Discrete Kirchoff Plate Bending and Shell Family of Finite Elements with Loof Nodes - Small and Large Displacements

The purpose of this paper is to present a flat facit family of plate and shell elements which has similar attractive features to those exhibited by the semi-Loof elements developed by Irons, but without some of the latter's shortcomings. The bending stiffness component of the second member of the present element family, labelled D.K.L. (for Discrete Kirchoff with Loof nodes), is modelled with the same nodal configuration as the triangular semi-Loof element. However it is not formulated through the isoparametric concept. Two element configurations of the family are presented. The first uses linear displacement and rotation fields with the three apex and three mid-side nodes. The second member of the family uses the linear strain triangle for the membrane shell component together with quadratic (and bubble) functions for the rotation terms. Several examples are given and convergence tests applied to this element. The membrane responses for the element are simply the C.S.T. and L.S.T. respectively. The theory in the paper concentrates on the bending response of the elements.