基于投影法的四面体网格切割算法

Tetrahedron Mesh-Cut Algorithm Based on Projective Method

四面体网格切割算法是有限元仿真中的重要组成部分,切割的结果决定了刚度矩阵的更新速度和精度。本文在研究Cotin算法和B ie lser算法的基础上,采用了预投影的方法,将部分顶点投影到切割平面上,使原先的四面体分割转化为相邻四面体分离,以达到简化分割的目的。与Cotin算法和B ie lser算法相比,由该算法得到的网格切割边界更加合理,剖分比更低,提高了刚度矩阵更新的速度和精度。

The tetrahedron mesh-cut algorithm is an important part of finite element method （FEM）. The mesh-cut result determines the speed and the precision of stiff matrix regeneration. Based on the Cotin and the Bielser algorithms, the algorithm proposed in this paper projects the original mesh before mesh-cutting. Parts of the vertexes are projected on the segmented face. After being projected, the mesh segmenting is changed as mesh separating, so that the mesh-cut algorithm becomes easier. Compared with Cotin and Bielser algorithms, the algorithm makes the mesh-cut results more reasonable. Meanwhile, the increasing of the tetrahedron number is lower, thus improving the speed and the precision of stiff matrix regeneration.