determining the elastic general-instability pressures o£ a perfect cylinder. 

 The basic approach was again the energy method in which an out-of round- 

 ness and a buckling pattern are assumed, and the principle of minimum 

 potential energy is invoked to determine the amplitude coefficients. In 

 his analysis, Kendrick assumed that the out-of-roundness coincides with 

 the buckling shape associated with the lowest elastic general-instability 

 pressure of the perfect cylinder; that is, the out-of-roundness function is 

 sinusoidal in both the circumferential and longitudinal directions, i.e., 



rmrx 



w (x,e) = C^cosnesin -; — (170) 



o^ ' ' o L.^ ^ ' 



where Wq is the radial deviation from perfect circularity and C_ is the 

 amplitude of this deviation. 



Since in actual construction of reinforced cylindrical pressure hulls, 

 the initial overall longitudinal "sagging" implied by Equation (170) is 

 highly improbable, Hom working at the Model Basin devised a new 

 analysis based on the following more realistic out-of-roundness shape: 



^^(6) = Cocosne (171) 



This function implies that the cylinder generators over the bulkhead spac- 

 ing L^3 are straight and parallel but that the circumferential profile of the 

 shell varies from the perfect circle in a sinusoidal manner. 



The mathematical techniques used by both Kendrick and Hom were al- 

 most identical, and they have already been discussed in connection with 



109 



