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Shock sensitivity in the localised buckling of a beam on a nonlinear foundation: The case of a trenched subsea pipeline
Journal of the Mechanics and Physics of Solids ( IF 5.3 ) Pub Date : 2020-06-23 , DOI: 10.1016/j.jmps.2020.104044
Zhenkui Wang , G.H.M. van der Heijden

We study jump instability phenomena due to external disturbances to an axially loaded beam resting on a nonlinear foundation that provides both lateral and axial resistance. The lateral resistance is of destiffening-restiffening type known to lead to complex localisation phenomena governed by a Maxwell critical load that marks a phase transition to a periodic buckling pattern. For the benefit of having a concrete and realistic example we consider the case of a partially embedded trenched subsea pipeline under thermal loading but our results hold qualitatively for a wide class of problems with non-monotonic lateral resistance. In the absence of axial resistance the pipeline is effectively under a dead compressive load and experiences shock-sensitivity for loads immediately past the Maxwell load, i.e., extreme sensitivity to perturbations as may for instance be caused by irregular fluid flow inside the pipe or landslides. Nonzero axial resistance leads to a coupling of axial and lateral deformation under thermal loading. We define a ‘Maxwell temperature’ beyond which the straight pipeline may snap into a localised buckling mode. Under increasing axial resistance this Maxwell temperature is pushed to higher (safer) values. Shock sensitivity gradually diminishes and becomes less chaotic: jumps become more predictable. We compute minimum energy barriers for escape from pre-buckled to post-buckled states, which, depending on the magnitude of the axial resistance, may be induced by either symmetric, or anti-symmetric or non-symmetric perturbations.



中文翻译:

非线性基础上梁局部屈曲的冲击敏感性:海底沟槽管道的情况

我们研究了由于外部扰动而产生的跳动不稳定性现象,该扰动是基于在非线性基础上提供轴向和横向阻力的轴向加载梁产生的。侧向电阻是加劲-减劲类型,已知会导致复杂的局部化现象,该现象由麦克斯韦临界载荷控制,麦克斯韦临界载荷标志着相态向周期性屈曲方向的过渡。为了有一个具体而现实的例子,我们考虑了部分埋入沟槽的海底管道在热负荷下的情况,但是我们的结果对于非单调侧向阻力的许多问题定性地成立。在没有轴向阻力的情况下,管道有效地承受了恒压负载,并且对刚超过麦克斯韦负载的负载(即,对扰动的极端敏感度,例如可能是由于管道内不规则的流体流动或滑坡造成的。非零轴向阻力导致热载荷下轴向和横向变形的耦合。我们定义了一个“麦克斯韦温度”,超过该温度直管可能会陷入局部屈曲模式。随着轴向阻力的增加,此麦克斯韦温度被推至更高(更安全)的值。震动敏感度逐渐降低,并且变得更少混乱:跳跃变得更加可预测。我们计算了从预屈曲状态到后屈曲状态时逃逸的最小能垒,这取决于轴向阻力的大小,可能是由对称,反对称或非对称扰动引起的。非零轴向阻力导致热载荷下轴向和横向变形的耦合。我们定义了一个“麦克斯韦温度”,超过该温度直管可能会陷入局部屈曲模式。随着轴向阻力的增加,此麦克斯韦温度被推至更高(更安全)的值。震动敏感度逐渐降低,并且变得更少混乱:跳跃变得更加可预测。我们计算了从预屈曲状态到后屈曲状态时逃逸的最小能垒,这取决于轴向阻力的大小,可能是由对称,反对称或非对称扰动引起的。非零轴向阻力导致热载荷下轴向和横向变形的耦合。我们定义了一个“麦克斯韦温度”,超过该温度直管可能会陷入局部屈曲模式。随着轴向阻力的增加,此麦克斯韦温度被推至更高(更安全)的值。震动敏感度逐渐降低,并且变得更少混乱:跳跃变得更加可预测。我们计算了从前屈曲状态到后屈曲状态时逃逸的最小能垒,这取决于轴向阻力的大小,可能是由对称,反对称或非对称扰动引起的。随着轴向阻力的增加,此麦克斯韦温度被推至更高(更安全)的值。震动敏感度逐渐降低,并且变得更少混乱:跳跃变得更加可预测。我们计算了从预屈曲状态到后屈曲状态时逃逸的最小能垒,这取决于轴向阻力的大小,可能是由对称,反对称或非对称扰动引起的。随着轴向阻力的增加,此麦克斯韦温度被推至更高(更安全)的值。震动敏感度逐渐降低,并且变得更少混乱:跳跃变得更加可预测。我们计算了从预屈曲状态到后屈曲状态时逃逸的最小能垒,这取决于轴向阻力的大小,可能是由对称,反对称或非对称扰动引起的。

更新日期:2020-06-23
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