ll 



^ . = 3 = 



1 



This is a three-dimensional, finite-element program for the 

 analysis of bi-mooring arrays under a uniform current. No 

 effort has been made to gcncrati7.c the program to other 

 mooring types or to include the effects of nonuniform 

 currents; however, the technique appears to have potential 

 in these areas. A program listing is given in [tcfercncc 12. 



This program solves for the steady-state, equilibrium posi- 

 tion of a cable when boundary conditions are specified at 

 two locations on the cable. Based on the Adam-Moulton 

 prediction-corrector integration method with a Runge- 

 Kutta starter, the program solves for the boundary-value 

 condition directly rather than by integrating a family of 

 initial-value problems and then selecting the desired solu- 

 tion. It utilizes the differential equations of cable equilib- 

 rium that result from three-dimensional velocity fields and 

 hydrodynamic loading functions. This technique should 

 be useful for simple systems, both moored and towed. 

 Attempts to validate the program with towed system data 

 have shown "fair agreement" between actual and predicted 

 data. The program is considered proprietary, and no list- 

 ings arc available. 



This is an Iterative, finite-clement solution technique that- 

 begins at any point on the cable system where conditions 

 art known or assumed and that then integrates through the 

 system. When the boundaries of the system are reached, 

 the calculated boundary conditions are compared with the 

 actual conditions; and corrections are then made to the 

 starting-point conditions. The integration process is 

 repeated until calculated and actual boundiiry conditions 

 agree within some limit of error. The program can handle 

 discrete elements along the cables, and provisions have 

 been maife to include aerodynamic drag if it should be 

 needed. Because the program is considered proprietary by 

 GK, some program details and capabilities arc not known. 

 Validation of the program by GE with model and full- 

 scale data has shown the program to be •'very good." 



Dcvelopcil to determine the steady-state geometry and 

 cable tensions in single-point, mooring systems, this 

 program is based on an iterative, numerical-integration 

 routine for the cable equations. Consideration is given 

 to discrete elements along the cable and to current profiles 



< 



A. Cnblri arc i scries of straight 

 segments. 



B. The cables arc perfectly clastic 

 and can sustain neither comprc»- 

 sive loads or bending torsional 



C. Tangential drag force is zero. 



A. Ciil'lcs arc completely flexible 

 and incxtensiMc. 



B. Ihe cable ends arc subject to 



A. Cables are a scries of straight 

 elements. 



B. Cables can transmit no moment. 



C. Cable miss and drag force arc 

 lumped on each cable segment. 



A. Cable is a series of 100 straight 

 segments, 



B. Tangential cable drag coefficient 

 is 2% of the normal drag cocffi- 



h 5 



It I i 





= 



t I ' I ' g 



1 



t I l I 



U 



1 5 



It s. I 



1 , 



E. S, I I 



1 ^ 



J ii 1 li 



1 = = 

 ? 1 1 



" 



1 E 



it? 



1 



1 1 . . ' ■ J 

 1 .J M . 1 



5-0 -5 = 5 • e-:i S & 

 =s" -is" • "°S ^5, 



nn ili-i iiiii 111 



