# The TDNNS method for Reissner-Mindlin plates

## TL;DR

This paper introduces a new family of locking-free finite elements for shear deformable Reissner-Mindlin plates, based on a novel elasticity formulation that treats bending moments as separate unknowns, achieving optimal convergence without shear treatment.

## Contribution

It presents a new finite element formulation for Reissner-Mindlin plates that avoids shear locking and does not require reduced integration, with optimal convergence properties.

## Key findings

- Elements are locking-free and achieve optimal convergence.
- No special shear treatment like reduced integration is needed.
- The formulation effectively models shear deformable plates.

## Abstract

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 rotations and normal-normal components of the bending strain. Contrary to other plate bending elements, no special treatment for the shear term such as reduced integration is necessary. The elements attain an optimal order of convergence.