Study on cracked spherical shells

The local-global anatysis method is systematically extended to the fracture analysis of spherical shells. On the basis of the shallow shell theory, which takes into account transverse shear deformations, governing equations for cracked spherical shells expressed in displacement and stress functions f, F and φ are proposed, and then a general solution including Modes, Ⅰ, Ⅱ, Ⅲ for stress-strain fields at crack tip in a spherical shell is obtained, which plays the same role as Williams's expansion in plane elasticity. The numerical results for finite-size spherical shells under different boundary conditions have been obtained. Furthermore, the bulging factors are analyzed with regard to shearing stiffness and an approximate formula is given.