A finite element formulation is developed for the prediction of
the large displacement response of pipelines which are placed upon
irregularly contoured marine sediments and are subsequently subjected
to episodic hydrodynamic loads. The equations of motion during each
episode of extreme wave activity are obtained from a variational form
of Hamiltons principle and this form of the equations of motion is
integrated using the Newmark method of implicit integration. Within
each time step a Newton-Raphson iteration scheme is used to achieve
equilibrium while accurately tracking the nonlinear path-dependent
response. An updated Lagrangian formulation shifts the pipeline
reference configuration and separates rigid body movements from
pipeline deformations. This provides a large deflection, small
strain transient analysis of the pipeline response.
Nonlinear, elastic-plastic springs simulate transverse and axial
bottom resistance from both cohesive and cohesionless sediments.
Inclusion of a pressure differential across the pipe wall modifies tensile stresses and influences the flexural stiffness of the finite
element model through the geometric stiffness matrix. Hydrodynamic
added mass and nonlinear, viscous drag forces are included by means
of the relative-motion form of the Morison equation. The formulation
results in a three-dimensional finite element model of a bottom-laid
pipeline that is constrained to follow the irregularly contoured
ocean bottom.
A finite element method computer model is developed and used to
predict the pipeline response to both monochromatic and random wave
loads. Numerical examples presented demonstrate the validity of the
formulation and illustrate the results obtained from sample
simulations. It is found that nonlinear structural behavior is a
dominant factor in predicting pipeline response and that inclusion of
nonlinear effects greatly reduces predicted pipeline displacements.
It is further shown that both the directionality of wave attack and
the wave length of incident waves significantly alters the magnitude
and location of the maximum pipeline response. Computational times
for the random wave simulations analyzed were substantial with an
approximate ratio of CPU to real time ratio of 105 to 1 being typical
for the finite element analysis of a prototype marine pipeline having
150 degrees of freedom
