the determinant of the coefficients vanish. This condition leads to a 

 determinantal equation for finding the critical pressure at which elastic 

 buckling of the cylindrical shell will occur. Some of the more important 

 details will be illustrated later in connection with the elastic general- 

 instability problem, the formulation of which follows along similar lines. 

 However, the general energy approach to solving shell buckling problems 



is discussed in great detail by Timoshenko in Reference 9. 



34 

 By using this energy method, Salerno and Levine derived the 



Von Mises solution as a starting point. They also developed solutions for 



the cylindrical shell having clamped edges, and later attempted to include 



the bending and torsional restraints afforded the cylindrical shell by ring 



35 

 frames possessing finite elastic properties. However, certain 



assumptions in their work led to some inconsistency in final results, so 



that a number of investigators after them used their basic formulation 



3<i 

 to get improved solutions. Shaw, Bodner, and Berks have reviewed 



the whole problem of the energy approach to the panel-instability failure 



of reinforced cylindrical shells in an attempt to clarify some of the 



questions which arose in regard to the analytical work of Salerno and 



Levine . 



The most recent and most useful solution derived by application of 



27 

 the Rayleigh-Ritz energy method is that by Reynolds. He developed a 



solution in which the influence of the elastic ring frames on both the pre- 



buckling and buckling deformations was included. The use of a several- 



53 



