采用应变差分离法的新型协同转动三边形曲壳单元  

Advanced co-rotational curved triangular shell element using discrete strain gap method

作　　者：李忠学[1] 徐晋[1] 刘永方[1] 俞冬良[1] 叶青会[1] 

机构地区：[1]浙江大学结构工程研究所,浙江杭州310058

出　　处：《浙江大学学报（工学版）》2009年第8期1506-1512,共7页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(50408022);教育部与浙江省留学回国人员科研启动基金资助项目

摘　　要：发展了一种能够解决结构大位移、大转角问题的新型协同转动三边形曲壳单元.不同于现有的其他协同转动有限元法,本单元有如下特色:1)采用了矢量型节点转动变量,它们是单元节点处曲壳中面法向矢量的2个较小分量;2)所有的节点变量在增量求解过程中都是采用简单的加法进行更新的;3)单元的切线刚度矩阵是通过计算单元应变能对节点变量的二阶微分得到,且节点变量间的微分次序是可互换的,因而得到的切线刚度矩阵是对称的.为消除可能出现的闭锁现象,在计算单元应变能时引入了假定膜应变和假定剪切应变.这些假定应变采用应变差分离法计算,它们不影响单元切线刚度矩阵的对称性.通过对4个典型算例的分析,验证了单元的可靠性、计算精度和计算效率.An advanced 6-node co-rotational curved triangular shell element for large displacement and large rotation analysis was presented. Different from other existing co-rotational finite element formulations, the present element has several features： 1） vectorial rotational variables are employed, which are the two smaller components of the mid-surface normal vector at each node;2） all nodal variables including three translations and two vectorial rotational variables are additive in an incremental solution procedure; 3） the element tangent stiffness is calculated as the second derivatives of the strain energy of an element with respect to nodal variables, and all nodal variables are commutative in calculating the differentiation, resulting in a symmetric element tangent stiffness matrix. To overcome locking phenomena, the assumed membrane strains and shear strains calculated respectively according to the discrete strain gap method are employed, and the achieved element tangent stiffness matrix is still symmetric. Finally, four well-chosen elastic shell problems were solved to illuminate the reliability, computational accuracy and efficiency of the proposed element formulation.

关 键 词：协同转动法 矢量型转动变量 对称的切线刚度 应变差分离 闭锁现象 

分 类 号：TU311.4[建筑科学—结构工程]