两个新的非协调膜元  

Two New Nonconforming Membrane Finite Elements

作　　者：石东洋[1,2] 赵海燕[1,2] 黄艾香 

机构地区：[1]郑州大学数学系 [2]西安交通大学机械工程学院

出　　处：《工程数学学报》1997年第3期50-56,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金河南省自然科学基金

摘　　要：利用分析ｓｐｅｃｈｔ元的技巧，构造了两种非协调任意凸四边形单元ＭＤ６１及ＭＤ６２，证明了由此产生的有限元对任意四边形网格通过Ｉｒｏｎｓ分片检查和广义分片检查，其形状函数不依赖于单元本身．理论精度同Ｗｉｌｓｏｎ元及类Ｗｉｌｓｏｎ元．数值计算的结果表明，ＭＤ６１元的整体效果好于Ｗｉｌｓｏｎ元及类Ｗｉｌｓｏｎ元；对不规则剖分，ＭＤ６２元也好于Ｗｉｌｓｏｎ元及类Ｗｉｌｓｏｎ元．In this paper, two new nonconforming arbitrary quadrilateral elements MD61 and MD62 are constructed by using the analysis technique of specht element. It is proved that these elements pass through Irons patch test and the generalized patch test for arbitrary quadrilateral meshes. The convergence behavior is similar to Wilson elements and like Wilson elements. The choice of shape functions is independent of the elements geometrical parameters. The numerical results of these elemensts are better than that of Wilson elements and like Wilson elements as a whole.

关 键 词：四边形单元 形状函数 非协调元 WILSON元 有限元 

分 类 号：O242.21[理学—计算数学]