Analysis and Evaluation of a Shell Finite Element with Drilling Degree of Freedom

Abstract

A flat shell finite element is obtained by superposing plate bending and membrane components. Normally, shell elements of this type possess five degrees of freedom (DOF), three displacement DOF, u, v and w, and two in-plane rotation DOF, qx and qy , at each node. A sixth degree of freedom, qz , is associated with the shell normal rotation, and is not usually required by the theory. In practice, however, computational and modeling problems can be caused by a failure to include this degree of freedom in finite element models.This paper presents the formulation and testing of a four node quadrilateral thin flat shell finite element, which has six DOF per node. The sixth DOF is obtained by combining by a membrane element with a normal rotation qz, the so-called the drilling degree of freedom, and a discrete Kirchhoff plate element. The flat shell has a 24 x 24 element stiffness matrix. Numerical examples are given for (a) shear- loaded cantilever beam, (b) square plate, (c) cantilever I- beam and (d) folded plate.