V = 0.3, have shown that the maximum difference between predictions 

 using Equations (59), (57), and the more exact formula. Equation (6), 

 given in Reference 32 was about 3.5 percent. 



The next major contribution to the panel buckling problem of ring- 

 stiffened cylinders was that of Von Sanden and TCJlke. By the use of 



33 

 trigonometric series, they outlined a general solution to the same dif- 

 ferential equations used by Von Mises. This approach also permits a 

 closer approximation of the true prebuckling deformations given by the 

 theory of either Reference 6 or Reference 8. However, Von Sanden and 

 Tolke did not attempt to work out the mathematical details of the general 

 solution, but they did develop a solution which was one step better than that 

 of Von Mises. They assumed a two-term trigonometric approximation for 

 the variability of the prebuckling circumferential stress with the axial 

 coordinate, and with this they showed that the "simple-support functions" 

 used by Von Mises for the buckling deformations permit satisfaction of 

 the differential equations. 



It is of interest to us here to give the final formula developed by 

 Von Sanden and Tolke for purposes of comparison with that of Von Mises. 

 In the notation adopted for this presentation, it can be shown to be as 

 follows: 



Eh 



P = 



cr R 



1 



"'(I^^S4(4f)'Jl&^r'''^)'J' ''"-■''' L 



A^) 



^60) 



50 



