Area co-ordinates used in quadrilateral elements

The area co-ordinate method has been successfully applied to construct triangular elements. In this paper, this method is generalized to construct quadrilateral elements, and the area co-ordinate theory for quadrilateral elements is systematically developed: (i) the area co-ordinates (L1 , L2 , L3 , L4) of any point in a quadrilateral are defined and two identical equations, which the four area co-ordinates should satisfy, are formulated and proved; (ii) two characteristic parameters for quadrilateral elements are defined and the degeneration conditions under which a quadrilateral degenerates into a parallelogram or a trapezoid or a triangle are given; (iii) transformation relations between the area co-ordinates and the Cartesian or isoparametric co-ordinates are presented, and several important formulae for quadrilateral area co-ordinates are listed. Copyright © 1999 John Wiley & Sons, Ltd.