The possibility of a theoretical confirmation of the experimental values of the external critical pressure of thin-walled cylindrical shells

The problem of the buckling of elastic, isotropic, thin-walled cylindrical shells with small initial shape defects that are under the action of an external pressure is solved in a geometrically non-linear formulation. Equations that are identical to Marguerre's equations for a shallow cylindrical shell are used in formulating the problem. The solution is constructed by the Rayleigh–Ritz method with the points of the middle surface of the shell approximated by double functional sums over trigonometric and beam functions. The system of non-linear equations obtained is solved by arc-length methods. Cases of the clamped and supported shells when loading with a lateral and uniform hydrostatic pressure are considered. Its deflections from the limit points of the postbuckling branches of its loading trajectory are used as the initial imperfections. An inspection of the different forms of the initial imperfections when they have maximum values of up to 30% of the shell thickness made it possible to obtain practically the whole range of experimentally found critical pressures.