龙驭球, 李聚轩, 龙志飞, 岑松. 四边形单元面积坐标理论[J]. 工程力学, 1997, 14(3): 1-11.
引用本文: 龙驭球, 李聚轩, 龙志飞, 岑松. 四边形单元面积坐标理论[J]. 工程力学, 1997, 14(3): 1-11.
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Long Yuqiu, Li Juxuan, Long Zhifei, Cen Song. AREA-COORDINATE THEORY FOR QUADRILATERAL ELEMENTS[J]. Engineering Mechanics, 1997, 14(3): 1-11.
Citation: Long Yuqiu, Li Juxuan, Long Zhifei, Cen Song. AREA-COORDINATE THEORY FOR QUADRILATERAL ELEMENTS[J]. Engineering Mechanics, 1997, 14(3): 1-11.
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四边形单元面积坐标理论

AREA-COORDINATE THEORY FOR QUADRILATERAL ELEMENTS

    摘要
  • 摘要: 本文建立了四边形单元面积坐标的系统理论,包括：(1)给出四边形单元两个特征参数g1,g2的定义以及四边形退化为平行四边形(含矩形),梯形,三角形时相应的特征条件；(2)给出四边形单元面积坐标的定义及其与直角坐标和四边形等参坐标之间的变换关系；(3)给出四边形单元四个面积坐标分量之间应满足的两个恒等式并予以证明；(4)给出相关的一些重要公式。可以看出,四边形面积坐标是构造四边形单元的有效工具。它既是自然坐标,具有不变性；同时它与直角坐标之间为线性关系,易于得出单元刚度矩阵的积分显式,无需依赖于数值积分。

     

    Abstract: 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.

     

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