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

摘要

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