航空学报 > 1982, Vol. 3 Issue (4): 36-40

九节点四边形等参数单元

吴永礼   

  1. 中国科学院力学研究所
  • 收稿日期:1982-02-01 修回日期:1900-01-01 出版日期:1982-12-25 发布日期:1982-12-25

9-NODE QUADRILATERAL ISOPARAMETRIC ELEMENT

Wu Yongli   

  1. Institute of Mechanics, Academia Sinica
  • Received:1982-02-01 Revised:1900-01-01 Online:1982-12-25 Published:1982-12-25

摘要: 某些作者给出的数值结果表明,在单元形状不规则时,八节点和十二节点的四边形等参数单元的刚度变硬。因此,应用不规则单元所得的结果误差很大。计算结果没有由二个或四个六节点三角形组成的四边形所得的结果妤。本文表明,假使四边形单元是九节点单元,拉格朗日多项式作为插值函数,那么不规则单元所得的结果与规则单元所得的结果基本上一致。数值结果表明,九节点等参数单元比八节点、十二节点四边形等参数单元和由二个或四个六节点三角形组成的四边形单元好。

Abstract: Several Authors have presented numerical results which demonstrated the stiffening of 8-node and 12-node quadrilateral isoparametric elements when distorted from a rectangular shape. In consequence the error introduced by using distorted 8-node or 12-node quadrilateral isoparametric element is significant. The results obtained by distorted elements are essentially consistent with those obtained by undistorted elements if 9-node element is used as quadrilateral isoparametric element and Lagrange polynomials as interpolation functions. Numerical results show that 9-node isoparametric element is superior to 8-node isoparametric element, 12-node isoparametric element and quadrilateral element consisting of two or four linear strain triangles.