A new quadrilateral area coordinate method (QACM‐II) for developing quadrilateral finite element models

Abstract

Abstract The quadrilateral area coordinate method proposed in 1999 (hereinafter referred to as QACM‐I) is a new and efficient tool for developing robust quadrilateral finite element models. However, such a coordinate system contains four components ( L 1 , L 2 , L 3 , L 4 ), which may make the element formulae and their construction procedure relatively complicated. In this paper, a new category of the quadrilateral area coordinate method (hereinafter referred to as QACM‐II), containing only two components Z 1 and Z 2 , is systematically established. This new coordinate system (QACM‐II) not only has a simpler form but also retains the most important advantages of the previous system (QACM‐I). Hence, as an application, QACM‐II is used to formulate a new 4‐node membrane element with internal parameters. The whole process is similar to that of the famous Wilson's Q6 element. Numerical results show that the present element, denoted as QACII6, exhibits much better performance than that of Q6 in benchmark problems, especially for MacNeal's thin beam problem. This demonstrates that QACM‐II is a powerful tool for constructing high‐performance quadrilateral finite element models. Copyright © 2007 John Wiley & Sons, Ltd.