In composite plate structures, it is common to combine di erent materials with very di erent Young's moduli and densities. Damping treatments can also be added to prevent high levels of vibration. For discretized problems, the static and dynamic behavior of such heterogeneous structures can be carried out with the 3D elasticity theory but this often leads to very large systems. Therefore, plate...

In this paper, we develop two least-squares approaches for the solution of the Stokes equations perturbed by a Laplacian term. (Such perturbed Stokes equations arise from finite element approximations of the Reissner–Mindlin plate.) Both are two-stage algorithms that solve first for the curls of the rotation of the fibers and the solenoidal part of the shear strain, then for the rotation itself...

—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...

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...

A new family of locking-free finite elements for shear deformable Reissner-Mindlin plates is presented. The elements are based on the "tangential-displacement normal-normal-stress" formulation of elasticity. In this formulation, the bending moments are treated as separate unknowns. The degrees of freedom for the plate element are the nodal values of the deflection, tangential components of the ...

A new technique for coupling one dimensional beam elements to three dimensional bodies is described. The essence of the problem is to ensure compatibility of the displacements at the interface. This is achieved by equating the work done at the dimensional interface by the 3D nodes with the work done at the 1D node. This is carried out in a manner similar to that used in the development of Reiss...

We consider the nite element (FE) approximation of the Reissner-Mindlin (RM) plate model, and indicate how to design meshes that yield accurate results when the p=hp version of the standard FE method is used. These guidelines allow quantities of engineering interest to be numerically predicted with great conndence near the boundary. We illustrate this through numerical computations in the case ...

A simple finite element method for the Reissner–Mindlin plate model in the primitive variables is presented and analyzed. The method uses nonconforming linear finite elements for the transverse displacement and conforming linear finite elements enriched by bubbles for the rotation, with the computation of the element stiffness matrix modified by the inclusion of a simple elementwise averaging. ...