Buckling of a Cylindrical Shell Joint with Annular Plates under External Pressure

The buckling of a thin cylindrical shell supported by identical annular plates under uniform external pressure is analyzed using an asymptotic method. The boundary conditions on an internal parallel of the shell joined to a thin plate are obtained. The free support conditions are introduced at the edges of the shell. The approximate solutions to the eigenvalue problem are sought as a sum of slowly varying functions and edge effect integrals. For the formulation of the zero-order eigenvalue problem, the main boundary conditions are obtained on the parallel of the interface between the plate and the shell. This problem also describes vibrations of a simply supported beam stiffened by springs. Its solution is sought as linear combinations of Krylov's functions. It is shown that in the zeroth approximation it is possible to replace a narrow plate with a circular beam. As the plate width increases, the stiffness of the corresponding spring tends to a constant. It occurs because of localized plate deformations in the proximity of the internal edge of the plate. As an example, the dimensionless critical pressure is determined in the case when the shell is supported by a single plate. Replacing a narrow plate with a circular beam does not lead to substantial variation in the critical pressure; however, for a wide plate the beam model provides an overestimated value of the critical pressure.