三维Wilson元及在近不可压弹性问题中的应用  

Wilson element and its application in nearly incompressible elasticity problems in three dimensions

作　　者：李真有 肖映雄[1] 

机构地区：[1]湘潭大学土木工程与力学学院,湖南湘潭411105

出　　处：《广西大学学报（自然科学版）》2016年第4期1271-1278,共8页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(10972191);湖南省自然科学基金资助项目(14JJ2063);湖南省教育厅资助科研项目(15A183)

摘　　要：为克服三维近不可压缩问题的体积闭锁现象,建立了两种基于六面体单元的Wilson非协调元计算格式,并将其应用于两类含混合边界条件的近不可压缩弹性问题的求解。数值结果表明:Wilson非协调元能有效克服三维体积闭锁现象,与相同规模下的协调元相比较,它具有更高的计算精度。在三维有限元分析中,剖分网格的质量将对计算精度影响很大,实际计算时若能采用各向同性网格,则对问题的分析将具有更好的收敛性。In order to overcome the volume locking phenomenon of nearly incompressible problems in three dimensions,two types of Wilson nonconforming finite elements have been presented based on the hexahedral elements,and the resulting methods are then applied to the solution of two nearly incompressible problems with mixed boundary conditions. The numerical results have been shown that Wilson elements can effectively overcome the locking phenomenon,and it has higher accuracy compared with the conforming elements under the same mesh size. In three-dimensional finite element analysis,the quality of the mesh will have a great effect on the accuracy,and if the isotropic grids can be used in the practical calculations,the method will have better convergence.

关 键 词：近不可压缩问题 体积闭锁 WILSON非协调元 网格质量 

分 类 号：O343.2[理学—固体力学]