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In this work we propose a discretisation method for the Reissner--Mindlinplate bending problem in primitive variables that supports general polygonalmeshes and arbitrary order. The method is inspired by a two-dimensionaldiscrete de Rham complex for which key commutation properties hold that enablethe cancellation of the contribution to the error linked to the enforcement ofthe Kirchhoff constraint. Denoting by $k\ge 0$ the polynomial degree for thediscrete spaces and by $h$ the meshsize, we derive for the proposed method anerror estimate in $h^{k+1}$ for general $k$, as well as a locking-free errorestimate for the lowest-order case $k=0$. The theoretical results are validatedon a complete panel of numerical tests.

A discrete de Rham method for the Reissner-Mindlin plate bending problem on polygonal meshes