Introduction To The Third Form Of The Quadrilateral Area Coordinate Method (QACM-III)

Abstract

Two quadrilateral area coordinate methods (hereinafter referred to as QACM‐I and QACM‐II) have already been proposed in 1999 and 2008, respectively. The QACM‐I contains four components (L1, L2, L3, L4), among which only two are independent. And the QACM‐II contains only two independent coordinate components (Z1, Z2). Many successful applications demonstrate that these new coordinate systems are efficient tools for developing robust quadrilateral finite element models. In this paper, another new quadrilateral area coordinate method (hereinafter referred to as QACM‐III), containing two components T1 and T2, is systematically established. This new coordinate system (QACM‐III) not only keeps the most important advantages of the QACM‐I and QACM‐II, but also possesses other distinguished characters. For instances, it can be directly applied to quadrilateral elements with curved sides, and may have a simpler form in element shape functions. Furthermore, three different quadrilateral area coordinate methods, QACM‐I, ‐II and ‐III, can be used simultaneously to develop new plane membrane element models which possess quite simple construction procedure.