ISOPARAMETRIC FINITE ELEMENTS BASED ON MINDLIN PLATE BENDING THEORY : (Part 3) Quadrilateral Element Using Continuous Shear Constraints

Finite Elements for Reissner-Mindlin plate bending problems

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) = ∫

Finite Elements for the Reissner-Mindlin Plate

Analysis of some low order quadrilateral Reissner-Mindlin plate elements

Four quadrilateral elements for the Reissner-Mindlin plate model are considered. The elements are the stabilized MITC4 element of Lyly, Stenberg and Vihinen [27], the MIN4 element of Tessler and Hughes [35], the Q4BL element of Zienkiewicz et al [39] and the FMIN4 element of Kikuchi and Ishii [21]. For all elements except the Q4BL element, a unifying variational formulation is introduced, and o...

Superconvergence in Projected-Shear Plate-Bending Finite Element Methods

Projected-shear nite element methods for periodic Reissner-Mindlin plate model are analyzed for rectangular meshes. A projection operator is applied to the shear stress term in the bilinear form. Optimal error estimates in the L 2-norm, H 1-norm, and the energy norm for both displacement and rotations are established and gradient superconvergence along the Gauss lines is justiied in some weak s...

Mixed Rectangular Finite Elements for Plate Bending

The paper describes three different rectangular plate bending elements based on Reissner's type stationary variational principles. They differ in the number of dependent variables approximated independently and also in the number of nodes per element. The first element types treats the transverse deflection and the three moments as unknowns at each of the corner nodes; the second element type t...