复杂边界几何体的结构网格生成方法

A Structured Mesh Generation Method for Complex Boundary Geometry

高质量的结构网格能够有效地提高有限元分析的精度.针对受限于结构网格节点分布的特殊要求,使当前的结构网格生成方法无法直接应用于边界复杂的几何体这一问题,提出结构网格生成方法.对于边界复杂的多边形区域,依据边界顶点分类,在计算空间内将边界简化为规则形状,在简化的多边形区域内进行分割并填充结构网格,再将其映射回原区域;对于边界特殊的三角形、圆形区域,依据边界节点分布计算分割线,将原区域分割为简单的四边形区域组合,再对各四边形区域分别进行结构网格填充;对于不同区域网格的连接,将区域边界相连并设置棱边方向,通过转化相应的棱边方向矩阵得出棱边方向闭合的多边形边界,在多边形边界内填充结构网格形成不同区域网格间的有效过渡.实例验证结果表明,该方法稳定、高效,能够解决复杂边界几何体的结构网格划分问题.

High-quality structured mesh is essential in finite element analysis. Limited by special requirement of node distribution in the structured mesh, current structured mesh generation methods are hard to be directly applied to geometries with complex boundary. To solve this problem, a new structured mesh generation method is proposed. For polygon area with complex boundary, the shape of boundary is simplified to be regular in computational space based on vertex classification, the simplified polygon area is splitted and filled with structured mesh, and then the structured mesh is mapped back to original area; for triangular and circular areas with special boundary, splitting lines are calculated based on the boundary node distribution to split original area into simple quadrilateral areas, each quadrilateral area is filled with structured mesh; for transition between neighbored meshing areas, different boundaries are linked and direction of boundary edges are set, the polygons with close direction boundary edges are identified through the transformation of the corresponding matrix of boundary edges, each identified polygon is filled with structured mesh to form an effective transition between different meshing areas. Examples verify the efficiency of the proposed method.