LOCKING EFFECTS IN THE FINITE-ELEMENT APPROXIMATION OF PLATE MODELS

We analyze the robustness of various standard finite element schemes f or a hierarchy of plate models and obtain asymptotic convergence estim ates that are uniform, in terms of the thickness d. We identify h vers ion schemes that show locking, i.e., for which the asymptotic converge nce rate deteriorates as d --> O, and also show that the p version is free of locking. In order to isolate locking effects from boundary lay er effects (which also arise as d --> O), 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-Min dlin 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.