Page 313 - Marine Structural Design

Chapter I4 OjJshore Structures Under Impact Loads 289

14.3 Collision Mechanics
14.3.1 Fundamental Principles
The analysis of collision mechanics is generally based upon the solution of the differential
equations of dynamic equilibrium. The collision force is a function of the relative indentation
of the ship and platform. Thus, an incremental solution procedure is required.
The problem is greatly simplified if the collision duration is considerably smaller than the
natural period of the governing motion. This assumption is often valid for relevant rigid body
motions of floating and articulated platforms. In this case, the solution can be based upon a
quasi-static solution using the principles of
Conservation of momentum
Conservation of energy
This way, the determination of impact kinematics and energy transfer during collisions can be
decoupled fiom the analysis of strain energy dissipation in colliding objects.
A static solution applies for collisions lasting significantly longer than the natural period of the
governing motion.
For jackets at medium water depths, the ratio between the collision duration and the natural
period of vibration for leg impacts may be such that significant dynamic effects are involved.
This has been investigated to a very small extent. Normally, a static analysis is considered
appropriate, but possible dynamic magnification should also be evaluated.
14.3.2 Conservation of Momentum
In the following sections, the energy to be dissipated as strain energy is determined by
considering translational motions only. More accuracy may be obtained by considering more
motion components (platform and vessel rotations), and therefore formulating a complex
derivation. It is always conservative to use the formulas given in Section 14.3.3.
The conservation of momentum for a central collision between a ship and a platform moving
in the same direction is expressed by:
msvs f mpvp = (m, + mp kc (14.8)

where,
v, = Common velocity after impact
v, = Velocity of ship vs > vp

vp = Wave induced velocity of platform
m, = Mass of ship including added mass

mP = Mass of platform including added mass
The common velocity is thus defined by:

(1 4.9)