An improved 4-node quadrilateral plate bending element of the Reissner-Mindlin type

Abstract

We develop a Reissner-Mindlin type plate bending element of 4-node quadrilateral shape with 12 d.o.f. To improve the basic bilinear element, we add all the isoparametric biquadratic terms to the assumed lateral deflection so that any pure bending states can be represented. Then we introduce coupling between the lateral deflection and the two rotations so as not to increase the element degrees of freedom with the interelement compatibility preserved. We can express the shape functions explicitly, and hence the element stiffness matrices and the load vectors can be easily obtained. A 3-node triangular element can be also derived by the node degeneration technique. We test the proposed element by several numerical examples, and we can see that the behavior of the element is actually improved in comparison with some existing elements with the same d.o.f. In particular, the element is shown to be relatively robust to shape distortion. We also proposed a trick to avoid locking, although it is originally unavoidable in the thin plate range for the present type of compatible elements.