含两个分量的四边形单元面积坐标理论  

A TWO-COMPONENT AREA COORDINATE METHOD FOR QUADRILATERAL ELEMENTS

作　　者：陈晓明[1] 岑松[1] 龙驭球[2] 傅向荣[3] 

机构地区：[1]清华大学航天航空学院,北京100084 [2]清华大学土木工程系,北京100084 [3]中国农业大学土木工程系,北京100083

出　　处：《工程力学》2007年第z1期32-35,共4页Engineering Mechanics

基　　金：国家自然科学基金资助项目(10502028);高等学校全国优秀博士论文作者专项基金资助项目(200242)

摘　　要：为了便于构造抗畸变的四边形单元,建立了一套新的四边形单元面积坐标理论(QAC-2),并给出了相关的积分和微分公式。该坐标系作为自然坐标,具有明确的物理意义,且只含有两个相互独立的坐标分量,因此易于实现与直角坐标和等参坐标的沟通,便于理解和应用;两个坐标分量与直角坐标之间满足线性变换,在构造单元时易于选择完备的多项式序列,且多项式的完备次数不会随着网格的畸变而下降,因此可以保证单元的精度和抗畸变性能。In order to construct quadrilateral elements insensitive to mesh distortion,a new kind of quadrilateral area coordinate method,denoted as QAC-2,has been successfully developed. And related differential and integral formulae are also presented. As a natural coordinate system,QAC-2 has explicit physical meanings. It includes only two independent components,Z1 and Z2,which make it easier to communicate with Cartesian coordinates and isoparametric coordinates. Furthermore,since Z1 and Z2 are linear functions of Cartesian coordinates x and y,it is convenient to establish a polynomial with high order completeness in Cartesian coordinates by using Z1 and Z2,and this polynomial will keep its completeness order invariable for mesh distortion cases. QAC-2 is a simple and novel tool for developing more accurate and robust quadrilateral element models.

关 键 词：有限元 四边形元 面积坐标 网格畸变 微分和积分公式 

分 类 号：O242.21[理学—计算数学]