Page 256 - Practical Design Ships and Floating Structures

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The velocity potential is obtained from Green's second identity as follows.

Where SH denotes the bottom of the pontoon-type VLFS sited on z=-d and G(<x) denotes the Green
function, which is given for the finite-depth case(Faltinsen and Michelson( 1974)).
To solve the integral equation of radiation problem, the unknown potential is represented by unit
vertical motion of a body of four neighboring panels. The vertical unit motion does not include the
rotational motion and include only heave motion(Yag0 and Endo( 1996)).
The body boundary condition of radiation potential is described in Eqn. (7) and (8).
a4
- (nz), = {~,o,o ,..., o,o)' on the body
=
an
z=(nz), ={o,o,o ,..., OJ}' on the fl body
an
To calculate these radiation potentials, the zero-th order panel method is employed. In diffraction
problem, when Eqn. (3) is inserted in Eqn. (6), the diffraction potential is calculated. The radiation
and diffraction potentials for N bodies are defined in Eqns. (9), (1 0), (1 I), and Fig. 2.

element in the FEM

An element in the BEM

Figure 2: Discretization of a VLFS by quadrilateral elements.
The added mass and wave damping coefficients can be expressed as follows.