Rostun M. Limit equilibrium of inhomogeneous cylindrical and spherical shells with cracks

An analytical-numerical method to define the stress-strain state and limit equilibrium of elastic and elastico-plastic inhomogeneous shells of rotation with through and surface cracks has been developed. The method utilizes the analogue of – model in the theory of thin shells and the distribution technique. It lies in reducing the corresponding key equations to a system of singular integral equations for the derivatives of displacement jumps and angles of rotation on the crack lines and interfaces.On this base new problems about stress state for inhomogeneous (composite, across the thickness) cylindrical and spherical shells with cracks (through, internal or surface) under elastic and elastico-plastic strain have been solved. In addition the obtained systems of singular integral equations have been solved by the method of mechanical quadratures and method of boundary elements together with plasticity conditions and conditions of efforts and moments boundedness near the crack tips. The influence of boundary conditions, geometric and mechanical characteristics of the shells on their limit equilibrium has been studied.