新型协同转动六节点三边形复合材料壳单元

A NEW 6-NODE CO-ROTATIONAL TRIANGULAR COMPOSITE SHELL ELEMENT

为分析复合材料层合板壳结构,提出了一种协同转动六节点三边形复合材料曲壳单元。不同于现有的其它协同转动有限单元:1)该单元中采用了增量可加的矢量型转动变量,因而在非线性增量求解过程中更新节点转动变量非常简单;2)在计算应变能对局部节点变量的二阶偏微分时,微分的次序是可以交换的,并且通过链式微分计算应变能对整体节点变量的二阶偏微分时,微分的次序也是可以交换的,因此,得到的局部和整体坐标系下的切线刚度矩阵都是对称的;3)在此有限单元公式中引入了混合公式法,以减轻膜闭锁和剪切闭锁的不利影响。对4个典型算例进行了分析,并与其他文献的结果进行对比,该文提出的单元的可靠性和计算效率得到了验证。

To model laminated composite plate and shell structures, a 6-node co-rotational curved triangular composite shell element is proposed. It is different from other existing co-rotational element formulations in the following ways: 1) Additive vectorial rotational variables are employed in the present element, thus updating nodal rotational variables is quite simple in a nonlinear incremental solution procedure; 2) Symmetric tangent stiffness matrices are achieved in both the local and global coordinate systems owing to the commutativity of the nodal variables in calculating the second derivatives of strain energy with respect to the local nodal variables and, through chain differentiation, with respect to the global nodal variables; 3) A mixed formulation procedure is employed to overcome membrane and shear locking problems. Four composite shell problems with large deformations are solved, and the results are compared with those from other literature, through which the proposed element formulation demonstrates its reliability and computational efficiency.