Cracked shells under skew-symmetric loading

Abstract

In this paper, the general problem of a shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and anti-plane elasticity solutions. Extensive results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform in-plane shearing, out of plane shearing, and torsion. Taking advantage of the fact that the problem is formulated for “specially” orthotropic materials, the effect of orthotropy on the results is also studied in some detail.