A hybrid-stress quadratic serendipity displacement mindlin plate bending element

A hybrid-stress plate bending element is developed for thin and moderately thick plates based on a Serendipity-type quadratic displacement assumption. The through-thickness displacement behavior is consistent with Mindlin plate theory, and all components of stress are included. By proper choice of the transverse shear stress distributions, the element stiffness possesses correct rank, and results show no signs of locking in the thin plate limit; these and other considerations discussed herein suggest that the stress assumption used is optimum for the 8-node element. Results are compared with 8-node Serendipity and 9-node Lagrange assumed-displacement elements. The present element demonstrates high accuracy for all problems considered and has no apparent deficiencies.