基于独立覆盖的高阶流形方法

High order Manifold Method with Independent Covers

摘要:

提出了一种基于独立覆盖的高阶流形方法(ICMM）.该方法基于完全独立的物理覆盖，在物理覆盖上可以定义一至高阶的覆盖位移函数，在独立的物理覆盖间采用具有真实物理意义的弹簧（区别于DDA（Discontinuous Deformation Analysis）和DEM（Discrete Element Method）方法中为迭代需要而设置的虚拟弹簧），避免了一般流形方法需要复杂的覆盖生成等前处理算法的困难，消除了高阶流形方法特有的线性相关性带来的总体刚度矩阵奇异性的问题，可以方便地应用于连续体分析、从连续到非连续破坏以及完全非连续问题的统一分析.算例分析初步验证了本文方法的正确性和有效性.

关键词:流形方法; 高阶; 独立覆盖; 线性相关性

Abstract:

An independent cover based manifold method (ICMM) is presented. In the ICMM, various high order cover functions can be naturally employed at the independent covers, and the springs with real physical significance are defined between the adjacent independent covers, which are different from the virtual springs in DDA(Discontinuous Deformation Analysis) and DEM(Discrete Element Method). The requirement for the complex algorithm for cover generation in conventional NMM(Numerical Manifold Method), and the rank deficiency due to the linear dependence of the global degrees of freedom in high order NMM are well treated in the present ICMM. The continuous deformation analysis, the discontinuous deformation analysis, and the switch from continuous analysis to discontinuous analysis can be unified in a same framework in the ICMM. Several test examples indicate the correctness and the validity of the proposed method.

Key words:manifold method; high order; independent cover; linear dependence