Analysis of hybrid methods of mixed-shear-projected triangular and quadrilateral elements for Reissner-Mindlin plates

TL;DR

This paper analyzes hybrid mixed-shear-projected triangular and quadrilateral finite elements for Reissner-Mindlin plates, demonstrating their stability and shear-locking-free behavior through numerical benchmarks.

Contribution

It provides a detailed analysis of the stability and shear-locking-free performance of MiSP3 and MiSP4 elements based on the Hellinger-Reissner principle.

Findings

MiSP3 and MiSP4 are robust in numerical tests.

Elements are stable regardless of plate thickness.

They effectively avoid shear-locking.

Abstract

It is known that the 3-node hybrid triangular element MiSP3 and 4-node hybrid quadrilateral element MiSP4 presented by Ayad, Dhatt and Batoz (Int. J. Numer. Meth. Engng 1998, 42: 1149-1179) for Reissner-Mindlin plates behave robustly in numerical benchmark tests. These two elements are based on Hellinger-Reissner variational principle, where continuous piecewise linear/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 approximation of bending moments/shear stresses. We show that the MiSP3 and MiSP4 elements are uniformly stable with respect to the plate thickness and thus free from shear-locking.