Equation (136), that is, as the sum of two effects. One is a shell effect 

 which reflects the membrane stiffness of the cylinder, as does the first 

 term of Equation (57) for the panel-instability problem, except in the 

 difference of the length (Li£ vs L^) of shell considered. The other is a 

 frame effect which reflects the bending stiffness of the cylinder. Thus, 

 Reynolds showed numerically that Kendrick's solution can be expressed 

 in the form 



cr ''s 



(^•^•"l^^'fe") ""' 



where the geometric parameters are the same as those for the Tokugawa- 

 Bryant formula. Equation (147) further demonstrates the usefulness of 

 the "split-rigidities" concept. 



Ball ° refined Reynolds' graphical solution and extended the range 

 of usefulness by carrying out additional computer calculations for 

 geometries of future interest. Figures 16 and 17 give the curves devel- 

 oped by Ball for both the Tokugawa- Bryant formula and the Kendrick 

 solution. One point of interest to the designer is that these curves in- 

 dicate the range of geometry for which disagreement exists between the 

 two formulations. In such cases, it goes without saying that the curves 

 corresponding to the Kendrick solution should be used. 



Another approach to the general-instability problem was first pro- 

 posed by FlUgge; see Reference 9. He derived a set of differential equa- 

 tions for an orthotropic shell and showed how its solution could be used 



91 



