A Simple Linear Nonconforming Shell Element

A new low order facet type triangular shell finite element is presented. The element is combined from the Arnold-Falk plate bending element and the membrane element based on the noncorming element of Crouzeix-Raviart with conforming drilling rotation. Formulation of the membrane element is based on the variational principle of Hughes and Brezzi employing independent rotation field. Interpolation for the in-plane translational components is nonconforming and continuous only at the midpoints of the element edges, while conforming linear interpolation is used for the drilling rotation. It will be shown that the utilization of the drilling rotation supresses the mechanism which is present in the Crouzeix-Raviart element, applied to plane stress or plain strain problems, for certain boundary conditions. In this element all three rotation components appear at corner nodes and translational components at the midpoints of the element edges resulting in 18 degrees of freedom. Reijo Kouhia, Rolf Stenberg