六面体单元体积坐标方法  

VOLUME COORDINATE METHOD FOR HEXAHEDRAL ELEMENTS

作　　者：李宏光[1] 岑松[1,2] 龙驭球[3] 岑章志[1,2] 

机构地区：[1]清华大学航天航空学院,北京100084 [2]清华大学破坏力学教育部重点实验室,北京100084 [3]清华大学土木工程系,北京100084

出　　处：《工程力学》2008年第10期12-18,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(10502028);高等学校全国优秀博士论文作者专项基金项目(200242);教育部新世纪优秀人才支持计划项目(NCET-07-0477)

摘　　要：基于二维问题四边形单元面积坐标法的成功思路,建立了三维六面体单元体积坐标的系统方法,包括:1)六面体单元特征参数的定义及单元退化模式研究;2)六面体单元体积坐标定义;3)六面体单元的体积坐标与直角坐标、等参坐标之间的关系;4)六面体体积坐标的微分公式。可以看到,六面体体积坐标保持了局部自然坐标的优点,并且与直角坐标始终保持线性关系。它为构造对网格畸变不敏感的新型六面体有限元模型提供了新工具。Based on the successful applications of the area coordinate method for quadrilateral elements in 2D problems, a new volume coordinate method is proposed for hexahedral elements in 3D problems, including： 1） the definition of characteristic parameters of a convex hexahedron, and related characteristic conditions under which a hexahedron degenerates into other special solids; 2） the definition of the volume coordinates for hexahedral elements; 3） the transformations between the volume coordinates and the Cartesian and isoparametric coordinates; 4） differential formulas for hexahedral volume coordinates. It can be readily observed that besides keeping the advantages of local natural coordinate system, the new coordinate system has the linearity with the global coordinate system. The volume coordinate method provides a new tool for developing high performance hexahedral elements which are insensitive to mesh distortion.

关 键 词：有限元 体积坐标 六面体单元 特征参数 列格畸变 

分 类 号：O242.21[理学—计算数学]