An unsymmetric 8‐node hexahedral element with high distortion tolerance
An unsymmetric 8‐node hexahedral element with high distortion tolerance
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DOI：
10.1002/nme.5318
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发表时间：
2017-02
影响因子：
2.9
通讯作者：
Pei Zhou;S. Cen;Junbin Huang;Chenfeng Li;Qun Zhang
中科院分区：
文献类型：
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作者：
Pei Zhou;S. Cen;Junbin Huang;Chenfeng Li;Qun Zhang
在现有有限元库中的所有3D八节点六面体实体单元中，“最好的”一个可以使用粗糙的规则网格对弯曲问题产生良好的结果。然而，一旦网格被扭曲，精度将急剧下降。如何解决这一问题仍然是一个悬而未决的挑战。本文基于虚功原理建立了一种8节点24自由度六面体单元，该单元同时采用两组不同的位移场来构造非对称单元刚度矩阵。第一组简单地利用了传统的8节点三线性等参元的公式，而第二组主要采用了三维斜坐标（R，S，T）的解析试函数。所得到的单元用US-ATFH 8表示，不包含可调因子，可用于各向同性和各向异性情况。数值算例表明，该方法能严格通过纯弯曲的一阶（常应力/应变）和二阶分片检验，消除体积锁定，并提供坐标旋转不变性.特别是，它是不敏感的各种严重的网格变形。版权所有© 2016约翰威利父子有限公司.
Among all 3D 8‐node hexahedral solid elements in current finite element library, the ‘best’ one can produce good results for bending problems using coarse regular meshes. However, once the mesh is distorted, the accuracy will drop dramatically. And how to solve this problem is still a challenge that remains outstanding. This paper develops an 8‐node, 24‐DOF (three conventional DOFs per node) hexahedral element based on the virtual work principle, in which two different sets of displacement fields are employed simultaneously to formulate an unsymmetric element stiffness matrix. The first set simply utilizes the formulations of the traditional 8‐node trilinear isoparametric element, while the second set mainly employs the analytical trial functions in terms of 3D oblique coordinates (R, S, T). The resulting element, denoted by US‐ATFH8, contains no adjustable factor and can be used for both isotropic and anisotropic cases. Numerical examples show it can strictly pass both the first‐order (constant stress/strain) patch test and the second‐order patch test for pure bending, remove the volume locking, and provide the invariance for coordinate rotation. Especially, it is insensitive to various severe mesh distortions. Copyright © 2016 John Wiley & Sons, Ltd.