Orientation-Preservation Conditions on an Iso-parametric FEM in Cavitation Computation
Orientation-Preservation Conditions on an Iso-parametric FEM in Cavitation Computation
复制标题
空化计算中等参数有限元的方向保持条件
DOI：
10.1007/s11425-016-0019-0
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Zhiping Li
中科院分区：
文献类型：
--
作者：
Chunmei Su;Zhiping Li
方向保持条件，即，要求变形梯度的雅可比行列式为正，这是弹性力学以及许多其它领域中的自然物理约束。众所周知，这种约束往往会给理论分析和数值计算带来严重的困难，特别是当材料受到大变形时。在一类径向对称的大展开容纳三角剖分上，得到了腔解的二次等参有限元插值函数保持方向的充要条件.研究结果为腔体附近的网格划分提供了实用的定量指导，并表明二次等参有限元法可以在合理的总自由度数下实现保向。
The orientation-preservation condition, i.e., the Jacobian determinant of the deformation gradient det ∇ubeing required to be positive, is a natural physical constraint in elasticity as well as in many other fields. It is well known that the constraint can often cause serious difficulties in both theoretical analysis and numerical computation, especially when the material is subject to large deformations. We derive a set of necessary and sufficient conditions for the quadratic iso-parametric finite element interpolation functions of cavity solutions to be orientation preserving on a class of radially symmetric large expansion accommodating triangulations. The result provides a practical quantitative guide for meshing in the neighborhood of a cavity and shows that the orientation-preservation can be achieved with a reasonable number of total degrees of freedom by the quadratic iso-parametric finite element method.