Since the differential equations used by Bodner to develop his 



orthotropic- shell solution were of the same approximation as Donnell's, 



? 2 



this resulted in the approximation n - l::;n in the denominator of both 



terms in Bodner's final formula (151). Basically, this approximation is 



in error because the general-instability buckling mode is associated with 



2 



a small number of lobes, i. e. , n is usually 2, 3, or 4, so that assuming n 



to be very large in comparison to unity could lead to appreciable discrep- 

 ancy. However, it turns out in numerical calculations that the frame 

 term dominates, and although Bodner's coefficient 



is different from (n -1) of Equation (136), better agreement has been 



48 

 shown by Ball to exist between pressures from Equation (151), than 



from Equation (136), with those computed using the solution of Kendrick. 



However, in the case of the infinite cylinder, i.e., \->0, the Bodner frame 



2 2 



coefficient reduces to n instead of (n -1). In this case, the Bodner 



formula gives pressures which are one third larger than the correct 



value given by the simple ring formula, i.e., p = 3EI/R Lf. 



55 

 Bijlaard also developed an analysis for the general-instability 



mode of collapse for ring -stiffened cylinders using the method of "split 



rigidities." Also, a rather complete discussion of the orthotropic- shell 



approach to the problem of general-instability of stiffened cylinders for 



56 

 various loadings is given by Becker, However, neither of these two 



96 



