Area co-ordinates used in quadrilateral elements

The area co-ordinate method has been successfully applied to construct tria ngular elements. In this paper, this method is generalized to construct qua drilateral elements, and the area co-ordinate theory for quadrilateral elem ents is systematically developed: (i) the area co-ordinates (L-1, L-2, L-3, L-4) Of any point in a quadrilateral are defined and two identical equatio ns, which the four area co-ordinates should satisfy, are formulated and pro ved; (ii) two characteristic parameters for quadrilateral elements are defi ned and the degeneration conditions under which a quadrilateral degenerates into a parallelogram or a trapezoid or a triangle are given; (iii) transfo rmation relations between the area co-ordinates and the Cartesian or isopar ametric co-ordinates are presented, and several important formulae for quad rilateral area co-ordinates are listed. Copyright (C) 1999 John Wiley & Son s, Ltd.