Closed system of limit equilibrium equations for axisymmetric shells

We consider rigid-plastic axisymmetric shells and use methods of control theory to construct the carrying capacity loss condition for such shells in formalized form. We show that solving limit equilibrium problems for such structures can be reduced to solving a multipoint boundary value problem for a system of nonlinear differential-algebraic equations with unknown matching boundaries between different plastic modes as well as between rigid and plastic domains. We present a complete system of resolving equations for the problem on the carrying capacity of axisymmetric shells, including the matching conditions for domains in different states.