Locking free quadrilateral continuous/discontinuous finite element methods for the Reissner–Mindlin plate

We develop a finite element method with continuous displacements and discontinuous rotations for the Reissner–Mindlin 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.