The problem of post-buckling behavior of long, vertical, circular cylindrical shells loaded by nonuniform pressure, tension, and their own weight is formulated in this paper. The global behavior is considered by assuming that local deformations do not influence the solution. The nonlinear effect is due to the softening of the relationship between the bending moment and curvature due to the effect of the flattening of the shell cross sections. The nonlinear differential equation obtained in this paper describes the post-buckling behavior of a shell with linearly distributed pressure along the axis and arbitrary boundary conditions. In the general case this problem must be solved numerically. An analytical solution is presented for a particular case of a shell loaded by a uniform external or internal pressure.

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