面向有限元网格生成的单元尺寸场光滑化算法

Element-sizing field smoothing algorithm for mesh generation of finite element analysis

针对单元尺寸场的合适与否会直接影响到后续有限元网格质量的问题,提出一种尺寸修正算法来优化单元尺寸场。在Borouchaki等提出的H变化量(BOROUCHAKI H,HECHT F,FREY P J.Mesh gradation control.International Journal for Numerical Methods in Engineering,1998,43(6):1143-1165)的基础上,引入尺寸梯度概念,进行一系列公式推导,得到二维的单元尺寸场的合理过渡要求,从而以定义在非结构背景网格的单元尺寸场为例,改进Borouchaki修正算法,提出了一种最少量地重置尺寸场中节点单元尺寸值,最大化地全局光滑单元尺寸场的新算法。最后给出若干实例的网格生成效果图,证明算法能帮助工程应用的模型生成更高质量的网格,跟其他修正算法相比,网格尺寸过渡明显更均匀。

Element-sizing fields are necessities for guiding the generation of high-quality meshes used in finite element analyses and smoothness of this field heavily affect the element quality of the resulting mesh. A new algorithm was proposed to smooth the element-sizing fields. Based on the H-variant proposed by Borouehaki, et al. （BOROUCHAKI H, HECHT F, FREY P J. Mesh gradation control. International Journal for Numerical Methods in Engineering, 1998, 43（6） ： 1143 - 1165）, some basic geometric concepts and a theory that aimed at analyzing the smoothness of 2D element-sizing fields quantitatively was established in this paper. The rule of the reasonable sizing transition for 2D area was achieved. Based on this rule, an improved algorithm from Borouchaki sizing-correcting method defined on unstructured background meshes was designed. This algorithm adjusted the size values attached on a small set of background mesh nodes to ensure the output of a well graded size field. Finally, mesh examples were given to validate the proposed theory and algorithm. Compared with other smoothing methods, the proposed algorithm in this paper can help get meshes with better quality.