改进的栅格法三维六面体网格局部加密算法
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摘要
有限元网格的相容性及质量是网格划分中必须考虑的问题。针对现有加密模板生成的新增单元数目较多,网格质量不佳,容易产生大范围加密外延,且在使用时加密情况考虑较为简单的问题,在栅格法生成六面体网格的基础上提出了一套基于8分法的加密模板,改进了面模板中新增小网格质量较差的问题,增加了拐角模板。为了使得所有加密情况均能直接加密,给出加密模板与网格单元中加密节点所有可能的排列情况之间的对应法则,并给出加密模板的集体应用方法。通过实验结果及对比分析,该套模板能够减少新增单元数量,改善新增单元的质量,减少加密外延现象。
The compatibility and the quality of finite element mesh are the problems have to be taken into account in grid partition. Existing refinement template generates more number of new cells,its grid quality is not good,is easy to produce a wide range of refinement extension,and considers simply in conditions of the refinement. In view of these problems,based on generating the hexahedral mesh with grid method,we present a set of eight-refinement-based refinement template. This set of template improves the problem of poorer qualities of newly added meshes in surface template,and increases corner template. In order to make all the refinement conditions be directly refined,we give the corresponding rule between all possible layout conditions of the refinement points in refinement template and grid cells,and provide the collective application method of template. By experimental results and their comparative analyses,the set of templates can decrease the number of new cells,improves the quality of new cells,and reduces refinement extension phenomena.
The compatibility and the quality of finite element mesh are the problems have to be taken into account in grid partition. Existing refinement template generates more number of new cells,its grid quality is not good,is easy to produce a wide range of refinement extension,and considers simply in conditions of the refinement. In view of these problems,based on generating the hexahedral mesh with grid method,we present a set of eight-refinement-based refinement template. This set of template improves the problem of poorer qualities of newly added meshes in surface template,and increases corner template. In order to make all the refinement conditions be directly refined,we give the corresponding rule between all possible layout conditions of the refinement points in refinement template and grid cells,and provide the collective application method of template. By experimental results and their comparative analyses,the set of templates can decrease the number of new cells,improves the quality of new cells,and reduces refinement extension phenomena.
引文
[1]Steven E.Benzley,Ernest Perry,et al.A comparison of all hexahedral and all tetrahedral finite element meshes for elastic and elastic-plastic analysis[C]//Proceedings of the 4th International Meshing Roundtable,1995:179-191.
[2]Schneiders R.Algorithms for quadrilateral and hexahedral mesh generation[S.l].
[3]张荣.四面体与六面体特征比较[J].企业技术开发,2012,31(23):101-10-2.
[4]孙璐.基于栅格法的三维六面体网格自适应生成算法及优化技术研究[D].山东大学,2012.
[5]彭威.三维实体六面体网格生成关键技术研究及软件开发[D].南京航空航天大学,2011.
[6]肖周芳,陈建军,曹建,等.多源多目标扫琼体全六面体网格自动生成算法[J].计算机辅助设计与图形学学报,2012,24(8):989-996.
[7]代星,崔汉国,刘建鑫,等.子域约束扫琼体的六面体网格生成方法[J].计算机辅助设计与图形学学报,2014,26(4):632-637.
[8]李想.面向地学研究的六面体网格生成方法研究[D].南京师范大学,2013.
[9]廖宏伟.基于迭代的六面体网格生成算法[D].浙江大学,2013.
[10]代星,崔汉国,罗欣.多特征几何体的全六面体网格自动生成方法[J].计算机力学学报,2013,30(2):224-229.
[11]王帅.基于实体变形的六面体网格生成方法研究[J].机械工程与自动化,2013(10):23-25.
[12]Schneiders R.A grid-based algorithm for the generation of hexahedral element meshes[J].Engineering with Computers,1996,12:168-177.
[13]Schneiders R,Aachen R.Automatic generation of hexahedral finite element meshes[J].Computer Aided Geomettic Design,1995,12(7):693-707.
[14]Schneiders R,Schindler R,Weiler F.Octree-based generation of hexahedral element meshes[S.l.].
[15]Su Y,Lee K H,Kumar A S.Automatic hexahedral mesh generation for multi-domain composite models using a hybrid projective grid-based method[J].Computer-Aided Design,2004,36(3):203-215.
[16]Zhang Y J,Bajaj C.Adaptive and quality quadrilateral/hexahedral meshing from volumetric data[J].Computer Methods in Applied Mechanics and Engineering,2006,195(9/12):942-960.
[17]Ito Y,Shih A M,Soni B K.Octree-based reasonable-quality hexahedral mesh generation using a new set of refinement templates[J].International Journal for Numerical Methods in Engineering,2008,77(13):1809-1833.
[18]张洪梅.三维六面体网格自适应生成算法研究及其应用[D].山东大学,2010.
[19]黄丽丽,赵国群,王忠雷.栅格法三维六面体网格局部加密算法[J].计算机辅助设计与图形学学报,2010,22(4):612-618.
[2]Schneiders R.Algorithms for quadrilateral and hexahedral mesh generation[S.l].
[3]张荣.四面体与六面体特征比较[J].企业技术开发,2012,31(23):101-10-2.
[4]孙璐.基于栅格法的三维六面体网格自适应生成算法及优化技术研究[D].山东大学,2012.
[5]彭威.三维实体六面体网格生成关键技术研究及软件开发[D].南京航空航天大学,2011.
[6]肖周芳,陈建军,曹建,等.多源多目标扫琼体全六面体网格自动生成算法[J].计算机辅助设计与图形学学报,2012,24(8):989-996.
[7]代星,崔汉国,刘建鑫,等.子域约束扫琼体的六面体网格生成方法[J].计算机辅助设计与图形学学报,2014,26(4):632-637.
[8]李想.面向地学研究的六面体网格生成方法研究[D].南京师范大学,2013.
[9]廖宏伟.基于迭代的六面体网格生成算法[D].浙江大学,2013.
[10]代星,崔汉国,罗欣.多特征几何体的全六面体网格自动生成方法[J].计算机力学学报,2013,30(2):224-229.
[11]王帅.基于实体变形的六面体网格生成方法研究[J].机械工程与自动化,2013(10):23-25.
[12]Schneiders R.A grid-based algorithm for the generation of hexahedral element meshes[J].Engineering with Computers,1996,12:168-177.
[13]Schneiders R,Aachen R.Automatic generation of hexahedral finite element meshes[J].Computer Aided Geomettic Design,1995,12(7):693-707.
[14]Schneiders R,Schindler R,Weiler F.Octree-based generation of hexahedral element meshes[S.l.].
[15]Su Y,Lee K H,Kumar A S.Automatic hexahedral mesh generation for multi-domain composite models using a hybrid projective grid-based method[J].Computer-Aided Design,2004,36(3):203-215.
[16]Zhang Y J,Bajaj C.Adaptive and quality quadrilateral/hexahedral meshing from volumetric data[J].Computer Methods in Applied Mechanics and Engineering,2006,195(9/12):942-960.
[17]Ito Y,Shih A M,Soni B K.Octree-based reasonable-quality hexahedral mesh generation using a new set of refinement templates[J].International Journal for Numerical Methods in Engineering,2008,77(13):1809-1833.
[18]张洪梅.三维六面体网格自适应生成算法研究及其应用[D].山东大学,2010.
[19]黄丽丽,赵国群,王忠雷.栅格法三维六面体网格局部加密算法[J].计算机辅助设计与图形学学报,2010,22(4):612-618.