用第三类四边形面积坐标构造一个四结点四边形膜元  

A FOUR-NODE QUADRILATERAL MEMBRANE ELEMENT FORMULATED BY THE THIRD VERSION OF THE QUADRILATERAL AREA COORDINATE METHOD

作　　者：王丽[1] 龙志飞[1] 龙驭球[2] 

机构地区：[1]中国矿业大学(北京)力学与建筑工程学院,北京100083 [2]清华大学土木工程系,北京100084

出　　处：《工程力学》2009年第8期1-5,共5页Engineering Mechanics

摘　　要：四边形第一类和第二类面积坐标(QAC-Ⅰ和QAC-Ⅱ)分别被提出以后,又提出了第三类面积坐标(QAC-Ⅲ),它不仅保留了QAC-Ⅰ和QAC-Ⅱ的主要优点,而且具有其他一些优异特性。该文应用第三类四边形面积坐标(QAC-Ⅲ),构造出一个含内参的四结点四边形膜元,记为QACⅢ-Q6元。这个新单元有以下优点:1)与Wilson的Q6元相比,新单元具有计算精度高,对网格畸变不敏感的优点;2)与基于QAC-Ⅰ和基于QAC-Ⅱ的Q6元相比,新单元不仅具有同样优异的单元性能,而且其推导方法更为简明,其形函数更为简洁。With the first version and second version of quadrilateral area coordinate method （QAC-Ⅰ and QAC-Ⅱ） developed, the third version of quadrilateral area coordinate method （QAC-Ⅲ） is proposed, which, except for retaining main advantages of QAC-Ⅰ and QAC-Ⅱ, owns some other distinguishing features. In this paper, QAC-Ⅲ is used to formulate a new 4-node membrane element with internal parameters, denoted as element QACIII-Q6. This new element exhibits the following advantages： 1） compared with Wilson＇s element Q6, this new element possesses high accuracy and is insensitive to mesh distortion. 2） this new element has comparable performance to the Q6 elements formulated by QAC-Ⅰ and QAC-Ⅱ, moreover, the procedure in formulation is simple, and the expression for the shape function matrix is concise.

关 键 词：有限元 四边形膜元 第三类面积坐标 位移函数 网格畸变 

分 类 号：O241.82[理学—计算数学]