A shear deformable plate element with an exact thin limit

Abstract

We present a quadrilateral finite element developed within the framework of a shear deformable plate theory. The interpolation for the rotation takes advantage of internal rotational degrees of freedom (through the use of bubble functions), while the interpolation for the transverse displacement is linked to the nodal rotations. A careful study of the element behavior is performed using an extensive set of mixed patch tests; results from several numerical examples are also presented. The element has proper rank and excellent interpolating capacity. Moreover, without using any ad-hoc assumption (e.g., energy balancing schemes) the element presents no locking effects at all; in fact, the shear energy may be set identically equal to zero without introducing any ill-conditioning in the problem, thus recovering a proper thin plate limit.