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自适应一致性高阶无单元伽辽金法

邵玉龙 段庆林 高欣 李锡夔 张洪武

邵玉龙, 段庆林, 高欣, 李锡夔, 张洪武. 自适应一致性高阶无单元伽辽金法[J]. 力学学报, 2017, 49(1): 105-116. doi: 10.6052/0459-1879-16-252
引用本文: 邵玉龙, 段庆林, 高欣, 李锡夔, 张洪武. 自适应一致性高阶无单元伽辽金法[J]. 力学学报, 2017, 49(1): 105-116. doi: 10.6052/0459-1879-16-252
Shao Yulong, Duan Qinglin, Gao Xin, Li Xikui, Zhang Hongwu. ADAPTIVE CONSISTENT HIGH ORDER ELEMENT-FREE GALERKIN METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(1): 105-116. doi: 10.6052/0459-1879-16-252
Citation: Shao Yulong, Duan Qinglin, Gao Xin, Li Xikui, Zhang Hongwu. ADAPTIVE CONSISTENT HIGH ORDER ELEMENT-FREE GALERKIN METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(1): 105-116. doi: 10.6052/0459-1879-16-252

自适应一致性高阶无单元伽辽金法

doi: 10.6052/0459-1879-16-252
基金项目: 

国家自然科学基金 11232003,11372066

中央高校基本科研业务费专项资金 DUT15LK07

辽宁省教育厅重点实验室基础研究 LZ2014002

水资源与水电工程科学国家重点实验室开放基金 2015SGG03

和地质灾害防治与地质环境保护国家重点实验室开放基金资助项目 SKLGP2016K007

详细信息
    通讯作者:

    段庆林,副教授,博士,主要研究方向为无网格法、材料破坏分析与模拟等.E-mail:qinglinduan@dlut.edu.cn

  • 中图分类号: O343.1

ADAPTIVE CONSISTENT HIGH ORDER ELEMENT-FREE GALERKIN METHOD

  • 摘要: 近来提出的一致性高阶无单元伽辽金法通过导数修正技术大幅度减少了所需积分点数目,并能够精确地通过线性和二次分片试验,显著改善标准无单元伽辽金法的计算效率、精度和收敛性.本文在此基础之上,充分利用无单元法易于在局部区域添加节点的优势,发展了一致性高阶无单元伽辽金法的h型自适应分析方法.根据应变能密度梯度该方法自适应地确定需节点加密的区域,基于背景积分网格的局部多层细化要求生成新的计算节点,同时考虑了节点分布由密到疏渐进过渡的情形.采用相邻两次计算的应变能的相对误差作为自适应过程的停止准则,将所发展自适应无网格法应用于由几何外形、边界外载和体力等因素造成的应力集中问题的计算分析.数值结果表明,所发展方法能够自适应地对高应力梯度区域进行节点加密,自动给出合理的计算节点分布.与已有的标准无网格法的自适应分析相比,所发展方法在计算效率、精度和应力场光滑性等方面均展现出显著优势.与采用节点均匀分布的一致性高阶无单元伽辽金法相比,它大幅度地减少了计算节点数目,有效提高了一致性高阶无单元伽辽金法在分析应力集中等存在局部高梯度问题时的计算效率和求解精度.

     

  • 图  1  QC3积分方法示意图

    Figure  1.  Schematic diagram of the QC3 integration method

    图  2  一层网格加密示意图

    Figure  2.  Schematic diagram of one-level mesh refinement

    图  3  两层网格加密示意图

    Figure  3.  Schematic diagram of two-level mesh refinement

    图  4  自适应QC3积分方案示意图

    Figure  4.  Schematic diagram of the adaptive QC3 integration scheme

    图  5  方板圆孔问题示意图

    Figure  5.  Schematic diagram of the plate with a hole problem

    图  6  方板圆孔问题的初始配置

    Figure  6.  Initial set-up for the plate with a hole problem

    图  7  方板圆孔问题的自适应结果

    Figure  7.  Adaptivity for the plate with a hole problem

    图  8  方板圆孔问题的位移误差-节点数曲线

    Figure  8.  Displacement error-number of nodes curve of the plate with a hole problem

    图  9  方板圆孔问题$\sigma _{yy} $应力场比较

    Figure  9.  Comparison of $\sigma _{yy} $ stress field of the plate with a hole problem

    图  10  受压半无限平面问题示意图

    Figure  10.  Schematic diagram of the pressure-loaded half plane problem

    图  11  受压半无限平面问题的自适应结果

    Figure  11.  Adaptivity for the pressure-loaded half plane problem

    图  12  受压半无限平面问题的位移误差-节点数曲线

    Figure  12.  Displacement error-number of nodes curve of the pressure-loaded half plane problem

    图  13  受压半无限平面问题$\sigma _{xx}$应力场比较

    Figure  13.  Comparison of the $\sigma _{xx} $ stress field of the pressure-loaded half plane problem

    图  14  变体力板示意图及初始节点分布

    Figure  14.  Schematic diagram of the plate with non-constant body force problem and its initial node distribution

    图  15  变体力板问题的自适应结果

    Figure  15.  Adaptivity for the plate with non-constant body force problem

    图  16  变体力板问题$\sigma _{xx} $应力场比较

    Figure  16.  Comparison of the $\sigma _{xx} $ stress field of the plate with non-constant body force problem

    表  1  方板圆孔问题的两种自适应方法比较

    Table  1.   Comparison of the two adaptive methods for the plate with a hole problem

    表  2  受压半无限平面问题的两种自适应方法比较

    Table  2.   Comparison of the two adaptive methods for the pressure-loaded half plane problem

    表  3  变体力板问题两种自适应方法比较

    Table  3.   Comparison of the two adaptive methods for the plate with non-constant body force problem

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出版历程
  • 收稿日期:  2016-09-07
  • 修回日期:  2016-11-04
  • 网络出版日期:  2016-11-07
  • 刊出日期:  2017-01-18

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