Buckling of the cylindrical shell joint with annular plates under external pressure

By means of an asymptotic method the buckling under the uniform external pressure of the thin cylindrical shell supported by identical annular plates is analyzed. Boundary conditions on an internal parallel of the shell joined to a thin plate are obtained. At the edges of the shell the free support conditions are introduced. We seek the approximate solutions of the eigenvalue problem as a sum of slowly varying functions and edge effect integrals. On a parallel, where the plate joint with the shell, the main boundary conditions for the formulation of an eigenvalue problem of zero approximation are obtained. This problem describes also vibrations of a simply supported beam stiffened by springs. Its solution we seek as linear combinations of Krylov's functions. It is shown, that in zero approximation it is possible to replace a narrow plate with a circular beam. At increase in width of a plate stiffness of the corresponding spring tend to a constant. It occurs because of localization plate deformations near to the internal edge of a plate. As an example the dimensionless critical pressure for the case when the shell is supported by one plate is found. The replacement of a narrow plate with a circular beam does not lead to appreciable change of the critical pressure, however for a wide plate the beam model gives the overestimated value of critical pressure.