Shock sensitivity in the localised buckling of a beam
on a nonlinear foundation: The case of a trenched subsea pipeline
Z.K. 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.
keywords: subsea pipelines, thermal buckling, localised lateral buckling,
nonlinear pipe-soil interaction model, trench, bifurcation, Maxwell load,
homoclinic snaking, periodic buckling, shock sensitivity
J. Mech. Phys. Solids 143, 104044 (2020)