Analysis of a 3‐node mixed‐shear‐projected triangular element method for Reissner–Mindlin plates

Abstract

This article analyses an existing 3‐node hybrid triangular element, called MiSP3, for Reissner–Mindlin plates which behaves robustly in numerical benchmark tests (Ayad, Dhatt, and Batoz, Int J Numer Method Eng 42 (1998), 1149–1179). Based on Hellinger‐Reissner variational principle and the mixed shear interpolation/projection technique of MITC family, the MiSP3 element uses continuous piecewise linear polynomials for the approximations of displacements and a piecewise‐independent equilibrium mode for the approximations of bending moments/shear stresses. Due to local elimination of the parameters of moments/stresses, the element is almost of the same computational cost as the conforming linear triangular displacement element. We derive uniform stability and convergence results with respect to the plate thickness. The main tools of our analysis are the self‐equilibrium relation of the moments/stresses approximations, the properties of the mixed shear interpolation and the discrete Helmholtz decomposition of the shear stress approximation. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 241–258, 2017