Bai and Yeung (1974) also have developed a numerical procedure 

 based on the Green's function method (or boundary integral method 

 as it is sometimes called) which utilizes simple sources dis- 

 tributed over the surface of the vessel as well as the free sur- 

 face, the bottom and an enclosing vertical cylindrical surface- far 

 from the vessel. A third numerical method for solution of the 

 three-dimensional free surface problems is referred to as the 

 hybrid-element method. This procedure, which has been applied by 

 Berkhoff (1972), Chen and Mei (1974), Bai and Yeung (1974), 

 Chenot (1975), Yue , Chen and Mei (1977) and Bettess and Zienkie- 

 wicz (1977), is based on the finite element method and uses a 

 "super-element" at the outer boundary of the discretized region to 

 infinity. Of the available methods indicated above, the distri- 

 buted source procedures of Garrison, and of Faltinsen and Michel- 

 son is believed to be the most versatile and simplest in appli- 

 cation, and has been most v/idely used in practice. 



2.1 Strip Theory 



The solution of the three-diiaensional boundary-value problem 

 for bodies of arbitrary shape requires computer runs, considerable 

 CPU time, and until recent years numerical methods for solving 

 three-dimensional problems were not available. Thus, it has been 

 common practice to use a strip-theory analysis for elongated 

 (shiplike) bodies in which the hydrodynamic coefficients are 

 determined by subdividing the body into a number of slices or 

 segments and assuming that each segment acts as a two-dimensional 

 body and that segments do not reflect mutual interaction effects. 

 The hydrodynamic coefficients for the complete body are obtained 

 by summing up the coefficients associated with each segment. 



Clearly, strip theory represents a valid approximation to a 

 truly three-dimensional hydrodynamic analysis provided the vessel 

 is highly elongated. Of course, one would expect the strip theory 

 approximation to break down as the length to beam ratio decreased 

 and it would be of practical value to know what value of the 

 length to beam ratio might represent a limit on the strip theory 

 approximation. An absolute limit for all vessels does not exist 

 since it is presumably dependent, if only mildly, on the hull 

 shape in addition to the overall proportions, but it appears that 

 few studies comparing three-dimensional theory with strip theory 

 h.ave been made. In fact, the only such comparison known to this 

 writer was made by Migliore and Palo (1979) for rectangular 

 barge configurations. For the series of cases considered, the 

 results indicated that the strip theory analysis tended to break- 

 down when compared to the three-dimensional theory for length to 

 beam ratios of less than 8. Thus, it would appear that for 

 barges, most cases of practical interest would require the appli- 

 cation of three-dimensional theory for predicting hydrodynamic co- 

 efficients. 



2.2 Comparison with Experiment 



Experimental results for hydrodynamic coefficients for three- 

 dimensional bodies are very limited but results of a few studies 

 have been reported. Faltinsen and Michelson (1974) have presente- 

 ed experimental results for a model of a simple barge 90 meters 

 by 90 meters by 40 meters draft. In general, although the scatt- 

 ter in the experimental data is large in some cases, the agree- 



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