流形切割及有限元网格覆盖下的三维流形单元生成  

MANIFOLD CUT AND GENERATION OF THREE-DIMENSIONAL MANIFOLD ELEMENT UNDER FE MESH COVER

作　　者：李海枫[1] 张国新[1] 石根华 彭校初[1] 

机构地区：[1]中国水利水电科学研究院,北京100038 [2]DDA公司,美国旧金山ca94002

出　　处：《岩石力学与工程学报》2010年第4期731-742,共12页Chinese Journal of Rock Mechanics and Engineering

基　　金："十一五"国家科技支撑计划项目(2008BAB29B05);国家自然科学基金资助项目(50909105);水利部行业公益科研专项(200801007)

摘　　要：三维流形单元生成和接触搜索算法问题是制约三维数值流形方法发展的瓶颈问题。系统详细地研究三维流形单元的生成方法,在前人工作基础上,采用三维有限元网格生成技术生成数学网格;通过块体数据结构、块体识别算法等方面的改进,将三维块体切割技术发展成流形切割技术,来解决流形块体生成问题;将石根华博士在二维NMM程序中采用的物理覆盖系统编码算法,扩展成三维流形编码算法,进而实现三维流形单元的生成。并在此基础上开发三维流形切割程序3D_MC.f90,可以实现四面体及六面体网格覆盖下任意形状三维流形单元的生成。通过几个例子可以看出,三维流形切割程序生成的流形块体形态、流形单元的节点与单元编码等均满足三维流形单元定义要求,从流形切割角度来看,说明此算法是正确的。The generations of three-dimensional manifold element and contact detection algorithm are the bottleneck problems that restrict the development of three-dimensional numerical manifold method.The generation of three-dimensional manifold element is studied.Based on previous works,the authors build mathematical cover system by three-dimensional finite element mesh generation technology,and develop three-dimensional block-cut technology into manifold cut technology for the formation of three-dimensional manifold element.Through the improvement of block data structure and block recognition algorithm,the authors extend coding algorithm of physical cover system by Dr.SHI Genhua from two-dimensional to three-dimensional;and then the generation of three-dimensional manifold element is achieved.And on this basis,the authors develop a three-dimensional manifold cutting program 3D_MC.f90;it can generate an arbitrary three-dimensional manifold element under tetrahedral and hexahedral mesh covers.As can be seen through several examples,manifold block shape and coding algorithm of node and element by three-dimensional manifolds procedure can meet the definition requirements of three-dimensional manifold element.It is proven that this algorithm is correct from the view of manifold cut.

关 键 词：数值分析 数值流形方法 三维流形单元 流形切割 

分 类 号：O241[理学—计算数学]