425 



BUCKLING INSTABILITY OF THIN CYLINDRICAL SHEU^ 



EXTERNAL STATIC LOADING 



1. Introduction and General Theory 



The buckling of cylindrical shells closed at both ends under 

 external hydrostatic loading has been treated by von Mise^^/ using the 



17 von Mises, Stodola Festschrift, p. 418 (1929) 

 ExperL-nental Model Basin Report 366 (1933) 

 Saunders and Windenburg, A.S.M.E. Trans, vol, 53 (1931) 

 Windenburg and Trilling, A.S.M.E. Trans, vol. 56 (1934) 



Poisson-Love theory of shells. Recently Epstein^ has corrected certain 



TJ Epstein, Jour. Math, and Phys., vol. XXI, 196, (1942) 



errors in the second-order terms in the equations of the classical theorj' 

 of shells. They arise in part from incorrect expressions for the curva- 

 tures, and in part from the premature introduction of the plane stress 

 approximation into the membrane terms of the shell equations. 



It is our purpose here to develop the theory of buckling of 

 cylindrical shells under static loading on the basis of the corrected 

 shell equations. Although the numerical corrections to the buckling pres- 

 sure are not large, it seemed to us worthwhile to present corrected tables 

 and graphs. Moreover, the theory of static buckling is presented from a 

 different point of view than the usual one. Envisaged from the dynamical 

 point of view, the condition for static buckling is found to be equivalent 

 to the condition for dynaruical instability for small displactiraents, in the 

 sense that one or more of the shell frequencies become complex when the 



