复杂三维组合曲面的有限元网格生成方法

Automatic finite element mesh generation over 3D combined surfaces

提出一种基于映射法的复杂三维组合曲面的有限元网格全自动生成方法。通过引入虚边界解决了闭合曲面在参数域中边界不完整的问题 ;通过调节虚边界提高了复杂组合曲面网格生成的质量。改进二维多边形区域的裁减算法 ,解决了闭合曲面在参数空间中的边界环形成问题。对曲面片公共边界进行统一离散化处理 ,以满足有限元网格的相容性要求。以边界表示 (B-Rep)数据结构为基础 ,实现了组合曲面全自动网格剖分的总成算法。改进了曲面网格剖分布点算法 ,并结合局部连接、诊断交换等技术 。

Based on the traditional mapping approach, a method for finite element mesh generation over 3D combined surfaces is presented. The main features of the method are: (1) The virtual boundaries are employed to assist the mesh generation on closed surfaces, and adjustment to the virtual boundaries can improve the quality of the mesh generation. (2) The clipping algorithm of 2D arbitrary domain is improved to form the parametric boundary loops of the closed surfaces. (3) The common boundaries of adjoining surfaces are discretized conformably to need the consistent requirement of the finite element meshes. (4) The boundary-representation structure is adopted to fulfill the mesh generation over combined surfaces. (5) The total quality of surface meshes is improved by the algorithm of point creation on 3D scan lines and the procedure of diagonal swapping. This method has been successfully applied to JIFEX system, a general-purpose software for the analysis and design optimization of structures.