pressure hulls should start with an attempt to integrate the three partial 

 differential equations for the shell deformations including elasto-plastic 

 effects. This is the topic of discussion in the next section. 

 INELASTIC BUCKLING BETWEEN RING FRAMES 



In recent years, advances in plasticity theory have made it possible 

 to approach shell buckling problems more rigorously. Investigations by 

 Biljaard,' Ilyushin, Stowell, and Gerard, among others, have con- 

 tributed greatly to the development of theory for the inelastic buckling of 

 plates and shells; this school of thought made use of the deformation 

 theory of plasticity. 



Using the general set of differential equations for a fully plastic 

 cylinder derived by Gerard in Reference 21, Reynolds has developed a 

 solution for the inelastic buckling of ring -stiffened cylinders, valid for 

 both cases in which the shell material exhibits elastic -perfectly plastic 

 and elastic strain-hardening characteristics. The buckling equations 

 obtained by specializing the more general ones for the case of hydro- 

 static pressure loading are: 



l^(ll^ + A±:,l^]+l.l^+li^ + ll:L-.0 (98) 



2 E V 2 2 axds Rax/4 2 4 2 4 dxds 



s \ ax / ax as 



^tflQ^a _^_ijL+l ^\ ^l^+li^=o (99) 



EV2axas 2 Ras/ 4_2 4axas 

 as 'ax 



66 



