An improved 4-node quadrilateral plate bending element of the Reissner-Mindlin type
An improved 4-node quadrilateral plate bending element of the Reissner-Mindlin type
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DOI：
10.1007/s004660050405
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发表时间：
1999-04
影响因子：
4.1
通讯作者：
F. Kikuchi;K. Ishii
中科院分区：
文献类型：
--
作者：
F. Kikuchi;K. Ishii
本文构造了一个四节点四边形Reissner-Mindlin型12自由度板弯曲单元。为了改进基本的双线性单元，我们将所有等参双二次项加入到假定的横向挠度中，从而可以表示任何纯弯曲状态。然后引入横向挠度和两个转角之间的耦合，在不增加单元自由度的同时保持单元间的协调性。我们可以显式地表示形函数，从而可以很容易地得到单元的刚度矩阵和荷载向量。三结点三角形单元也可以通过结点退化技术得到。通过几个数值算例对所提出的单元进行了测试，结果表明，与已有单元相比，该单元的性能有了明显的改善，特别是在形状变形方面表现出了较强的鲁棒性。我们还提出了一个避免锁定的技巧，尽管对于目前类型的兼容元件来说，这在薄板范围内最初是不可避免的。
We develop a Reissner-Mindlin type plate bending element of 4-node quadrilateral shape with 12 dof To improve the basic bilinear element, we add all the isoparametric biquadratic terms to the assumed lateral deflection so that any pure bending states can be represented. Then we introduce coupling between the lateral deflection and the two rotations so as not to increase the element degrees of freedom with the interelement compatibility preserved. We can express the shape functions explicitly, and hence the element stiffness matrices and the load vectors can be easily obtained. A 3-node triangular element can be also derived by the node degeneration technique. We test the proposed element by several numerical examples, and we can see that the behavior of the element is actually improved in comparison with some existing elements with the same dof In particular, the element is shown to be relatively robust to shape distortion. We also proposed a trick to avoid locking, although it is originally unavoidable in the thin plate range for the present type of compatible elements.