Mixed finite element method for nonclassical boundary value problems of shallow shell theory

The necessary and sufficient conditions for the solvability of the variational problems of the geometrically and physically nonlinear shallow shell theory by nonclassical boundary conditions modeling the rigid contact of the shell boundary or the normal load in the tangent plane on the shell boundary are obtained. The mixed finite element schemes for approximate solving of these problems are constructed. The solvability conditions for the corresponding discrete problems are deduced. The convergence of the approximate solutions by refinement of the domain triangulation is proved.