Axi-Symmetric Collapsing of Circular Cylindrical Shells of Submarines

Abstract

Collapsing of circular cylindrical shells under external pressure has been investigated in relation to the strength of pressure hulls of a submarine. Cylindrical shells collapse by causing shell yielding when they are reinforced closely by circular frames. This phenomenon takes place suddenly with a loud noise, and it seems therefore to be a sort of buckling accompanied by large plastic deformations. If shells are made literally in a circular form, the collapsing pattern will be axially symmetric ; hence, such collapsing shoild be called axi-symmetric collapsing rather than shell yielding.Axi-symmetric collapsing was investigated by Sanden-Giinther and Trilling. Their theories are based on an assumption that shells will collapse as soon as the stress condition reaches a certain state. The behaviors of shells are different from those expected by these theories, and there follows even a marked discrepancy between experiments and the theory of Sanden-Gunther.In this paper a rational theory is developed on the basis of the theories of plasticity and buckling ; the validity of this theory was confirmed by experiments. When the sectional area of frames is comparatively small, collapsing occurs over three frame spaces, and when large enough, between two consecutive frames. In respective cases, the pressure factor for axi-symmetric 'collapsing is given by (22) and by (20) or (21).