A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner–Mindlin plates

This paper proposes a quadrilateral finite element method of the lowest order for Reissner–Mindlin (R–M) plates on the basis of Hellinger–Reissner variational principle, which includes variables of displacements, shear stresses and bending moments. This method uses continuous piecewise isoparametric bilinear interpolation for the approximation of transverse displacement and rotation. The piecewise-independent shear stress/bending moment approximation is constructed by following a self-equilibrium criterion and a shear-stress-enhanced condition. A priori and reliable a posteriori error estimates are derived and shown to be uniform with respect to the plate thickness t. Numerical experiments confirm the theoretical results.