular Tube, Under Axial Load
Author(s)
M. Gh. Munteanu & A. Barraco
Abstract
This paper deals with the study of the behaviour of a slender beam introduced in
a cylindrical tube and subjected to an axial compressive force. The beam is very
long compared to its transversal dimensions and therefore it will buckle to a very
small axial force. The post-buckling behaviour is examined. The study has
important applications in the petroleum industry, for coiled tubing in the case of
drilling in horizontal or inclined wellbores. The slender beam has a constant
cross-section that can have any form, although a circular cross-section is the
most used in practice. The problem has a geometrical non-linearity to which the
non-linearity caused by the friction has to be added. Rotations could be large and
a special isoparametric 3D beam finite element is elaborated: the Euler-
Rodrigues quaternion was preferred to describe the finite cross-section rotations.
The paper presents only the static case, but extending the presented approach to
dynamic analysis is quite natural. The method is very accurate and it is rapidly
convergent due to the fact that the exact equations, written for the deformed
configuration, are solved. The iterative Newton-Raphson method was used to
solve the nonlinear differential equations.
Keywords: coiled tubing, finite element method, post-buckling behaviour, Euler
quaternion, geometrical non-linearity.
1 Introduction
A long slender initially straight beam compressed and constrained within a
circular cylinder is studied in this work. This problem presents a great interest in
rock engineering and petroleum production. The beam buckles within the narrow
space of a drill hole under the action of axial force and its own weight. Due to its
Keywords
coiled tubing, finite element method, post-buckling behaviour, Euler
quaternion, geometrical non-linearity.
Related Book
Other papers in this volume
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