Reissner-Mindlin板的非协调稳定化三角形有限元方法分析  

Analysis of a Nonconforming Stabilized Triangular Element for the Reissner-Mindlin Plate

作　　者：杨艳[1] 冯民富[2] 

机构地区：[1]西南石油大学理学院,南充637001 [2]四川大学数学学院,成都610064

出　　处：《工程数学学报》2009年第4期653-662,共10页Chinese Journal of Engineering Mathematics

基　　金：四川省科技攻关课题(05GG006-006-2)

摘　　要：本文提出了一种新的格式,讨论了Reissner-Mindlin板问题的一种非协调三角形有限元逼近。取挠度空间为协调的一次元,角位移空间为非协调一次元,剪切力空间取分片常数元,证明了该格式对任意板厚都收敛,可以避免剪切闭锁现象,并有最优一致误差估计,比Arnold("Analysis of a linear-linear finite element for the Reissner-Mindlin plate model")一文中的收敛结果好。最后还给出了零范数估计。A new formulation is proposed to approximate the Reissner-Mindlin plate by using non- conforming triangular elements. The method uses conforming linear elements to approximate the transverse displacements, nonconforming linear elements to approximate the rotations, and piecewise elements to approximate the shear strain. We have proved that the method is convergent for thin plates and it can avoid the locking phenomenon. We also get the optimal error estimate, which is better than the result in Arnold＇s paper ＂Analysis of a linear-linear finite element for the Reissner-Mindlin plate model＂. Finally, we give the zero-norm estimate.

关 键 词：REISSNER-MINDLIN板 非协调元 剪切闭锁现象 

分 类 号：O241[理学—计算数学] O343[理学—数学]