displacements. 



Kendrick attempted many solutions by using different buckling 



patterns in the energy integrals. However, the most plausible solution 



52 

 found and the one which has been confirmed by model tests at the Model 



Basin is that based on the following buckling pattern used in the solution 



of Reference 51: 



u(x,8) = Ai cos nS cos — 

 Lb 



v(x,e) = Bj sinne sin"^ + B2 sinnS (l-cos ) (143) 



Lb Lf 



w X Zttx 



w(x,9) = Ci cos n6 sin — + C2 cos n9 (l-cos ~z ) 



^b ^ 



Implicit in the above functions are the assumptions that the cylinder 

 buckles into one -half sine wave from end to end, i.e., corresponding to 

 simple- support conditions, and the interframe buckle shape is such that 

 a zero-rotation condition exists at the ring frames, i.e., corresponding 

 to clamped conditions. The radial component w of the buckling defor- 

 mations defined by Equation (143) is shown in Figure 15. 



Substituting Equation (143) into the energy integrals, Equations (138) 

 through (142), the total potential energy given by Equation (137) becomes 

 a function of the shell and frame geometry, the pressure loading, and the 

 mode- shape parameters A, , B-^, C-., B2, and C2 of the buckling dis- 

 placements. Hence, for a given geometry it can be seen that 



Vt = Vt(Ai,Bi,Ci,B2,C2) (144) 



88 



