Elastoplastic Limit State of Inhomogeneous Shells of Revolution with Internal Cracks

By using an analog of the δc -model, we reduce the problem of stressed state and limit equilibrium of an inhomogeneous shell of revolution weakened by an internal crack of any configuration with plastic strains developed on the continuation of the crack in the form of a narrow strip to an elastic problem. The indicated elastic problem is then reduced to a system of singular integral equations with unknown limits of integration and discontinuous functions on the right-hand sides. We propose an algorithm for the numerical solution of these systems with regard for the conditions of plasticity of thin shells and the conditions of boundedness for stresses. The effects of loading, geometric parameters, and mechanical characteristics on the crack-opening displacement and the sizes of plastic zones are investigated for cylindrical and spherical shells made of functionally graded materials and containing internal parabolic cracks.