of the shell is integrated over the entire length Lt^ of the cylinder, and the 

 ring energies are summed over the total number of ring frames. Bodner 

 and Shaw review the whole problem of the energy approach to both lobar 

 (sometimes referred to as panel) and general-instability failure of rein- 

 forced cylindrical shells. 



The work of Salerno and Levine constituted the basis for theoretical 

 developments by investigators who followed them. The most acceptable 

 solution of the elastic general-instability problem is that attributed to 

 Kendrick of the Naval Construction Research Establishment. Extensive 



confirmation of this theory has been reported by Reynolds and Blumenberg 

 at the Model Basin. It is of interest here to summarize the basic equations 

 and integrals used by Kendrick in his formulation. 



The total potential energy Vj. of the elastic system, comprised of the 

 cylindrical shell and the ring frames, is given by 



N N 



V^ = U +U^+y(F) +y (F ) +W (137) 



T e h u e T Li br 



r=l r=l 



where 



U and Ui^ are the extensional and bending strain energies of the 



shell, respectively 

 F and F^^ are the extensional and bending strain energies of the 



ring frames, respectively 

 W is the total work done on the elastic system by the 



external loads due to the pressure, and 



85 



