Stabilization of bi‐linear mixed finite elements for tetrahedra with enhanced interpolation using volume and area bubble functions
Stabilization of bi‐linear mixed finite elements for tetrahedra with enhanced interpolation using volume and area bubble functions
复制标题
使用体积和面积气泡函数增强插值的四面体双线性混合有限元的稳定性
DOI：
10.1002/nme.2264
复制
发表时间：
2008
影响因子：
2.9
通讯作者：
I. Caylak
中科院分区：
文献类型：
--
作者：
R. Mahnken;I. Caylak
为了克服四面体元混合双线性伽辽金公式的振荡效应，提出了一种稳定方法。为此，对不相容模态混合法和增强应变混合法进行了重新表述，从而给出了具有稳定化项的混合有限元法的解释。对于非线性问题，这些是非线性依赖于当前变形状态的，因此被线性相关的稳定项所取代。这种方法对于数值实现来说是最有吸引力的，因为它完全避免了使用与前一个牛顿迭代步骤相关的量，这些步骤通常是在混合增强元素中出现的。利用体积气泡函数和面积气泡函数，得到了不相容模式混合法和强化应变混合法的稳定矩阵。给出了各种数值算例，成功地说明了双线性四面体单元的稳定效果。版权所有©2007 John Wiley & Sons， Ltd
In order to overcome the oscillatory effects of the mixed bi‐linear Galerkin formulation for tetrahedral elements, a stabilization approach is presented. To this end the mixed method of incompatible modes and the mixed method of enhanced strains are reformulated, thus giving both the interpretation of a mixed finite element method with stabilization terms. For non‐linear problems, these are non‐linearly dependent on the current deformation state and therefore are replaced by linearly dependent stabilization terms. The approach becomes most attractive for the numerical implementation, since the use of quantities related to the previous Newton iteration step, typically arising for mixed‐enhanced elements, is completely avoided. The stabilization matrices for the mixed method of incompatible modes and the mixed method of enhanced strains are obtained with volume and area bubble functions. Various numerical examples are presented, which illustrate successfully the stabilization effect for bi‐linear tetrahedral elements. Copyright © 2007 John Wiley & Sons, Ltd.