The first attempt at a rigorous mathematical solution of the elastic 

 general-instability problem for long cylindrical shells, which are stiffen- 

 ed by a uniform distribution of typical light ring frames closely spaced, 



and a set of two or more, depending on the length L^^, intermediate heavy 



57 

 ring frames widely spaced apart, is that attributed to Kendrick of the 



C Q 



Naval Construction Research Establishment. Later, Reynolds at the 

 Model Basin discovered certain shortcomings in the buckling functions 

 assumed by Kendrick, and he revised the original analysis to conform 

 more realistically to the experimental observations reported in Reference 

 58. 



The basic approach used in the mathematical formulations by both 

 Kendrick and Reynolds was that of using the energy method and writing 

 expressions for the elastic strain energies for the shell, the typical light 

 ring frames, and the intermediate heavy ring frames. The procedure is 

 almost identical to that followed in connection with Equations (137) through 

 (142), except that the ring energy terms 



l.(^^)'n?:M 



in Equation (137) must be rewritten as follows to include the strain 



energies of the heavy frames: 



(N^+1)(N^+1)-1 

 V . = Y (f +F\- ) (F +F\+ ) If +F\ (152) 



(N^+1)(N^+1)-1 N^ N^ 



»where 



N-i is the number of light ring frames, 



98 



