We consider a stabilized finite element formulation for the Reissner-Mindlin plate bending model. The method uses standard bases functions for the deflection and the rotation vector. We apply a standard multigrid algorithm to obtain a preconditioner. We prove that the condition number of the preconditioned system is uniformly bounded with respect to the multigrid level and the thickness paramet...

Nonlinear plate bending within Mindlin's strain gradient elasticity theory (SGT) is investigated by employing somewhat non-standard finite element methods. The main goal to compare the results provided geometrically nonlinear three-dimensional (3D) and Reissner–Mindlin theory, i.e., first-order shear deformation (FSDT), SGT. For 3D Green–Lagrange relations are adopted, while von Kármán strains ...

The thickness stretch vibrations of piezoelectric ceramic plates are analyzed by solving the first-order Mindlin plate equations with finite element method in the twodimensional domain. The precise resonance frequency and distribution of displacements are obtained from the analysis in detail. The results based on the two-dimensional solutions are more important particularly in the evaluation of...

1. Abstract Equations governing the behavior of rectangular plates made of functionally graded materials (FGMs) are determined in this paper using the variational approach. Derivation of such equations is based on Reissner–Mindlin plate theory that is extended to handle two-constituent material distribution through the thickness. Material properties are assumed to vary with the power law in ter...

In this paper a least squares method, using the minus one norm developed in 6] and 7], is introduced to approximate the solution of the Reissner-Mindlin plate problem with small parameter t, the thickness of the plate. The reformulation of Brezzi and Fortin is employed to prevent locking. Taking advantage of the least squares approach, we use only continuous nite elements for all the unknowns. ...