Some Aspects of Very Large Offshore Structures 



:. = ^(x-a) 2 + (y-b) 2 



k tan (k . d) + \> = 

 n n 



The source strength q(a) can be obtained after substitution of (11) in 

 the boundary condition at the body surface : 



of d^ t% 



-r— = -z— + -z = for x = s (13) 



fin n On — — v ' 



or : 



7 (x, a) dA | = ^- for x = s (14) 



For a restricted number of discrete sources, this integral 

 equation changes into a set of linear equations in the unknown source 

 strengths. For an infinitely great number of sources, the numerical 

 solution approaches the exact solution. It will be clear that the accu- 

 racy obtained in the calculations depends on the number of sources 

 applied and on the location of the sources. 



II. 4 Pressure, forces and wave diffraction 



Once the velocity potential is known, the different aspects of 

 the interaction between structure and waves can be calculated without 

 much difficulty. According to Bernoulli's theorem, the pressure is 

 given by : 



The dynamic wave load on the structure is given by the linea- 

 rized pressure : 



P = Pf£ (16) 



The total wave excited forces (and moments) can be found by 

 integration of the pressure over the surface of the body. The total 

 force is composed of a periodic and a constant part. The oscillating 

 part of the wave force is found from the linearized pressure : 



— = J/ p (?) • £• dA ( 1? ) 



A 

 •Similarly we find for the moment : 



963 



