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A high-order numerical manifold method with nine-node triangular meshes

机译：九节点三角网格的高阶数值流形方法

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摘要

The numerical manifold method (NMM) is a unified framework that is used to describe continuous and discontinuous problems. The NMM is derived based on the finite cover approximation theory and gains its name after the mathematical notion of manifold. It is also a method based on the partition of unity (PU) and it introduces two cover systems: the mathematical cover (MC) and the physical cover (PC). There are two approaches for constructing high-order approximations. The first approach involves a non-constant PU function and non-constant local approximations. This results in the linear dependence (LD) problem and leads to the singularity in a global matrix. The second approach involves a higher PU function and constant local approximations. The increase in the order of approximations should go along with the increase in star but the LD problem can be avoided completely in theory. In this paper, a new high-order NMM with nine-node triangular meshes is proposed. The upgrade from first-order NMM to high-order NMM is illustrated in detail. Moreover, the initial stress matrix is analyzed in detail. The effectiveness and accuracy of the proposed high-order NMM are validated using several typical examples. The proposed high-order NMM supplements the existing family of non-LD high- and low-order NMM under MC with triangular meshes.
机译：数值流形方法（NMM）是一个统一的框架，用于描述连续和不连续的问题。 NMM是基于有限覆盖近似理论派生的，并以流形的数学概念命名。这也是一种基于单位划分（PU）的方法，它引入了两个封面系统：数学封面（MC）和物理封面（PC）。有两种构造高阶近似的方法。第一种方法涉及非恒定的PU函数和非恒定的局部近似。这导致线性相关性（LD）问题，并导致全局矩阵中的奇异性。第二种方法涉及较高的PU函数和恒定的局部近似值。近似量级的增加应该与恒星的增加一起进行，但是从理论上讲，LD问题可以完全避免。本文提出了一种新的具有九节点三角网格的高阶NMM。详细说明了从一阶NMM升级到高阶NMM的过程。此外，详细分析了初始应力矩阵。使用几个典型示例验证了所提出的高阶NMM的有效性和准确性。拟议的高阶NMM用三角形网格对MC下现有的非LD高阶和低阶NMM系列进行了补充。

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  • 来源
    《Engineering analysis with boundary elements》 |2015年第12期|172-182|共11页
  • 作者

    Huo Fan; Siming He; Zhongming Jiang;

  • 作者单位

    Key Laboratory of Mountain Hazards and Surface Process, Chinese Academy of Sciences, Chengdu 610041, China,Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu 610041, China,Center for Excellence in Tibetan Plateau Earth Sciences, Chinese Academy of Sciences, Beijing 100101, China,University of Chinese Academy of Sciences, Beijing 100049, China;

    Key Laboratory of Mountain Hazards and Surface Process, Chinese Academy of Sciences, Chengdu 610041, China,Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu 610041, China,Center for Excellence in Tibetan Plateau Earth Sciences, Chinese Academy of Sciences, Beijing 100101, China;

    School of Hydraulic Engineering, Changsha University of Science & Technology, Changsha 410004, China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    High-order NMM; Non-linear dependence; Nine-node triangle; Initial stress matrix; Large deformation;

    机译：高阶NMM;非线性相关性;九节点三角形;初始应力矩阵;大变形;

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