The effects of selected membrane, plate and flat shell finite element formulations on optimal topologies are numerically investigated. Two different membrane components are considered. The first is a standard 4-node bilinear quadrilateral, and the other is a 4-node element accounting for in-plane (drilling) rotations. Plate elements selected for evaluation include discrete Kirchhoff quadrilater...

The nite element method with rectangular meshes for the Reissner-Mindlin plate is analyzed. For a plate with thickness bounded below by a positive constant (moderately thick plate), derivative superconvergence of the nite element solution at the Gaussian points is justiied and optimal error estimates for both rotation and displacement are established.

The Reissner-Mindlin plate theory models a thin plate with thickness t. The condition number of finite element approximations of this model deteriorates badly as the thickness t of the plate converges to 0. In this thesis, we develop an overlapping domain decomposition method for the Reissner-Mindlin plate model discretized by Falk-Tu elements with a convergence rate which does not deteriorate ...

The Reissner-Mindlin plate theory models a thin plate with thickness t. The condition number of finite element approximations of this model deteriorates badly as the thickness t of the plate converges to 0. In this thesis, we develop an overlapping domain decomposition method for the Reissner-Mindlin plate model discretized by Falk-Tu elements with a convergence rate which does not deteriorate ...

In this paper we analyze the convergence of mixed finite element approximations to the solution of the Reissner-Mindlin plate problem. We show that several known elements fall into our analysis, thus providing a unified approach. We also introduce a low-order triangular element which is optimalorder convergent uniformly in the plate thickness.

A new method for the Reissner-Mindlin plate has been proposed. The nonconform-ing Wilson element is used for transverse displacement, rotation is approximated by the usual bilinear element, and an orthogonal projection is applied to the shear stress term. The uniform convergence with respect to the plate thickness is established. Numerical results are provided. The new method is simple in imple...

In this investigation, a modified Fourier solution based on the Mindlin plate theory is developed for the free vibration problems of orthotropic rectangular Mindlin plates subjected to general boundary supports. In this solution approach, regardless of the boundary conditions, the plate transverse deflection and rotation due to bending are invariantly expressed as a new form of trigonometric se...

We consider the plate bending problem in the framework of the Reissner-Mindlin theory. For a clamped plate, the problem can be written in variational form as follows. Find (θ, w) ∈ (H 0 (Ω)) ×H 0 (Ω) : ∫ Ω Cε(θ) : ε(η) + μ t−2 ∫ Ω (∇w − θ) · (∇v − η) = ∫