Locking Free Quadrilateral Continuous/Discontinuous Finite Element Methods for the Reissner-Mindlin Plate

TL;DR

This paper introduces a locking-free finite element method for the Reissner-Mindlin plate model on quadrilaterals, ensuring optimal convergence and numerical validation across different plate thicknesses.

Contribution

It develops a novel finite element approach with continuous displacements and discontinuous rotations that avoids shear locking on quadrilateral meshes.

Findings

Achieves optimal convergence rates

Remains stable regardless of plate thickness

Numerical results confirm theoretical predictions

Abstract

We develop a finite element method with continuous displacements and discontinuous rotations for the Mindlin-Reissner plate model on quadrilateral elements. To avoid shear locking, the rotations must have the same polynomial degree in the parametric reference plane as the parametric derivatives of the displacements, and obey the same transformation law to the physical plane as the gradient of displacements. We prove optimal convergence, uniformly in the plate thickness, and provide numerical results that confirm our estimates.