基于假定应变法的协同转动四边形复合材料壳单元

Co-rotational quadrilateral composite shell element based on assumed strain method

为对复合材料层合板壳结构进行精确的大变形数值模拟,提出一种采用假定应变法的能分析层合结构大转动问题的协同转动四边形壳单元.该方法在建立有限元公式时引入假定应变法以克服膜闭锁和剪切闭锁的不利影响.与其他能分析大转动问题的复合材料壳单元相比,在新的协同转动框架中采用矢量型转动变量,可大大降低在非线性增量求解过程中更新转动变量的难度,且能得到对称的单元切线刚度矩阵,提高单元的计算效率.分析两个典型算例,并与其他学者的结果进行对比,结果表明在计算层合结构大转角问题时拥有较好的精度和收敛性.

To perform accurate numerical simulation on large deformation of composite laminate shell structure,a co-rotational quadrilateral composite shell element for large rotation analysis of laminated structures is proposed.To overcome the disadvantages of membrane locking and shear locking,the assumed strain method is introduced into the finite element formulations.Being different from other composite shell element formulations which are used to analyze large rotation analysis,the vectorial rotational variables are employed within the new co-rotational framework,so the difficulty of updating rotational variables is greatly decreased during incremental non-linear solution procedure,the tangent stiffness matrix is symmetric,and the computation efficiency can be improved.Two classical large rotation problems for composite shell structures are solved and the results are compared with the results obtained by other scholars.The results indicate that the accuracy and convergence of large rotation computation of laminated structures can be improved with the proposed element.