三维数值流形方法的理论研究

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．

Theoretical Study of Three-Dimensional Numerical Manifold Method

The three-dimensional Numerical Manifold Method(NMM) is studied on the basis of two-dimensional 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-dimensional 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 efficiency is agreeable.