Locking Effects in the Finite Element Approximation of Plate Models

We analyze the robustness of various standard finite element schemes for a hierarchy of plate models and obtain asymptotic convergence estimates that are uniform in terms of the thickness d . We identify h version schemes that show locking, i.e., for which the asymptotic convergence rate deteriorates as ¿->0, and also show that the p version is free of locking. In order to isolate locking effects from boundary layer effects (which also arise as d —► 0), our analysis is carried out for the periodic case, which is free of boundary layers. We analyze in detail the lowest model of the hierarchy, the well-known Reissner-Mindlin model, and show that the locking and robustness of finite element schemes for higher models of the hierarchy are essentially identical to the Riessner-Mindlin case.