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 effec...

—Multigrid methods for parameter dependent problems are discussed* The contraction numbers ofthe algoriîhms are proved within a unifying framework to be bounded awayfrom one, independent ofthe parameter and the mesth levels. Examples include the pure displacement and pure traction boundary value problems in planar linear elasticity, the Tïmoshenko béant problem, and the Reissner-Mindlin plate p...

"Well-posedness and stability of a semilinear Mindlin-Timoshenko plate model" I will discuss well-posedness and long-time behavior of Mindlin-Timoshenko plate equations that describe vibrations of thin plates. This system of partial differential equations was derived by R. Mindlin in 1951 (though E. Reissner also considered an analogous model earlier in 1945). It can be regarded as a generaliza...

Finite element methods for the Reissner–Mindlin plate theory are discussed. Methods in which both the tranverse displacement and the rotation are approximated by finite elements of low degree mostly suffer from locking. However a number of related methods have been devised recently which avoid locking effects. Although the finite element spaces for both the rotation and transverse displacement ...

The high frequency vibrations of quartz crystal plates have been extensively studied for the design and optimization of resonators which work at the thickness-shear vibration mode with relatively high frequency in the RF range. Earlier research work started from the development of special plate equations required for the high frequency vibrations of quartz crystal plates by Mindlin, known as th...

In this paper, we propose two lower order nonconforming rectangular elements for the Reissner-Mindlin plate. The first one uses the conforming bilinear element to approximate both components of the rotation, and the modified nonconforming rotated Q1 element to approximate the displacement, whereas the second one uses the modified nonconforming rotated Q1 element to approximate both the rotation...