Buckling of a ring joint with the cylindrical shell under internal pressure in the shell

Abstract

Buckling under the uniform internal pressure of a thin circular cylindrical shell supported by the rings with T-shaped cross-section is studied. As a model of the ring the annular plate supported on outer edge by a circular beam is used. The classical model of a ring — a beam with T-shaped cross-section does not allow to solve the given problem, because the buckling deformations are localized on the surface of the ring. It is impossible to find the critical pressure corresponding to such loss of stability by means of the beam model. In the first approximation the buckling problem for the annular plate joint with the cylindrical shell is reduced to the solution of an eigenvalue problem for the bending equation of the annular plate. In the assumption, that the width of the plate is much less than its internal radius the approximate formulas for calculation of the critical pressure are obtained. The results found by Rayleigh—Ritz method and shooting procedure differ a little from each other. It is shown, that the critical pressure for the rings with the rectangular cross-section section is greater, than for the rings with T-shaped cross-section. Refs 9. Figs 3. Tables 2.