Small Rotationally Symmetric Deformations of Shallow Helicoidal Shells.

摘要

Known solutions for transverse bending and plane stress of flat circular ring plates are generalized so as to apply to shallow helicoidal shells. The pitch of the middle surface of the shell is responsible for a coupling of what would be separate problems of plane stress and transverse bending for flat plates. Explicit results are obtained for an important sample problem. A general property of helicoidal cantilever shells is stated. Criteria are obtained indicating, in terms of the parameters of the shell (a) the range of applicability of the results obtained, and (b) the range in which the shell behaves like a flat plate. (MM).