基于自定义单元法的自由曲面网格划分研究

Research on free-form surface meshing based on self-defined element method

为实现对任意自由曲面的建筑网格划分,采用自定义单元法,以网格节点为对象,以"代"为整体进行节点推进。首先,根据节点的演化规律进行网格单元自定义。其次,在节点推进过程中,根据曲面特征进行单元选择生成下代节点,自适应曲面尺寸变化,将每一推进步单元"组装",建立网格拓扑的参数化表达;采用黎曼度量表征单元节点参数距离,考虑适应曲面曲率特征,确定节点参数坐标。最后,参数网格映射到自由曲面形成空间网格结构。结果表明,自定义单元法能够通过参数选择实现对网格规模和形式的量化控制,为自由曲面提供多样化网格划分方案,生成的网格杆件均匀、线条流畅、形式多样。

To realize the meshing of any free-form surface,the node was taken as the object and node in the same generation was taken as a whole to realize the advancing based on self-defined element method. Firstly,grid elements were defined based on the evolutional law of nodes. Besides,proper elements were selected automatically according to the surface feature to generate the nodes of next generation in the advancing process of nodes. In this way,it could be adaptive to change in surface size and elements in each step were assembled to establish parametric expression of grid topology. Riemannian metric was used to represent the parametric distance in consideration of curvature variation on surface and parametric coordinates of nodes were determined accordingly. Finally,the parametric grid was mapped back onto surface to form spatial grid. The results show that self-defined element method can control the scale and form of grid quantitatively through the selection of parameters and offer diverse meshing plans for free-form surface. Grid generated by the method has uniform rods,fluent lines and multiple forms.