PLANNING, DESIGNING, AND CONSTRUCTING TENSION LEG PLATFORMS 61
behavior through use of appropriate distributions or factors on the Rayleigh distribution. Guidance on
selection of the extreme value distribution may be found through examination of appropriate model test
results, full-scale data, or validated time domain calculations.
7.5.6 Stiffness and Mass Modeling
7.5.6.1 For a general problem, the tendon/riser stiffness will contribute terms for each element of the
stiffness matrix, K. This is accomplished using a fully coupled model as described in 7.4.4.
7.5.6.2 For an uncoupled model, a simple approach that can be used to model vertical vessel motions
(heave, pitch, and roll) and tendon/riser tension variations is to represent each tendon and riser (or group of
tendons/risers) as an elastic spring with no mass or fluid interaction effects. If this simple elastic spring model
is used for modeling tendon/riser attachment point forces on the vessel, the forces can be linearized to
generate the stiffness terms of K. However, this simple spring model for the tendons and risers neglects
geometric nonlinearities that cause the terms of K to change depending on the offset point chosen for
linearization.
7.5.6.3 In all but very shallow water, the tendon/riser mass may be an important contribution to vertical and
horizontal mode natural frequencies. One simple approach is to augment the mass or added mass matrices
to reflect the contribution of tendons and risers. Uncoupled time or frequency domain tendon/riser analysis
may be used to generate terms added to M, K, and N to model tendon/riser dynamic effects as a function of
frequency. Classic lumped-mass methods for structural dynamics analysis (Clough and Penzien, 1993
[116]
)
may also be used to allocate tendon and riser mass to the appropriate rigid body degrees of freedom.
7.5.7 Modeling Hydrodynamic Added Mass, Damping, and Exciting Forces
7.5.7.1 There are various assumptions and degrees of approximation that can be used in modeling hull
hydrodynamics for frequency domain analysis.
7.5.7.2 The primary method accepted for design calculations is use of 3D integral equation (source-sink or
panel model) techniques to model inviscid wave interactions with the hull (i.e. wave radiation and diffraction).
When performed to first order, these techniques model the linear free surface effects and hydrodynamic
interactions. When performed to second order, these techniques model the second-order surface potential
and the first-order body/free surface interaction.
7.5.7.3 If hull members have large cross-sectional dimensions compared with the wavelength, then free
surface effects become important and these methods should be employed. Also, as members become larger
compared with the wavelength and member-to-member spacing then hydrodynamic interaction between the
members becomes important, and again these methods are appropriate. However, the viscous drag
contribution is not modeled and, if significant, should be accounted for by linearized drag terms added to the
damping matrix and forcing vector.
7.5.8 Modeling of Wind, Wave-drift, and Current Forces
7.5.8.1 In frequency domain analysis, the steady and oscillatory forces due to wind, wave drift, and current
can be taken into account using a number of different assumptions and approximations. In most cases it is
appropriate to account for steady and low-frequency forces and moments by adding constant forces and/or
moments to arrive at a quasistatic equilibrium point. The TLP dynamics, including tendon/riser stiffness, may
be linearized for motions about this quasistatic equilibrium point.
7.5.8.2 For some analyses, such as the analysis of offset, it is important to account for the low-frequency
motions as accurately as possible. In such cases, force or moment spectra including wind and low-frequency
wave-drift excitation may be applied as input to a frequency domain model. Such an approach is useful where
the response to forces or moments is linear. This does not require a linear relationship between the
environment (wind speed, wave amplitude, etc.) and the forces or moments. If a force spectrum can be
estimated, it can be added to the other contributions to the force vector F in Equation (16). This technique is
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