Page 225 - Practical Design Ships and Floating Structures

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Frequency response of the elastic horizontal deflection of combined model under regular wave
conditions had been computed using a finite element method, and the results of the response
considering the shearing rigidity of main structure are also obtained. the results of the selected points
are shown in from Fig. 2 to Figure 4.

Fig. 2 and Fig.3 are the frequency response of amplitude of horizontal deflection at the free end and
the center of main structure under low mooring rigidity, Fig.4 is the frequency response of amplitude
of deflection at the top end of dolphin located at the free end of the main structure.
It can be seen that the different harmonic vibration point exists from the dotted line and real line due to
the effects of shearing rigidity of main structure. the difference is bigger in the second eigen circular
frequency than the first one.
On the other hand, it can be seen that the frequency response of amplitude of horizontal deflection is
small except for harmonic vibration points ,but it will become bigger when long wave appears.

4 NONLINEAR DYNAMIC FINITE ELEMENT ANALYSIS

The structure response to a dynamic load under the wave environment will become nonlinear, because
of the existence of clearance between main floating structure and its mooring equipment and the
disability of mooring fender or dolphin when the applied load exceed their ultimate strength. It is
therefore necessary to predict the response in the design, and especially, evaluate the step of mooring
dolphins under a critical status.

Thus, A nonlinear, three dimensional finite element modeling technique was developed for computing
the dynamic response of a very large floating structure with the nonlinear elements. And a series of
computation study were conducted to several sizes of mooring clearance and damaging path of the
mooring equipment due to the difference incident angle.

4.1 Nonlinear EIement

In our present work, we deal a combined model consisted of VLFS and its mooring equipment, we
assume the clearance (gap) exists between VLFS and the mooring fender. So the VLFS, under the
wave force applied or enforced displacement of the fender, will moves and deflects until the gap closes
and continues to deflect with the gap closed. The characteristic of fender with clearance can be
simplified as a gap element as shown Figure %(right) and the image of the fender behavior .can be
illustrated as shown in Figure S:(left)
On the other hand, the mooring fender has a ultimate strength, they will be broken if the applied force
exceeds the ultimate strength under the severe circumstance, we consider the mooring fender has a
relation between the deformation and applied force as shown in Figure 6. Once the fender is damaged
it will not work, the image of some fender’s behavior on this case can be illustrated as shown in
Figure , and we take it out from model in the next numerical calculating time step. These two statuses
also account for the geometric changes that may occur in the structure.
4.2 Numerical Calculation Method

When considering a problem in which dynamic (time integration) finite element analysis is to be used
as commented above, because of the existence of nonlinear element such as mooring clearance and the
damaged fender, the stiffness matrix is reconstructed in each time step.