新型九节点协同转动四边形弹塑性壳单元

Advanced nine-node co-rotational quadrilateral elasto-plastic shell element

为求解板壳结构的弹塑性大变形问题,发展了一种新型九节点协同转动四边形壳单元.与现有的其他协同转动壳单元相比,由于在单元中采用了增量可直接累加的矢量型转动变量,大大降低了非线性增量求解过程中更新转动变量的难度,且在整体与局部坐标系下能得到对称的单元切线刚度矩阵,单元的计算效率得到明显提高.在单元公式中,引入了von Mises材料屈服准则,采用向后欧拉迭代法进行材料本构关系的隐式积分,并选用一致材料模量矩阵.为减轻闭锁现象的不利影响,单元中还引入了假定应变法.通过2个典型算例,证明了这种新型九节点协同转动四边形壳单元在求解板壳结构弹塑性大变形问题时的计算精度和收敛性是令人满意的.

A nine-node co-rotational quadrilateral shell element for elasto-plastic shell structures undergoing arbitrarily large rotations was presented.Different from other existing co-rotational shell element formulations,additive vectorial rotational variables were employed in the proposed formulation,thus,updating nodal variables in a nonlinear incremental solution procedure becomes very simple,and symmetric element tangent stiffness matrices were achieved in both local and global coordinate systems,resulting in better computational efficiency.For analyses of elasto-plastic shell problems,the von Mises yield criterion was introduced,and an implicit integration of the flow rules using the backward-Euler return approach was employed,meanwhile,consistent tangent moduli were derived.An assumed strain method was used to overcome locking phenomena,and the computational efficiency and accuracy of the present element were verified through several elasto-plastic shell problems undergoing arbitrarily large rotations.