Page 322 - Marine Structural Design

298 Part 11 Ultimate Strength

The plastic yield condition used in this example is the same as in EXAMPLE 14.2.
The ABAQUS FEM analysis employs the true stresdtrue strain curve, shown in Figure 14.5
(b). This analysis assumes the material has linear kinematic strain hardening and each side of
the beam is modeled as one element. Figures 14.5 (c-e) show that the structural response is
sensitive to the yield stress. However, the agreement between the results predicted by both
programs is good.
The examples presented in this section demonstrated that the nodal displacements and forces
predicted by the actual beam-column element agree with those obtained by experiments and
by general finite element program analyses. Reasonable results can be obtained by the beam-
column element even when the structural member is discretized by the absolute minimum
number of elements (normally one element per member).
14.4.3 Application to Practical Collision Problems

The procedure implemented in the SANDY program can be used to simulate many different
ship collision problems, such as side central collisions, bow collisions, and stem collisions
against structures like offshore platforms and ridges. The simulation results include: motion
(displacements), velocities/accelerations of the striking and the struck structures, indentation
in the striking ship and the hit member, impact forces, member forces, base shear and
overturning moments for the affected structures, kinetic energy, and elastidplastic
deformation energy of the striking and the affected structures.
In this section three typical ship collision problems are selected. These are ship-unmanned,
platform, and ship-jacket platform collisions.

EXAMPLE 14.5: Unmanned Platform Struck by a Supply Ship
The small unmanned platform, shown in Figure 14.6 (a), which is struck by a 5000 ton supply
vessel, is considered first. The dominant design criterion for this platform type is often ship
collisions, while it is normally wave loading for traditional platforms. The supply ship is
supported to drift sideways with a speed 2.0 ms-1 under calm sea conditions. The added mass
for the sideways ship sway motion is taken to be 0.5 times the ship mass. The force-
indentation relationship for the ship is taken as is shown in Figure 14.6 (b). The added mass is
included following Morison's equation and the added mass and drag coefficients are taken to
be 1.0. The tubes under the water surface are assumed to be filled with water. Therefore, the
mass due to the entrapped water is also included. The force-indentation relationship is
established by following Eqs. (14.2) and (14.7) by following further approximations such as
multi-linear lines, as illustrated in Figure 14.6 (c). The soil-structure interaction is taken into
account using linear springs.
First, a linear analysis was carried out by using a load vector given by the gravity loading on
the structures. Then, a dynamic analysis considering large displacements, plasticity, and
hardening effects followed. The plastic yield condition was taken to be:

(14.24)

It is noted that the indentation in the hit tube will reduce the load carrying capacity of the tube
greatly. This effect has not been taken into account in the present analysis. However, a