Area co-ordinates used in quadrilateral elements

✍ Scribed by Long, Yuqiu ;Li, Juxuan ;Long, Zhifei ;Cen, Song

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 127 KB
• Volume: 15
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/(sici)1099-0887(199908)15:8<533::aid-cnm265>3.0.co;2-d

✦ Synopsis

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 (L 1 , L 2 , L 3 , L 4 ) of any point in a quadrilateral are de®ned and two identical equations, which the four area co-ordinates should satisfy, are formulated and proved; (ii) two characteristic parameters for quadrilateral elements are de®ned 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.