Modification of the 8-node serendipity element

This paper presents modification of the 8-node serendipity quadrilateral element which is widely used in finite element analysis. First we give basic principle of constructing 8-D spaces including the Cartesian quadratic polynomial space when the quadrilateral is of bilinear isoparametric shape. Then we derive a concrete example of such a space. in which the isoparametric quadratic space is included as well. Explicit expressions of shape functions are given for the sake of practical use. It is also shown that the usual 6-node quadratic triangle is obtained by applying the node degeneration technique to the present element. Comments are also given on the isoparametric use of the present element and on some existing elements related to ours. Moreover, numerical results are included to show the effectiveness of our modification. (C) 1999 Elsevier Science S.A. All rights reserved.