New Locking-Free Mixed Method for the Reissner--Mindlin Thin Plate Model

Abstract

We are interested here in the Reissner--Mindlin model for a bending thin plate with physical boundary conditions. It is well known that this problem depends singularly upon the plate's thickness \( \varepsilon \). By decomposing the bending moment and by dualizing its symmetry, we obtain an equivalent mixed formulation of the initial problem whose unknowns now belong to classical Sobolev spaces. We then propose a low-order conforming finite element method for which we obtain optimal error estimates independently upon the small parameter \( \varepsilon . \) Thus, the discrete method is unconditionally convergent and locking-free. It directly gives an approximation of the bending moment and allows us to recover the two other variables, which are the deflection and the rotation vector.