attention will be focused mainly on the small-deflection theories. 



ELASTIC ASYMMETRIC (LOBAR) SHELL 

 BUCKLING BETWEEN RING FRAMES 



The first attempt at a rigorous solution of the elastic lobar-buckling 



problem of a thin cylindrical shell on the basis of the theory of elasticity, 



29 

 and later on the basis of thin- shell theory, was made by Southwell. 



Although he concentrated his efforts on the case of radial pressure loading 



only, his work paved the way for the theoretical developments by those who 



followed after him, notably Von Mises and Tokugawa. An excellent 



discussion of the most important theoretical formulas developed by these 



three authors is given in Reference 32. 



For our purposes, it suffices to say that the first satisfactory solution 



to the elastic buckling problem of a thin cylindrical shell of finite length 



30 

 is attributed to Von Mises. He assumed simple -support boundary con- 



ditions at the ends of the shell, thus enabling him to obtain an exact 

 solution to the thin-shell equations in closed form. At a later date, 

 Windenburg and Trilling simplified the original theoretical results of 

 Von Mises, and this led to the developinent of some convenient formulas 

 for design purposes. Some details covering both of these accomplish- 

 ments will now be reviewed. 



Instead of using the original notation of Von Mises, recourse will be 

 made to the terminology and form of solution given by Timoshenko, de- 

 tails of which can be found in Reference 33. In terms of the displace- 

 ments u, V, and w, the three differential equations of equilibrium for an 



45 



