Locking-free Argyris–Lagrange finite elements for the Reissner–Mindlin plate

The \(C^1\) $C^1$ - \(P_{k+1}\) $P_{k+1}$ ( \(k\ge 4\) $k\ge 4$ ) Argyris finite elements combined with the \(C^0\) $C^0$ - \(P_k\) $P_k$ Lagrange finite elements are locking-free with respect to the plate thickness, and quasi-optimal when solving the Reissner–Mindlin plate equation on triangular meshes. The method is truly conforming or consistent in the sense that no reduction operator is introduced to the formulation. Theoretical proof and numerical verification are presented.