In this paper, a set of non-linear equations of motion for a single-tendon
tension leg platform are developed. The equations of motion consist of part
ial differential equations representing the transverse and longitudinal res
ponse of the tendon. In addition, a mixed formulation partial differential
equation describing the surge response of the hull and tendon, coupled with
an ordinary differential equation for the pitch response of the rigid hull
is presented. Many of the simplifying assumptions used by prior researcher
s have been eliminated. The hull is modelled as a hollow rigid cylindrical
body, and the tendon as a hollow cylindrical beam pinned at its top to the
hull and at its bottom to the template connected to the seafloor. The Exten
ded Hamilton's Principle is applied and the Lagrangian is fully developed.
Terms include the kinetic energy, bending and membrane strain energies and
the potential energy due to gravity and buoyancy. The normalized equations
of motion are also detailed. The full derivation with assumptions are prese
nted. The response, analyzed for stochastic wave and current loading, is pr
esented with a planar motion assumption. The tension leg platform will osci
llate about its vertical position due to ocean waves. Current will cause a
tension leg platform to oscillate about an offset position rather than its
vertical position. This offset in the surge direction has a corresponding s
etdown, the lowering of the hull in the heave direction, which increases th
e buoyancy forces. This results in a higher tension in the tendons than if
the tendon and hull were in a vertical position. Forces on the tendon have
been neglected in much of the literature. The responses presented in this w
ork show that the inclusion of forces on the tendon will result in both a g
reater amplitude and offset position when compared to studies where these f
orces are neglected. This offset position, which is the surge displacement
from the vertical position, is significant in the operation of a tension le
g platform. A Monte Carlo simulation was performed on the drag and inertia
coefficients in Morison's equation. A uniform random distribution of coeffi
cients was selected from 0.6 to 2.0 for each coefficient. Twenty computer s
imulations were implemented for each coefficient. The response showed that
the offset position and the amplitude are both dependent on the drag coeffi
cient. The surge of the hull shows a maximum offset approximately three tim
es greater for the coefficient that resulted in the maximum displacement th
an the minimum. The response did not show a significant dependence on the i
nertia coefficient, however, this is not necessarily true for unsteady curr
ent. large hull and tendon diameters, ocean wave frequencies greater than 1
rad/s, and low current velocity. (C) 1999 Academic Press.