多边形单元网格自动生成技术

近年来兴起的多边形有限元方法,在有限元计算中采用多边形单元划分网格,不仅可以更好地适应求解区域的几何形状,而且增加了网格划分的灵活性。为了更方便有效地生成多边形单元网格,在Delaunay三角形的基础上,通过将共圆Delaunay三角形合并为一个圆内接多边形,首先提出了Delaunay多边形的概念,进而提出了一种多边形网格自动生成的Delaunay多边形化算法。利用该Delaunay多边形化技术,对工程中常见的几何形状进行网格划分的具体算例表明,Delaunay多边形化方法可以生成性质优良的多边形单元网格。

Automatic Generation Technique for Polygonal Element Meshes

In polygonal finite element method, using polygons to generate meshes can describe complexity geometric shapes more accurately and can enhance the flexibility of meshes generation. In this paper the Delaunay polygon is constructed based on Delannay triangulation by incorporating the Delaunay triangulars of a shared Delaunay circumcircle. The algorithm of Delaunay polygonization for polygonal elements grids generation is presented. Each polygonal mesh generated by Delaunay polygoniztion is unique. Some geometric domains usually used in engineering are meshed using the proposed technique. Mesh examples demonstrate that the Delaunay polygoniztion technique can generate excellent polygonal networks.