RESULTANT FIELDS FOR MIXED PLATE BENDING ELEMENTS

In this work the Hellinger-Reissner variational principle is used to formulate plate bending elements based upon Reissner-Mindlin plate theory. The formulation introduces an explicit coupling between interpolations of the shear and moment stress resultant fields. Because of the coupling, shear locking is avoided at the element level rather than at the global level. The coupling term is obtained by constraining the shear and moment resultant fields, that are initially assumed independent, to perform no work when subjected to a set of incompatible displacement modes. The resultant fields are formulated as a complete polynomial expansion in the element's natural coordinates and then transformed to the physical domain. Thus, frame invariant elements are always obtained. The resulting elements are shown to perform well on a set of standard problems for thin and thick plates. © 1990.