In some past discussions in literatures, the roots of the bending differential equation of a ring-stiffened cylindrical shell acted under the homogeneous water pressure were taken to be complex numbers. In this paper, the existence of five cases was verified using model experiment, theory and a series of computation. The paper shows that it is unreasonable to use internal pressure test of the submarine pressure hull specified by the current rules for submarine construction as the pressure corresponding to the extreme depth of submergence. The errors of stress caused by the internal pressure test would be dangerous, and the internal testing pressure should be raised.
The pressure hull structure of submarines is usually described as a series of ring-stiffened cylindrical shell. There are tour roots of the characteristic equation derived from the bending differential equation of a ring-stiffened cylindrical shell acted under the homogeneous water pressure. These roots may be real, or complex numbers, or purely imaginary. Although some of these possible forms of roots were recognized in theory, only one possible root corresponding to the case r2< 1 was considered practical. Thus the roots of the characteristic equation were taken to be complex numbers. The current method of calculating the ring-stiffened cylindrical shell stress. The bending differential equation of the ring-stiffened cylindrical shell is given in Ref. , as follows. If can be seen from the above expression, that the characteristic roots may have different forms in accordance with the different values of m and n. These roots may be real (r ≤ -1) purely imaginary (r ≥ 1)or complex numbers (-l < r < l). But the current calculating method[l] deems that n 2 >m 2 (i.e. r >1 and the four roots are complex numbers).