采用面积坐标的抗畸变四边形曲边膜元  

Curved-side membrane elements insensitive to mesh distortion using quadrilateral area coordinates

作　　者：陈晓明[1] 岑松[1,2] 宋德坡[1] 

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

出　　处：《清华大学学报（自然科学版）》2007年第2期248-255,259,共9页Journal of Tsinghua University(Science and Technology)

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：目前普遍采用的传统等参元族对网格的曲边、直边畸变均十分敏感。该文在已有的采用四边形面积坐标四边形4结点膜元基础上,构造了4个新型四边形广义协调曲边膜元5结点元ACG-Q5、6结点元ACG-Q6、7结点元ACG-Q7和8结点元ACG-Q8,形成一个完整的采用面积坐标的膜元系列。这4个单元列式简单、便于应用,且位移场实现了直角坐标的二次完备,单元精度高,对网格曲边和直边畸变都不敏感。算例表明这4个单元可以有效克服MacNeal梁、薄曲梁等传统等参元无法克服的多种闭锁现象。此外,通过这4个单元的建立还提供了一种将4结点单元推广到更多结点单元的一种通用方法。Traditional isoparametric elements are usually sensitive to various curved or straight edge mesh distortion. The quadrilateral area coordinate （QAC） method, which was established recently, can be used to eliminate such sensitivity. Here a series of curved-side membrane elements with 5 to 8 nodes were developed based on the QAC method and generalized conforming theory. All the displacement fields of the four elements possess second-order completeness in Cartesian coordinates, so they are more accurate and robust in curved or straight edge distorted meshes. Numerical results show that the elements will not lock in various benchmark problems, such as MacNeal^s beam and thin curved beam problems, which isoparametric elements can not achieve easily. Furthermore, this paper also presents a universal procedure for constructing high performance curved-side membrane elements from a 4-node model.

关 键 词：有限元 四边形面积坐标 曲边膜元 网格畸变 

分 类 号：TU32[建筑科学—结构工程]