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二维弹性力学问题的光滑无网格伽辽金法

马文涛

马文涛. 二维弹性力学问题的光滑无网格伽辽金法[J]. 力学学报, 2018, 50(5): 1115-1124. doi: 10.6052/0459-1879-18-135
引用本文: 马文涛. 二维弹性力学问题的光滑无网格伽辽金法[J]. 力学学报, 2018, 50(5): 1115-1124. doi: 10.6052/0459-1879-18-135
Ma Wentao. A SMOOTHED MESHFREE GALERKIN METHOD FOR 2D ELASTICITY PROBLEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1115-1124. doi: 10.6052/0459-1879-18-135
Citation: Ma Wentao. A SMOOTHED MESHFREE GALERKIN METHOD FOR 2D ELASTICITY PROBLEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1115-1124. doi: 10.6052/0459-1879-18-135

二维弹性力学问题的光滑无网格伽辽金法

doi: 10.6052/0459-1879-18-135
基金项目: 1)国家自然科学基金项目(51769026)和宁夏自然科学基金重点项目(NZ17002)资助.
详细信息
    作者简介:

    2)马文涛, 教授, 主要研究方向: 计算力学及其工程应用.E-mail:wt-ma2002@163.com

    通讯作者:

    马文涛

  • 中图分类号: O241,O343;

A SMOOTHED MESHFREE GALERKIN METHOD FOR 2D ELASTICITY PROBLEM

  • 摘要: 计算效率低的问题长期阻碍着无网格伽辽金法(element-free Galerkin method, EFGM) 的深入发展. 为了提高EFGM 的计算速度, 本文提出一种求解二维弹性力学问题的光滑无网格伽辽金法. 该方法在问题域内采用滑动最小二乘法(moving least square, MLS)近似、在域边界上采用线性插值建立位移场函数; 基于广义梯度光滑算子得到两层嵌套光滑三角形背景网格上的光滑应变, 根据广义光滑伽辽金弱形式建立系统离散方程. 两层嵌套光滑三角形网格是由三角形背景网格本身以及四个等面积三角形子网格组成. 为了提高方法的精度, 由Richardson外推法确定两层光滑网格上的最优光滑应变. 几个数值算例验证了该方法的精度和计算效率. 数值结果表明, 随着光滑积分网格数目的增加, 光滑无网格伽辽金法的计算精度逐步接近EFGM 的, 但计算效率要远远高于EFGM的. 另外, 光滑无网格伽辽金法的边界条件可以像有限元那样直接施加. 从计算精度和效率综合考虑, 光滑无网格伽辽金法比EFGM具有更好的数值表现, 具有十分广阔的发展空间.

     

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出版历程
  • 收稿日期:  2018-04-25
  • 刊出日期:  2018-09-18

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