weight design of ring- stiffened cylinders under external pressure. 



One of the basic assumptions underlying all the mathematical 

 formulations presented in the main portion of this paper is that associated 

 with thin- shell theory. Immediately, the question arises as to what is the 

 limit of applicability of the equations and formulas which have been pre- 

 sented. If we accept the thesis of Novozhilov, then it appears that the 

 approximations of thin- shell theory may introduce errors on the order of 

 5 percent for thickness-radius ratios of about 1/ZO for cylindrical 

 pressure hulls. This small magnitude of error provides the designer a 

 great deal of flexibility because the wall thicknesses required for pres- 

 sure-hull structures to withstand the pressures for operation at great 

 depths, even those depths covering 98 percent of the world's oceans, may 

 still be no thicker than the 1/20 ratio so that the equations we have set 

 forth can provide adequate solutions. Of course, this is also contingent 

 on the hull material used, which, in turn, influences the thickness, but in 

 general, it can be said that probably the upper limit on the error 

 introduced by using thin- shell theory should be less than 10 percent. 



The assumptions of thin-shell theory have been examined by Klosner 

 and Kempner in light of results they found from a three-dimensional 

 elasticity solution for the case of a long thick cylinder under the action of 

 a single radial band load around its periphery. These investigators 

 concluded that the classical shell theories of Timoshenko and Flugge 

 represent good approximations to the three-dimensional stress problem 



118 



