李忠学, 胡万波. 用于光滑/非光滑壳的稳定化新型协同转动4节点四边形壳单元[J]. 工程力学, 2020, 37(9): 18-29. DOI: 10.6052/j.issn.1000-4750.2019.10.0611
引用本文: 李忠学, 胡万波. 用于光滑/非光滑壳的稳定化新型协同转动4节点四边形壳单元[J]. 工程力学, 2020, 37(9): 18-29. DOI: 10.6052/j.issn.1000-4750.2019.10.0611
LI Zhong-xue, HU Wan-bo. A STABILIZED FOUR-NODE CO-ROTATIONAL QUADRILATERAL SHELL ELEMENT FOR SMOOTH AND NON-SMOOTH SHELL STRUCTURES[J]. Engineering Mechanics, 2020, 37(9): 18-29. DOI: 10.6052/j.issn.1000-4750.2019.10.0611
Citation: LI Zhong-xue, HU Wan-bo. A STABILIZED FOUR-NODE CO-ROTATIONAL QUADRILATERAL SHELL ELEMENT FOR SMOOTH AND NON-SMOOTH SHELL STRUCTURES[J]. Engineering Mechanics, 2020, 37(9): 18-29. DOI: 10.6052/j.issn.1000-4750.2019.10.0611

用于光滑/非光滑壳的稳定化新型协同转动4节点四边形壳单元

A STABILIZED FOUR-NODE CO-ROTATIONAL QUADRILATERAL SHELL ELEMENT FOR SMOOTH AND NON-SMOOTH SHELL STRUCTURES

  • 摘要: 该文发展了一种适用于光滑壳和非光滑壳的新型协同转动4节点四边形壳单元。在单元中每个节点采用了3个平动自由度和2/3个矢量型转动自由度,每个光滑壳的节点或非光滑壳的非交界节点采用壳中性面法向矢量的2个最小分量作为矢量型转动变量,在非光滑壳中性面交界线上的节点采用3个矢量型转动变量,他们分别是节点定向矢量组中一个定向矢量的较小或最小分量和另一定向矢量的2个最小分量。在非线性增量求解过程中,这些矢量型转动变量可以采用简单的加法将增量累加到原矢量中直接进行更新,且采用了协同转动框架的单元在局部和整体坐标系下得到的切线刚度矩阵都是对称的,结构整体切线刚度矩阵可以采用一维线性存储,可节省大量的计算机存储资源和计算时间。为消除膜闭锁和剪切闭锁的不利影响,采用单点积分方案计算单元内力矢量和切线刚度矩阵,并借鉴Belytschko提出的物理稳定化零能模态控制法来消除可能出现的零能模态。通过对2个光滑壳和2个非光滑壳进行非线性分析,检验了单元的可靠性、计算效率与计算精度。

     

    Abstract: A four-node co-rotational quadrilateral shell element for smooth and non-smooth shell structures is presented. Each node of the element has three translational degrees of freedom and two or three vectorial rotational degrees of freedom. For the nodes of smooth shells or nodes away from the intersection of non-smooth shells, the two smallest components of the mid-surface normal vector are defined as the nodal rotational variables. For the nodes at intersections of non-smooth shells, two smallest components of one orientation vector, together with one smaller or the smallest component of another nodal orientation vector, are employed as rotational variables. In a nonlinear incremental solution procedure, the vectorial rotational variables are additive and the symmetric tangent stiffness matrices are obtained in both global and local coordinate systems, thus, one-dimensional linear storage scheme can be adopted, saving computer storage and computing time effectively. To alleviate membrane and shear locking phenomena, one-point quadrature is adopted in calculating the element tangent stiffness matrices and the internal force vector, and the physically stabilized method is employed to avoid the occurrence of spurious zero energy modes. The reliability and computational accuracy are verified through two smooth shell problems and two non-smooth shell problems undergoing large displacements and large rotations.

     

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