参数曲面三角网格生成的改进波前法
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摘要
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.
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.
引文
[1]黄晓东,丁问司,杜群贵.基于波前法的参数曲面有限元网格生成算法[J].计算机辅助设计与图形学学报,2010,22(1):51-59.HUANG Xiaodong,DING Wensi,DU Qungui.Parametric surface mesh generation based on advancing front technique[J].Journal of Computer Aided Design&Computer Graphics,2010,22(1):51-59.
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[2]樊文刚,李建勇,黄泽华,等.多点切触加工在复杂凸曲面中的应用[J].西安交通大学学报,2012.46(3):53-58.FAN Wengang,LI Jianyong,HUANG Zehua,et al.Application of multi-point contact machining to convex sculptured surface[J].Journal of Xi’an Jiaotong University,2012,46(3):53-58.
[3]关振群,宋超,顾元宪,等.有限元网格生成方法研究的新进展[J].计算机辅助设计与图形学学报,2003,15(1):1-13.GUAN Zhenqun,SONG Chao,GU Yuanxian,et al.Recent advancing of research on finite element mesh generation methods[J].Journal of Computer Aided Design&Computer Graphics,2003,15(1):1-13.
[4]CUILLIERE J C.A direct method for the automatic discretization of 3Dparametric curves[J].Computer Aided Design,1997,29(9):639-647.
[5]CUILLIERE J C.An adaptive method for the automatic triangulation of 3D parametric surfaces[J].Computer Aided Design,1998,30(2):139-149.
[6]LEE C K,HOBBS R E.Automatic adaptive finite element mesh generation over arbitrary two-dimensional domain using advancing front technique[J].Computers&Structures,1999,71(1):9-34.
[7]LEE C K.Automatic metric advancing front triangulation over curved surfaces[J].Engineering Computations,2000,17(1):48-74.
[8]LO S H.Automatic mesh generation over intersecting surfaces[J].International Journal for Numerical Methods in Engineering,1995,38(6):943-954.
[9]ITO Y,NAKAHASHI K.Surface triangulation for polygonal models based on CAD data[J].International Journal for Numerical Methods in Fluids,2002,39(1):75-96.
[10]董亮,刘厚林,谈明高,等.离心泵四面体网格质量衡量准则及优化算法[J].西安交通大学学报,2011,45(11):100-105.DONG Liang,LIU Houlin,TAN Minggao,et al.Quality measurement criteria and optimization algorithm of tetrahedral mesh for centrifugal pumps[J].Journal of Xi’an Jiaotong University,2011,45(11):100-105.