On the problem of shear-locking in finite elements based on shear deformable plate theory

The phenomenon of shear locking in plate finite elements, or the loss of accuracy when thin plates are modelled by shear deformable elements, is explained in terms of the presence of boundary layer-type solutions to the equations of shear deformable plate theory, coupled with existing arguments in the literature. To demonstrate this, the governing equations of Reissner shear deformable theory were derived and reduced to two independent equations expressed in terms of a displacement potential ~b and rotational stream function ~, for a transversely isotropic plate. A four node thirty-six degree of freedom C 2 continuous plate finite element which ignored the edge-effect equation in ~, was derived using an interpolation of the displacement potential th. A similar finite element based on classical plate theory was also shown. A square plate with simply-supported edges was modelled using these finite elements over a wide range of span-to-thickness ratios. All results converged rapidly to accepted solutions and did not exhibit shear-locking behavior under full integration. A discussion on the actual cause of shear-locking and recommendations for future development and implementation of the concepts in this study were made. ʹ(~ 1997 Elsevier Science Ltd. All rights reserved