A 4-noded mixed-hybrid finite element, using unsymmetric stresses, for linear analysis of plates

Shells in general, and flat shells (i.e. plates) in particular have received a lot of attention in the finite element research world: as a matter of fact in a recent survey [1], spanning the last 15 years, more than 350 contribution are enlisted, and in another one [2], covering only papers about plates appeared in the years 1992-94 a list of 250 titles is presented. Such a research effort is justified by the quest of plate models which may both deal with general thickness/shape and provide a higher accuracy in evaluating shear stress distributions, especially when laminated structures are considered. In order to achieve better performances mixed models [3] have been often exploited. In the present paper a mixed-hybrid model for a Reissner-Mindlin-type plate is presented where local stresses (rather than stress resultants and moments) are explicitly modelled. Moreover, by following the ideas already used for membranes in [4], it is assumed that in plane shear stresses are not a priori symmetric [5]. This choice allows the decoupling of the equilibrium equations, and involves introducing an in plane infinitesimal rotation field, corresponding to drilling dofs. Out-of plane shear stresses are then chosen such that equilibrium equation are exactly satisfied. Details of the formulation are provided, and the performances of the new element are assessed with reference to well-established benchmark problems. The analysis of laminated plates appears possible [6].