# An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation

## TL;DR

This paper introduces an ultraweak variational formulation for the Reissner-Mindlin plate model, proves its well-posedness and convergence properties, and develops a locking-free DPG discretization with optimal convergence.

## Contribution

It presents a novel ultraweak formulation for the Reissner-Mindlin model and a DPG discretization that is locking-free and uniformly convergent for all plate thicknesses.

## Key findings

- Proved well-posedness of the ultraweak formulation.
- Established weak convergence to Kirchhoff-Love model as thickness approaches zero.
- Numerical experiments confirm locking-free behavior of the method.

## Abstract

We develop and analyze an ultraweak variational formulation of the Reissner-Mindlin plate bending model both for the clamped and the soft simply supported cases. We prove well-posedness of the formulation, uniformly with respect to the plate thickness $t$. We also prove weak convergence of the Reissner-Mindlin solution to the solution of the corresponding Kirchhoff-Love model when $t\to 0$. Based on the ultraweak formulation, we introduce a discretization of the discontinuous Petrov-Galerkin type with optimal test functions (DPG) and prove its uniform quasi-optimal convergence. Our theory covers the case of non-convex polygonal plates. A numerical experiment for some smooth model solutions with fixed load confirms that our scheme is locking free.