The principle of minimuin potential energy is invoked to determine 

 the equilibrium state of the structure, for which the elastic energy V-p 

 must have a stationary value. Any arbitrary variation from this value 

 must vanish, and this leads to the following mathematical criterion: 



av av av av av 



6V^ = = — — 6A^ + -— 5B, + — ^ 6C, + -=- 6B + -— ^6C (145) 



T aA^ 1 aB 1 ac i as z ac 2 



Now, since the variations 5A]^, 5B]^,5 C-,, 6^2' ^^^ ^^2 ^^ ^^^ buckling 

 displacements are arbitrary so that they need not be zero, then, for equi- 

 librium to exist, the following conditions must be satisfied simultaneously: 



av^ av^ av^ av^ av^ 



"aA^ ~ "aB^ ~ ^ ~ "al^ " ac^ ^ ° ^ ^^^^ 



The above conditions lead to a system of five linear, homogeneous, 

 algebraic equations which must be solved simultaneously. In order that 

 the nontrivial solution exist, which is Aj^ ^^ Bj # Cj ^ B2 =^C2 ¥" 0> the 

 determinant formed by the coefficients of these shape parameters must 

 vanish. This 5X5 stability determinant when expanded leads to a 

 fifth-degree equation for the instability pressure. Extensive calculations 

 conducted by Reynolds at the Model Basin with the aid of a UNIVAC 

 computer have shown that the linearized form of the determinantal 

 equation is more than adequate; the higher order terms in the pressure 



are almost insignificant. Reynolds developed a convenient graphical 



5 3 

 solution of the Kendrick equations; he showed that the overall instability 



of a ring- stiffened cylinder can be expressed in a form similar to 



90 



