DEVELOPMENT OF 3D NUMERICAL MANIFOLD METHOD
DEVELOPMENT OF 3D NUMERICAL MANIFOLD METHOD
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DOI：
10.1142/s0219876210002088
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发表时间：
2010-03
影响因子：
1.7
通讯作者：
Lei He;G. Ma
中科院分区：
文献类型：
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作者：
Lei He;G. Ma
数值流形方法是有限元方法和非连续变形分析方法的结合。它提供了一个强大的数值解决方案，固体介质与密集的不连续性。本文在二维基本原理的基础上，将NMM扩展到三维域。介绍了三维数值流形方法的总体框架，包括六面体到四面体划分结构的覆盖几何模式（GP）和基于虚功原理的一般公式。通过对块体拓扑结构的描述，讨论了生成离散块体的块体切割过程，并说明了块体的操作规则。所提出的3D块生成算法允许任何离散结构或块系统。三个数值算例表明，所开发的三维数值流形程序是有效的，适用于三维连续体。进一步发展的目标是将接触模型，以模拟复杂的离散块体系统。
The numerical manifold method (NMM) is a combination of the finite element method (FEM) and discontinuous deformation analysis (DDA) method. It provides a robust numerical solution to a solid medium with dense discontinuities. This paper extends NMM to the three-dimensional domain based on the 2D fundamentals. The general framework of the 3D NMM is introduced, including the cover geometry patterns (GP) with division structure from hexahedron to tetrahedron, and general formulations based on the virtual work principle. The block cutting process to generate discrete blocks are discussed through the topological structure description of blocks, and the operation rule of blocks is explained. The proposed 3D block generation algorithm allows for any arbitrary discrete structure or block system. Three numerical examples are presented to demonstrate that the developed 3D numerical manifold code is effective and applicable to 3D continuum solids. Further developments aim to incorporate contact models to simulate complicated discrete block system.