混合应用三类四边形面积坐标构造八结点四边形膜元

EIGHT-NODE QUADRILATERAL MEMBRANE ELEMENT FORMULATED BY MIXED USE OF THE THREE TYPES OF THE QUADRILATERAL AREA COORDINATE METHOD

三类四边形面积坐标已先后提出。如果对三类面积坐标加以混合应用,这将使构造四边形单元的工作更加灵活多样,具有更加广阔的优选空间。该文混合应用三类四边形面积坐标构造一个8结点四边形膜元。新单元具有如下优点:1)新单元具有优异性能,特别是对网格畸变不敏感,优于8结点等参元,显示出三类四边形面积坐标的共同优点;2)新单元的推导过程和主要列式都非常简洁。这是由于巧妙地混合应用三类面积坐标并进行优选而取得的结果。

Three types of the quadrilateral area coordinate method have been proposed. If these three types are used mixedly, the optimal model of quadrilateral element will then be obtained. In this paper, these three types of the quadrilateral area coordinate method are mixedly used to develop one eight-node quadrilateral membrane element. The new element exhibits the following advantages： i） the new element possesses distinguished performance and is insensitive to mesh distortion. In contrast, the eight-node isoparametric element Q8 is very sensitive to mesh distortion. This advantage reflects the common characteristics of the three types （ I, II, III）of the quadrilateral area coordinate method, ii） The formulation procedure and the expression of the shape function matrix of the new element are very simple. This advantage is due to the ingenious and optimal combination of the three types （ I, II, III） of the quadrilateral area coordinate method.