Snapping of Imperfect Thin-Walled Circular Cylindrical Shells of Finite Length

The nonlinear partial differential equations of von Karman and Donnell governing the deformations of initially imperfect cylindrical shells are reduced to a consistent set of ordinary differential equations. A numerical procedure is then used to solve the equations together with the associated boundary conditions and to determine the number of waves at buckling as well as the load-carrying capacity of imperfect cylindrical shells of finite length subjected to uniform axial compression in the presence of a reduced restraint along the simply supported boundaries. It is found that details of the boundary conditions have little effect on the number of waves into which the shell buckles around the circumference. This number is determined essentially by the length-to-radius and radius-to-thickness ratios. The absence of an edge restraint to circumferential displacement reduces the classical value of the buckling load by a factor of about two. On the other hand, shells with these boundary conditions appear to be less sensitive to initial imperfections in the shape, and thus the maximal load supported in the presence of unavoidable initial deviations can be the same for shells with and without a restraint to circumferential displacements along the edges.