5-node hybrid/mixed finite element for Reissner–Mindlin plate

In this paper, a new quadrilateral 5-node plate bending element (HP5) for hybrid/mixed finite element method is presented in the global Cartesian coordinates by the Hellinger–Reissner functional. This new element is based on the independent interpolations for displacement and stress. Its convergence is proven by theory and through detailed numerical investigations. The numerical studies demonstrate the validity of the resulting new element HP5 and show that the present element possesses many ideal qualities, i.e. remarkable convergence for thin and thick plates, a lower sensitivity to geometric distortion and invariability to the rotation of coordinates, freedom of shear locking phenomenon in the thin plate limit, suppression of spurious zero energy deformation modes, and the accuracy of solution is improved over that of 4-node hybrid/mixed finite element (HP4). Very good results have been obtained for thin and thick plates and show that it is a satisfactory foundation of developing h-version and p-version adaptive hybrid/mixed finite element method.