A cylindrical shell with an axial crack under skew-symmetric loading.

The skew-symmetric problem for a cylindrical shell containing an axial crack is considered. It is assumed that the material has a special orthotropy - namely, that the shear modulus may be evaluated from the measured Young's moduli and Poisson ratios and is not an independent material constant. The problem is solved within the confines of an eighth-order linearized shallow shell theory. As numerical examples, the torsion of an isotropic cylinder and that of a specially orthotropic cylinder (titanium) are considered. The membrane and bending components of the stress intensity factor are calculated and are given as functions of a dimensionless shell parameter. In the torsion problem for the axially cracked cylinder the bending effects appear to be much more significant than that found for the circumferentially cracked cylindrical shell. Also, as the shell parameter increases, unlike the results found in the pressurized shell, the bending stresses around crack ends do not change sign.