AREA-COORDINATE THEORY FOR QUADRILATERAL ELEMENTS

The area-coordinate theory for quadrilateral elements has been developed in this paper. (1) Two characteristic parameters, g¹ and g², for quadrilateral elements are defined and the characteristic conditions under which a quadrilateral degenerates into a parallelogram or a trapezoid or a triangle are given. (2) The area-coordinates for quadrilateral elements are defined and the transformation relations between the area-coordinates and the rectangular or isoparametric coordinates are presented. (3)Two identical equations which the area-coordinates for quadrilateral elements should satisfy are formulated and proved. (4) Several important formulas for quadrilateral area-coordinates are listed. The area-coordinate method is a new way to comstruct quadrilateral elements.