三维数值流形方法的理论研究  

Theoretical Study of Three-Dimensional Numerical Manifold Method

作　　者：骆少明[1] 张湘伟[1] 吕文阁[1] 姜东茹[1] 

机构地区：[1]广东工业大学机电工程学院,广州510090

出　　处：《应用数学和力学》2005年第9期1027-1032,共6页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(10272033)

摘　　要：在二维数值流形方法的基础上,对三维数值流形进行了理论研究.研究了三维覆盖位移函数,进行了三维数值流形的力学分析,给出了三维流形单元的刚度矩阵,详细推导了三维数值流形的Hammer积分及剖分规则,系统地研究三维数值流形的理论体系与数值实现方法.作为数值算例,给出了相应的悬臂梁的计算结果,计算结果表明算法的精度和计算效益较高.The three-dimensional Numerical Manifold Method（NMM） is studied on the basis of twodimensional numerical manifold method. The three-dimensional cover displacement function is studied. The mechanical analysis and Hammer integral method of three-dimensional numerical manifold method are put forward,the stiffness matrix of three-dimensional manifold element are derived and the dissection rules are given. The theoretical system and numerical realizing method of three-doimensional numerical manifold method are systematically studied. As an example, the cantilever with load on the end is calculated, the results show that the precision and effidency is agreeable.

关 键 词：数值流形方法 三维分析 有限覆盖 

分 类 号：O176[理学—数学]