this way, he derives an expression for the inelastic buckling of ring- 

 stiffened cylindrical pressure hulls. 



The basic differential equation used by Lunchick in his analysis is 



d'*w' 7 pR d^w 12 



A, — + 6(1-1/^) — _ + 



dx-^ 



Esh^ dx2 r2j^2 



<^- 



Az -V 



4 



w = 



(42) 



where the plasticity coefficients Aj^ , A2, A]^2 a-nd the variable Poisson 

 ratio P are expressed in terms of the elastic modulus E, secant modulus 

 Eg, tangent modulus E^., elastic Poisson ratio I/g, and the prebuckling 

 stress ratio k by the following expressions; 



(l-^t/Eg) 



Ao = 1 



4(1-i/2)k2h 



[(2-1/) - (l-2z/)k]' 

 [[l-2i/) - (2-i/)k] 



4(1-z/2)k2h 

 (1-Et/Es) r- -1 2 



(43) 



(44) 



A^2 = 1 + i^-^^^^^) [J2-1/) - (l-2v)k] [(1-2,/) - (2-v)kJ (45) 



4i/(1-i/^)k2h 



1/1 \Es 

 v=- -[- -vJ 



2 \2 / E 



(46) 



and in which 



K 



Om' Xm 

 1 - k + k^ 



(l-Et/Eg) 



4(1-v2)k2 



J [(2-1/) - (l-2i,)k]^ -3(l-J/2)"l 



(47) 



41 



