粗网格划分下具有高精度的六面体广义协调元

Hexahedral Generalized Conforming Element with High Coarse-mesh Accuracy

针对薄壁结构三维实体有限元分析存在单元划分过多的问题,构造了一种能适应粗单元网格划分的六面体广义协调元.该单元以六面体十二结点等参元为基础,通过在单元不同坐标方向有选择性地补充非协调位移插值项,使得单元在粗网格划分下仍能保持良好的性能.所构造的非协调位移场满足网格无限划分时的边界极限协调条件,因而能确保单元收敛性.数值计算表明,该广义协调元具有很高的计算精度,能适应边长尺寸相差悬殊的单元网格划分.

The paper presents a new hexahedral generalized conforming element with coarse-mesh high accuracy to avoid resorting to a large number of elements in the 3-D finite element analysis of thin-walled structures. The element is developed on the basis of the 12-node hexahedral isoparametric elements. By introducing different unconforming displacement functions into the different coordinate directions, the element maintains good performance even if the element is coarse meshed. The unconforming displacement field satisfies the generalized conforming condition so that the element is convergent. Numerical examples indicate that the element yields good results even if one of the three dimensions is much longer than the other two.