薄元分解与Laplacian光顺相结合的四面体有限元网格优化方法

Tetrahedral mesh optimization method combining sliver decomposition and Laplacian smoothing

提出一种有效的三维实体四面体有限元网格质量优化方法以满足有限元分析对网格质量的要求。对薄元分解法进行改进,改进的薄元分解法更全面地考虑了各种劣质单元类型,能够对三维实体网格剖分中产生的各种类别的孤立劣质单元进行有效的分解;将改进的薄元分解法与Laplacian光顺优化方法相结合以解决某些网格剖分算法如推进波前法和Delaunay三角化方法产生的非孤立劣质单元问题。经过实例检验,本文提出的四面体单元网格优化算法健壮有效、易于实现,能够显著提高最差单元的质量。

To meet the requirements of finite element analysis on the mesh quality, an effective mesh optimization method is presented in this paper to improve the quality of tetrahedral mesh. The sliver de- composition method is extended to deal with all kinds of isolated poor-quality tetrahedral elements generated by various meshing method for three-dimensional solids. A new mesh smoothing method combining the extended sliver decomposition method and the Laplacian smoothing method is proposed to solve the problem of clustering poor-quality elements frequently occurred in some mesh generation algorithms such as Advancing Front Technique （AFT） and Delaunay Triangulation. Computational experiments show that the method proposed is robust, efficient and easily implemented in practical applications, the quality of the worst elements is improved noticeably.