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Locking effects in the finite element approximation of plate models


Authors: Manil Suri, Ivo Babuška and Christoph Schwab
Journal: Math. Comp. 64 (1995), 461-482
MSC: Primary 65N30; Secondary 65N12, 73K10, 73V05
MathSciNet review: 1277772
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Abstract: 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 $ d \to 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 \to 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.


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DOI: https://doi.org/10.1090/S0025-5718-1995-1277772-6
Keywords: Reissner-Mindlin, locking, finite element, p version
Article copyright: © Copyright 1995 American Mathematical Society