Local mesh refinement algorithm based on analysis-suitable T-spline in numerical manifold method

LIU Deng-xue; ZHANG You-liang; DING Xiu-li; HUANG Shu-ling; PEI Qi-tao

doi:10.16285/j.rsm.2017.2478

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Local mesh refinement algorithm based on analysis-suitable T-spline in numerical manifold method

更新时间：2026-06-25

- Local mesh refinement algorithm based on analysis-suitable T-spline in numerical manifold method
- Vol. 40, Issue 4, Pages: 1584-1595(2019)
- 作者机构：
  
  1. 长江科学院水利部岩土力学与工程重点实验室
  2. 海南大学土木建筑工程学院
  3. 武汉市政工程设计研究院有限责任公司
- 作者简介：
- 基金信息：
- DOI：10.16285/j.rsm.2017.2478
  CLC： TU452
- Published：2019
- 稿件说明：
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[1]刘登学,张友良,丁秀丽,黄书岭,裴启涛.数值流形法中基于适合分析T样条的局部网格加密算法[J].岩土力学,2019,40(04):1584-1595.

LIU Deng-xue, ZHANG You-liang, DING Xiu-li, et al. Local mesh refinement algorithm based on analysis-suitable T-spline in numerical manifold method[J]. 2019, 40(4): 1584-1595.
[1]刘登学,张友良,丁秀丽,黄书岭,裴启涛.数值流形法中基于适合分析T样条的局部网格加密算法[J].岩土力学,2019,40(04):1584-1595. DOI： 10.16285/j.rsm.2017.2478.

LIU Deng-xue, ZHANG You-liang, DING Xiu-li, et al. Local mesh refinement algorithm based on analysis-suitable T-spline in numerical manifold method[J]. 2019, 40(4): 1584-1595. DOI： 10.16285/j.rsm.2017.2478.

摘要

数值流形方法中一般采用有限元网格或规则网格作为其数学覆盖系统

而规则的网格突出的优点是不需要适应求解域的边界和各种不连续面。采用规则的矩形网格作为数值流形方法中的数学网格

并借助适合分析的T样条实现了数值流形方法中的局部加密。适合分析的T样条定义在一个限制的T网格上

其基函数具有线性无关、单位分解、局部加密等许多重要性质

使得其非常适合用于工程设计及分析。当对一个适合分析的T网格加密后

所产生的新的网格往往不再是适合分析的T网格。基于此

提出了一种简单的数学网格加密算法

该算法能保证局部加密后的数学网格仍然是适合分析的。算例结果表明:在应力集中区和裂纹尖端等应力梯度较大区域

该算法均具有较强的适用性。

Abstract

Generally

a finite element mesh or a regular mesh is used as the mathematical covering system in the numerical manifold method（NMM）. The advantage of the regular mesh is that it has no requirement to conform to the boundary of the solution domain and various discontinuities. In this paper

the regular rectangular mesh was used as the mathematical mesh in NMM

and the analysis-suitable T-spline was introduced into NMM to realize the local refinement. As the analysis-suitable T-spline was defined over a mildly restricted T-mesh

it presents many important mathematical properties

such as linear independence

partition of unity and highly localized refinement capability. However

after an analysis-suitable T-mesh was locally refined

the generated new T-spline was not analysis-suitable. Therefore

a simple local refinement algorithm was developed in this paper to make sure that the refined mathematical mesh was still analysis-suitable. Moreover

the results from numerical examples show that the algorithm has strong applicability in large-stress gradient areas such as stress concentration area and crack tips.

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