曲面有限元网络的密度控制

Density Control of Mesh Generation on Free-Form Surfaces

有限元网格自动生成过程的最重要阶段是产生内部结点，网格的质量在最大程度上取决于结点的分布情况．本文提出的最佳结点分布场方法，以曲面的二叉树分割算法为基础，自动地适应曲面几何模型的要求，给出曲面上各处的结点分布密度．以此为基础可以产生过渡均匀、逼近精度满足要求的曲面有限元网格，且在同等要求下该方法使用的结点最少．

Instead of commonly used quad-tree subdivision of parametrics surfaces, a binary subdivision approach is taken to tessellate NURBS surfaces into quadrilateral facets with desired accuracy. Since the sizes of resultal facets reflect to a certain extent the global curvature of the freeform surface, they are taken to token to control the density of mesh generation. Good results with minimum number of grid nodes and smooth Variation of nodal density throughout the surface are obtained. Issues on the optimal nodal distribution are discussed.