Analysis of a Mixed-Shear-Projected Quadrilateral Element Method for Reissner-Mindlin Plates

Abstract

This paper analyzes an existing 4-node hybrid mixed-shear-projected quadrilateral element MiSP4, presented by Ayad, Dhatt and Batoz (Int. J. Numer. Meth. Engng 1998, 42: 1149-1179) for Reissner-Mindlin plates, which behaves robustly in numerical benchmark tests. This method is based on Hellinger-Reissner variational principle, where continuous piecewise isoparametric bilinear interpolations, as well as the mixed shear interpolation ⁄ projection technique of MITC family, are used for the approximations of displacements, and piecewise-independent equilibrium modes are used for the approximations of bending moments ⁄ shear stresses. Due to local elimination of the parameters of moments ⁄ stresses, the computational cost of MiSP4 element is almost the same as that of the conforming bilinear quadrilateral displacement element. We show that the element is free from shear locking in the sense that the error bound in the derived a priori estimate is independent of the plate thickness.