Theoretical Study of Three-Dimensional Numerical Manifold Method
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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.Abstract: 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.
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Key words:
- numerical manifold method /
- three-dimensional analysis /
- finite cover
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