A locking-free finite element method for Naghdi shells

In this paper a locking-free method, using mixed finite elements, is introduced to approximate the solution of Naghdi shell problems with small parameter t, the thickness of the shell. The approach of Arnold and Brezzi (1997) is employed with some important changes. Instead of proving the discrete Inf-Sup condition for arbitrary geometric coefficients, which does not seem possible, we prove a weaker stability condition for smooth enough geometrically dependent coefficients, which is sufficient for deducing the optimal error estimate as long as h2t is uniformly bounded. For extremely small t, we can relax this condition either using a larger bubble space or stabilizing the problem by replacing t2 by t2 + h4. In either case an optimal error estimate still holds.