Finite element methods for a modified Reissner-Mindlin free plate model

The solution of the Reissner–Mindlin plate problem with free boundary conditions presents a strong layer effect near the free edges. As a consequence, the solution is not even uniformly bounded even in H3/2, which implies that at most an O(h1/2) uniform convergence rate can be reached by finite element methods in the H1 norm. Following instead the modified free boundary model presented by Beir˜ao da Veiga and Brezzi, which gives more regular solutions, better error estimates can be obtained in principle. In this paper we present and analyze the extension of different families of well-known optimal plate methods to this new model. All the modified methods presented are proved to be optimal and free of locking.