参数曲面三角网格生成的改进波前法

A New Algorithm for Triangular Mesh Generation by Advancing Front Technique

为了消除基于波前法的有限元三角网格算法在参数曲面网格剖分过程中单元形状映射畸变的问题,结合直接法和映射法各自的优点,提出了一种新的三角网格生成算法,即:对当前节点进行剖分,并在三维空间直接产生新节点且进行节点的合法性判断,再将物理网格映射到参数空间形成参数域网格;对相邻波前段形成的角度进行剖分,依据角度大小生成个数不等的单元,通过优先剖分锐角节点使波前段始终构成钝角多边形。经剖分算例表明:所提算法减少了节点合法性判断内容和判断次数,避免了重复剖分,取消了剖分结束算法,提高了网格剖分效率,生成了高质量的三角网格;仅需对网格排列情况的直观分析,便可定性判断三维曲面的空间曲率变化。该算法对叶片加工中振动分析、精密加工研究等具有指导意义。

A new algorithm for triangular mesh generation by advancing front technique is proposed to remove the mapping distortion when the parametric mesh is generated by mapping method. For the current node, this algorithm combines direct method with mapping method to directly locate a new node and to determine the validity in the real space, the mesh in the parametric spaces is generated by mapping method. The angle formed by the adjacent fronts is divided into several units according to the angle scope. The acute angles of nodes is firstly divided, to always retain the polygon fronts with obtuse angle. The proposed algorithm enables to reduce the content and number of validities, avoid the repeated subdivision, cancels the part of the convergence checking, and generate a highly quality mesh. The mesh arrangement can also be used to determine spatial curvature distribution of 3D surfaces for analyzing vibration and precision cutting of the blade.