Abstract
We propose a method for the investigation of the limiting equilibrium of an elastoplastic orthotropic cylindrical shell with cracks. The idea of this method is to reduce the elastoplastic problem, by using an analog of the δc-model, to the problem of elastic equilibrium of an orthotropic shell with cracks of unknown length whose lips are subjected to the action of unknown forces and moments satisfying the conditions of plasticity of thin shells. The equations of the Timoshenko-type theory of shells and the methods of generalized functions are used to reduce the elastic problem to the system of singular integral equations with unknown limits of integration and discontinuous right-hand parts. We construct a numerical solution of this system and study the dependence of the crack-tip opening displacement and the sizes of the plastic zones on the geometric and mechanical parameters of the orthotropic and transversely isotropic shell.
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