A mixed co‐rotational formulation of 2D beam element using vectorial rotational variables
A mixed co‐rotational formulation of 2D beam element using vectorial rotational variables
复制标题
使用矢量旋转变量的二维梁单元的混合共旋转公式
DOI：
10.1002/cnm.882
复制
发表时间：
2006
影响因子：
--
通讯作者：
Z. Li
中科院分区：
文献类型：
--
作者：
Z. Li
基于共转框架，提出了一种用于二维梁大位移分析的三节点等参混合元列式，该列式不存在薄膜/剪切闭锁问题。首先，将共转框架固定在单元的内节点处，框架随节点刚性平移和转动，但不随单元变形。然后，定义了一组矢量旋转变量来精确描述单元的变形，这些旋转变量在增量求解过程中可以具有不同的含义。在计算混合Hellinger-Reissner泛函时，引入绿色应变场和独立假设的应变场，通过对混合泛函施加平稳性，得到内力矢量，然后由内力矢量对局部变量求导得到单元切线刚度矩阵，得到对称的单元切线刚度矩阵。最后，通过算例分析，验证了该方法在大位移、大转角平面刚架结构建模中的可靠性和有效性。版权所有© 2006约翰威利父子有限公司。
Based on a co-rotational framework, a three-noded iso-parametric mixed element formulation for large displacement analysis of 2D beam was presented, this formulation is free of membrane/shear locking problems. Firstly, the co-rotational framework was fixed at the internal node of the element, which translates and rotates rigidly with this node, but does not deform with the element. Then, a set of vectorial rotational variables were defined to describe accurately the element deformation, these rotational variables may have different connotations in an incremental solution procedure. Thirdly, Green strain and independently assumed strain fields were introduced in calculating the mixed Hellinger–Reissner functional, and the internal force vector was derived by enforcing the stationarity to the mixed functional, thereafter, the element tangent stiffness matrix was calculated from the internal force vector by differentiating it with respect to local variables, and a symmetric element tangent stiffness matrix was achieved. Finally, several examples were analysed to illustrate the reliability and efficiency of the proposed procedure in modelling of 2D frame structures with large displacements and large rotations. Copyright © 2006 John Wiley & Sons, Ltd.