全四边形有限元网格的拓扑优化策略

Topological Improvement for Quadrilateral Finite Element Meshes

基于有限元网格的局部拓扑结构,给出一些非结构化全四边形有限元网格的拓扑优化策略,这些策略被组织成“型-操作”的形式.型是指一类满足一定约束条件的局部区域网格,而操作则是指与特定型相对应的拓扑变换,它能优化局部网格中节点的度值,从而优化局部网格质量.这些策略可分成针对网格内部单元和针对网格边界单元2类.实验结果表明,这些策略能较好地改善四边形网格的质量.

Based on the local topological structures of finite element meshes, this paper presents several procedures for improving the topology of unstructured quadrilateral meshes. These procedures are established in the form of ＂case-operations＂. A case is a kind of local meshed region, which satisfies some constrained conditions, and its topology can be improved by means of topological transformation. These procedures can be classified into two types： one for interior elements and the other for elements connected to the boundary. Several sample meshes are presented to illustrate the effectiveness of the approach.