薄壁梁空间分析的六面体十二结点广义协调元

A 12-Node Hexahedral Generalized Conforming Element for 3-D Analysis of Thin-Walled Beams

为了减少薄壁梁空间分析的单元分割数,在六面体十二结点等参元的基础上,构造了一种具有八个非协调位移函数的新型六面体十二结点广义协调元。通过在单元自然坐标η方向有选择性的引入高阶非协调位移插值函数,使得单元在边长尺寸相差悬殊的网格划分下仍有较高的精度。单元的非协调位移场能满足网格无限划分时的边界极限协调条件,因此能确保单元收敛。数值计算表明,该广义协调元具有很高的计算精度,可适应边长尺寸相差悬殊的网格划分,能有效减少有限元分析的单元分割数。

In order to enhance the computation efficiency in the 3-D analysis of thin-walled beams, a new hexahedral generalized conforming element with eight additional unconforming displacement functions was developed based on the 12-node hexahedral isoparametric element. With the introduction of high order unconforming displacement functions in the η direction of natural coordinate, the element yields good results even if one of its dimensions is much longer than the two others. The unconforming displacement field satisfies the generalized conforming condition so that the element is convergent. Numerieal examples were presented to demonstrate the precision and effectiveness of this element.