li 



* O. O „ 



1 



Based on an iterative technique called the Metliod uf 

 Imaginarj' Reactions (MIR), this very general program 

 can handle complex structures with internal rcdundint 

 elements and still reach a solution rapidly. All forces on 

 the structure must be known; and sufficient reactions 

 muM be known, or assumed, to make the structure 

 statically determinate. Assumed reactions provide ■ 

 starting point, and these arc corrected during each 

 iteration until a predetermined level of accuracy has 

 been reached. I'osition-dependent forces arc handled 

 by using successive approximations. The MIR technique 

 is used by most people for static anaJysis of niuliilcg 

 mooring systems. The latest version of this program is 

 able to analyze complex mooring configuration with up 

 to 22 cables under any current profile. A computer pro- 

 gram listing of the latest version of this technique is gi\-cn 

 in Reference 8. 



This program, based on Skop's MIR (Reference 4). was 

 used to perform design and performance studies on the 

 Woods Hiilc Internal Wave Kxpcrineni (IWF'X) tri- 

 mooring. Discrete elements and normal and tangential 

 drag forces could be handled, but not internally redundant 

 structures. Reference 9 does not provide a program listing. 



A Ncwton-Raphson iteration procedure is used lo solve 

 the fund.imental equilibrium and compjiibility cq uiions 

 for single, bi-, and tri-moored cable systems without 

 internal redundants. Included arc the effects of nnrmaJ 

 and tangential drag forces. The procedure was set up for 

 operation on the General Klectric (CI-:) Desk Side Com- 

 puter System (DSCS). Assumption A may cause the 

 results to be grossly in error if the program is applied to 

 a ca.se where currents varj' in magnitude and direction 

 with depth. 



SKASNAKR uses a solution method similar to Skups MIK. 

 The basic computational element is a cablc-integra'ion rnu- 

 tine, integration along the cables is used for an initial esti- 

 mated tension and then the tension estimates are refined 

 based on how far away cable ends arc from mooring points 

 after an iteration. The bi- and tri-moonng configurations 

 without inlernal redundants arc handled is are discrete ele- 

 ments on the cables, but the program appears to require 

 more computer time to reach a solution with Reference 8. 

 A program listing is not presented in Reference 11. 



1 

 1 

 < 



A. Cables arc a scries of elements. 



B. Current profile is linear on each 

 cable element. 



D. Tangential drag force is zero, 



E. The mooring must be completely 

 submerged or the location of 

 surface devices must be completely 

 specified. 



F. No cables or cable segments can lie 

 on the ocean floor. 



A. Cables arc a scries of straight 

 elements. 



B. A lumped parameter representation 

 of the structure is used. 



C. Tangential drag coefficient is 2.5% 

 of the normal drag coefficient. 



D. Cables cannot transmit moment. 



A. Current loading on cables arc 

 distributed and arc constant in 

 magnitude and direction. 



A. Cables arc a series of straighi-Iincd 

 segments. 



B. Dragforccon the cable is com- 

 puted a.ssuming the projected 

 cable area. 



II 



-5 



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1 



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1 



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gl 



5 " 



^ E _ 1 I 



\\ 



I I ^. I 



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General 



Tri-raoor 



General 

 without 

 internal 

 redundants 



Ui-moor 

 Tri-moor 



1 = = 



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Ijl 



Dr. R. A. Skop 

 Naval Research Laboratory 

 Washington. D.C 

 Comm (202) 767-2904 

 Autovon 297-291W • 



Dr. N. N. Panickcr 

 Department of Ocean Engineering 

 Woods Hole Oceanographic Institute 

 UoodsHole, MA 

 Comm 1617) S4S-1400 

 E.xt.417 



Dr. J. M. Cormally 



Bell Telephone Laboratory 



Whippany. .New Jersey 



Now with TRW Systems Group 



Washington Operations 



McLcin, VA 



Comm (703)893-2000 



H. Forbes Little 

 Instrumentation Laboratory 

 Massachusetts Insiirote of Technology 

 Cambridge. .MA 



