Brooklyn, for cylinders with simply supported ends. 



The approach used by Galletly and Bart was similar to that of Bodner 



and Berks except that instead of attempting to find a solution directly to 

 the Donnell-type shell equations, they employed Galerkin's method 

 in conjunction with the Donnell equations modified to include the effects 

 of eccentricity. One of the limitations of using Donnell' s equations is 

 that the number of circumferential lobes n should be fairly high, and thus 

 the results will be somewhat in error for very long cylinders which buckle 

 into two or three circumferential lobes, i.e., n = 2 and n = 3, respectively. 



The initial out-of- roundness pattern assumed by Bodner and Berks 

 was of the form 



Wq(x, 6) = esinnecos— (H"?) 



(origin at midbay) while Galletly and Bart assumed 



2lTX 



Wq(x,6) = — sinnS 



1- cos - 



(118) 



(origin at one end of the cylinder). Thus, in both cases, the initial out-of- 

 roundness was similar in form to one of the assumed buckling modes. 

 The two solutions represent lower and upper bounds, respectively, for the 

 effect of initial eccentricities on the collapse pressures of elastically 

 supported cylinders when the initial eccentricities have the same shape as 

 one of the assumed buckling miodes of the perfect cylinder. 



For the case of uniform external hydrostatic pressure, Galletly and 



75 



