Finite element method in equilibrium problems for a nonlinear shallow shell with an obstacle

The purpose of this paper is to use a weak setup to justify application of the finite element method (FEM) to the equilibrium problem for a nonlinear model of a shallow shell clamped along part of an edge constrained by a frictionless obstacle. A suitable energy space is constructed and the generalized (weak) solutions are introduced. The obstacle condition is represented by a linearized model, and convergence of approximate FEM solutions to a weak solution is established. In particular, existence of a weak solution to the problem is proved. The result essentially extends that obtained in the paper Lebedev and Neymark (2006).