The Reissner-Mindlin plate is the Γ-limit of Cosserat elasticity

Finite Elements for the Reissner-Mindlin Plate

Wilson's element for the Reissner-Mindlin plate

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...

The Boundary Layer for the Reissner–mindlin Plate Model*

The structure of the solution of the Reissner–Mindlin plate equations is investigated, emphasizing its dependence on the plate thickness. For the transverse displacement, rotation, and shear stress, asymptotic expansions in powers of the plate thickness are developed. These expansions are uniform up to the boundary for the transverse displacement, but for the other variables there is a boundary...

Some New Elements for the Reissner–Mindlin Plate Model

In this work-in-progress we report on a new approach to obtaining stable locking-free discretizations of the Reissner–Mindlin plate model. For a plate of thickness t with midplane section Ω ⊂ R the clamped Reissner–Mindlin plate model determines ω , the transverse displacement of the midplane, and φ , the rotation of fibers normal to the midplane, as the unique minimizer over H̊1(Ω)× H̊(Ω) of the...

Finite Element Computations for the Reissner-mindlin Plate Model

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 ...