Buckle Propagation in Tubular Structures
Authors: Nogueira A.C. , Tassoulas J.L. 
Published: October 2008

Abstract
A novel method for the analysis of buckle propagation in tubes such as tendons of tension leg platforms and pipelines for deepwater applications is presented. Results are reported for the propagation pressure and state deformation in tubes of various materials (SS- 304, CS-101O and X-52 steel tubes) with a wide range of values of the diameter-to-thickness ratio (D/t). Not only the method overcomes the prohibitive computational demands of earlier procedures, but also it is in excellent agreement with experimental data for all values of D/t investigated (from D/t = 78 to as low as D/t = 12.8).

Introduction
Tubular structures subjected to external pressure must be designed against progressive collapse, an elastoplastic failure mode that spreads in the longitudinal direction and has become known as the propagating buckle. The pressure required to initiate a propagating buckle is known as initiation pressure pi. It is dependent on the material characteristics, the diameter-to-thickness ratio and the local integrity of the structure [1]. Once initiated, the buckle can be sustained as long as the pressure does not fall below a minimum, the propagation pressure,pP. This is the pressure required for quasistatic propagation of the buckle. Typically, pp is much less than pi with the ratio pp/pi in the range 0.15 &lt; Pp/Pi &lt; 0.6. Therefore, unless an adequately designed arrestor is encountered on the tube, the buckle will continue its destructive path as long as the ambient pressure remains above Pp
Most studies of the phenomenon to date have sought to determine the value of the propagation pressure experimentally and develop empirical formulae [2][3]. In addition, analytical studies have been conducted usually relying on simplified kinematics, such as reducing the three-dimensional problem to a two-dimensional one by assuming that the cross sections of a tube collapse as a ring [4][5][6], or considering approximate configurations of the propagating profile [71[8]. While empirical equations and simplified analytical procedures predict pp very well for tubes with D/t &gt; 60, estimates differing by as much as 35% from experimental results have been. obtained [9][10], especially for D/t &lt;35.
In order to examine the mechanics of buckle propagation and to predict the propagation pressure correctly, a rigorous nonlinear finite element analysis applied specifically to the problem has been developed at The University of Texas at Austin. Studies of both quasistatic buckle propagation [11] and the dynamics of the phenomenon [12][13] [14] have been conducted, yielding excellent predictions of the propagation pressure. In these studies, computationally intense simulations were used to track the phenomenon from initiation to propagation.
More recently, a technique for steady-state finite element analysis of buckle propagation has been developed [9][15][16]. The technique takes advantage of the steady-state nature of the phenomenon and leads directly to the propagating buckle, thus avoiding the computationally demanding process of buckle initiation. This paper presents a brief summary of the formulation, propagation pressure predictions vs. experimental results, and the predicted distribution of strains along the propagating profile.