Area Coordinates Used in Quadrilateral Elements
Long, Yuqiu, Juxuan Li, Zhifei Long and Song Cen
Communications in Numerical Methods in Engineering, John Wiley & Sons, Num 15, pp.533-545, 1999
Department of Civil Engineering, Tsinghua University Beijing, China
Abstract
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.
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