the general direction of N. J. Hoff. In particular, Salerno, Levine, Pulos, 

 and, later, Shaw and Bodner, developed formulations for elastic lobar 

 (panel) buckling of ring- stiffened cylinders by application of the principle 

 of minimum potential energy (Rayleigh-Ritz method). The approach was 

 quite distinct from that used by the earlier investigators who attempted 

 solutions of the differential equations. The energy method involves the 

 assumption of buckling functions which satisfy some chosen ideal boundary 

 conditions, and these are then used to satisfy the condition of minimum 

 energy which implies satisfaction of the differential equations in this 

 sense. It is of interest here to outline some of the more important 

 results with regard to the application of this very potent method in the 

 solution of shell-buckling problems of interest to naval architects. 



First, expressions for the elastic strain energy in the shell and also 

 in the ring frames are written in terms of the displacement components 

 of a point in the middle surface of the shell. Then, expressions for the 

 work done by the external pressure forces acting on the cylinder are also 

 written in terms of these displacement components. Various displacement 

 configurations for the buckled shell are then introduced to approximate 

 the actual case. After the total potential is expressed in terms of these 

 displacements containing arbitrary mode- shape parameters, the energy 

 is then minimized with respect to these parameters and this process leads 

 to a set of linear homogeneous algebraic equations. In order that a non- 

 trivial solution to this system of equations exists, it is necessary that 



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