A Locking-Free Finite Element Method for Naghdi Shells

In this paper a locking-free method, using mixed nite elements, is introduced to approximate the soluton of Naghdi shell problems with small parameter t, the thickness of the shell. The approach of Arnold and Brezzi 1] is employed with some important changes. Instead of proving the discrete Inf-Sup condition for arbitrary geometric coeecients, which does not seem possible, we prove a weaker stability condition for smooth enough geometrically dependent coeecients, which is suucient for deducing the optimal error estimate as long as h 2 =t is uniformly bounded. For extremely small t, we can relax this condition either using a larger bubble space or stabilizing the problem by replacing t 2 by t 2 + h 4. In either case an optimal error estimate still holds.