427 



membrane term due to the uniform load P, we have the following equa- 

 tions of motion for the shell excited by the excess load p, 



where E is the elastic modulus, VPoisson's ratio, and /® the density of 

 the material of the shell. The shell operators D., and t he buckling 



operator B-q are given in Appendix A, In Equations (l), terms of order 



4 2 f) 



^ and 0^ (f' have been neglected and will also be neglected in the ex- 

 pansion of detenninants entering into their solution. Ilany of the terms 

 in the Epstein operators are really redundant, since after elimination 

 betvreen Equations (2) they would be found to contribute only to terms 

 of higher order. 



The boiondary conditions for the problem considered are satis- 

 fied by the Fourier series 



•veO CO 



s^"'-'^^=^)''■' • 



+ «w 



The boundary conditions are single-valuedness of all displacements in 6, 

 vanishing of w and v at cylinder ends due to support by rigid frames, and 

 vanishing of the supplanentary axial strain at the ends. The last 



