A new hybrid-mixed variational approach for Reissner-Mindlin plates. The MiSP model

A valuable variational approach for plate problems based on the ReissnerÐMindlin theory is presented. The new MiSP (Mixed Shear Projected) approach is based on the HellingerÐReissner variational principle, with a particular representation of transversal shear forces and transversal shear strains. The approximations of the shear forces are derived from those of the bending moments using the corresponding equilibrium relations. The shear strains are deÞned in terms of the edge tangential strains that are projected on the element degrees of freedom. Two Þnite elements are developed on the MiSP approach basis: 3-node triangular element MiSP3 and 4-node quadrilateral element MiSP4. Both elements can be considered as the most simple among the existent mixed elements. A modiÞed MiSP model with a derived 4-node element is also presented. Numerical experiments are presented which show that the MiSP elements do not exhibit shear locking and give excellent results for thick and thin plates. They also pass the patch test for a general triangle and quadrilateral.