含面内刚性转角自由度的四边形广义协调膜元  

Generalized conforming quadrilateral membrane element with vertex rotational freedom

作　　者：陈朝晖[1] 郭益[1] 蒋锐[1] 管前乾 

机构地区：[1]重庆大学土木工程学院,重庆400030 [2]成都基准方中建筑设计事务所,四川成都610017

出　　处：《重庆大学学报（自然科学版）》2009年第1期31-36,共6页Journal of Chongqing University

基　　金：国家科技部技术创新基金资助项目(01C6215);教育部高校博士点基金资助项目(9562001)

摘　　要：在常规4结点膜单元内增加独立的平面内刚体转角自由度,采用四边形等参元形式,基于广义协调理论建立了含转角自由度的四边形广义协调膜元,避免了常规平面膜元由于忽略平面内转动而引发转动零刚度、导致刚度阵奇异的缺陷。广义协调元法具有非协调元不要求精确协调的优点,且随着单元细分可趋近于协调元,保证了广义协调元的收敛性。应用于经典的Cook问题、悬臂梁问题和MacNeal梁问题,该单元计算精度高、收敛性好、无零能模式。网格畸变分析表明,该单元弱梯形闭锁、单元抗畸变性较好,与矩形单元相比,具有单元划分的灵活性和适应性。A new generalized conforming quadrilateral membrane element is developed by introducing additional rigid vertex rotational freedoms to the normal 4-node quadrilateral membrane element. The rotational stiffness of the present element is not zero so that the singularity of the stiffness matrix is avoided. Numerical analysis of the Cook problem cantilever beam shows that the EAE/Mem element passes the patch test and possesses good convergence, reliability, and precision without a zero energy mode. It provides a lock-free solution to the MacNeal beam problem. Numerical results also show that the EAE/ Mem element is insensitive to mesh distortion. The results demonstrate that the generalized conforming technique is an efficient tool for developing high performance finite element models.

关 键 词：有限元法 广义协调理论 转角自由度 膜元 网格畸变 零能模式 

分 类 号：TU375.2[建筑科学—结构工程]