between the fluid forces and the motion variables or if a simulation 

 of an extended time period of platform operation is required in 

 order to obtain, e.g., the response statistics in random seas, 

 this procedure may become quite demanding of computer resources. 



III. THE EXTERNAL FORCES 



The external force system acting upon the structure usually 

 originates in four sources: 



(1) The incident waves and currents. 



(2) The motions of the structure itself. 



(3) The anchoring or other position keeping system. 



(4) Wind. 



The first two categories comprise fluid forces resulting from 

 the relative motion between the water and the structure. In computing 

 these forces, several simplifying assumptions may be made, which 

 depend upon the geometry of the structure, the expected severity 

 of the motion, and the nature of the computational process to be 

 used in the motion analysis. 



Structure made up of slender members . As an example of the simpli- 

 fication noted above, consider a structure comprising a space fram.e 

 made up of slender cylindrical members. In this case, it is pos- 

 sible to obtain a good estimate of the total fluid force by computing 

 the force which would act on each member individually in the 

 absence of any hydrodynamic interference between individual members, 

 and then taking the sum of such forces for all members. Examples 

 of platform motion analyses using this procedure may be found in 

 papers by Burke (1969), Paulling (1970) and Hooft (1971). 



It is assumed that a variation of Morison's formula (Morison, 

 et al (1951)) may be applied to the computation of the fluid forces 

 on a slender cylinder oriented at an arbitrary inclination to the 

 flow direction. The fluid force is assumed to be dependent upon 

 the pressure gradient in the flov; field, and the components of 

 relative fluid velocity and acceleration which are normal to the 

 centerline of the cylindrical member, this is illustrated in 

 Figure 2. 



129 



