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裂纹面分布加载裂尖SIFs分析的广义参数Williams单元

徐华 曹政 邹云鹏 杨绿峰

徐华,曹政,邹云鹏,杨绿峰. 裂纹面分布加载裂尖SIFs分析的广义参数Williams单元 [J]. 应用数学和力学,2022,43(7):1-9 doi: 10.21656/1000-0887.420317
引用本文: 徐华,曹政,邹云鹏,杨绿峰. 裂纹面分布加载裂尖SIFs分析的广义参数Williams单元 [J]. 应用数学和力学,2022,43(7):1-9 doi: 10.21656/1000-0887.420317
Hua XU, Zheng CAO, Yunpeng ZOU, Lüfeng YANG. Generalized Degrees of Freedom for Loading on the Crack[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420317
Citation: Hua XU, Zheng CAO, Yunpeng ZOU, Lüfeng YANG. Generalized Degrees of Freedom for Loading on the Crack[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420317

裂纹面分布加载裂尖SIFs分析的广义参数Williams单元

doi: 10.21656/1000-0887.420317
基金项目: 国家自然科学基金(重点项目)(51738004);广西自然科学基金项目(2019GXNSFAA245012).
详细信息
    作者简介:

    徐华(1979—),男,副教授,博士,硕士生导师(通讯作者. E-mail: xuhua@gxu.edu.cn

  • 中图分类号: O346.1

Generalized Degrees of Freedom for Loading on the Crack

  • 摘要: 带裂缝服役是工程结构的常态,由于流体侵入到裂缝内部,裂纹面直接受荷,使得裂缝进一步扩展,甚者影响结构的安全性。广义参数Williams单元(简记W单元)在分析断裂问题中,利用Williams级数建立裂尖奇异区的位移场,通过求解广义刚度方程可直接获得应力强度因子(stress intensity factors,SIFs),具有高精高效性;但W单元需满足奇异区内裂纹面自由的边界条件,故在分析裂纹面加载的问题中受限。该文基于SIFs互等,在等效奇异区范围中,将裂纹面的荷载等效至奇异区外围边界的裂纹面上集中力,避免奇异区内裂纹面受荷,故采用W单元即可简便计算。算例分析表明:等效奇异区尺寸取裂纹长度的1/20,等效荷载系数P建议取2.0,W单元计算精度均满足1%的误差限,证明该文在奇异区裂纹面受荷等效处理方法上具有合理性、通用性,克服了W单元在分析裂纹面加载问题的局限性。
  • 图  1  裂尖局部面荷载等效

    注 为了解释图中的颜色,读者可以参考本文的电子网页版本,后同。

    Figure  1.  Crack tip local surface load equivalent

    图  2  裂尖奇异区网格划分及分布荷载等效

    Figure  2.  Discretization and distributed load equivalent in singular region of crack tip

    图  3  常规区网格离散

    Figure  3.  Discretization in regular region

    图  4  边界裂纹面受均布压力计算结果

    Figure  4.  Calculation results of uniformly distributed pressure on crack surface

    图  5  中心裂纹面受均布荷载

    Figure  5.  Uniformly distributed load on the central crack surface

    图  6  常规区网格离散

    Figure  6.  Discretization in regular region

    图  7  中心裂纹面受均布压力计算结果

    Figure  7.  Discretization in regular region

    图  8  裂纹面受线性压力计算结果

    Figure  8.  Calculation results of linear pressure on crack surface

    图  9  无量纲SIFs随尺寸变化的计算结果

    Figure  9.  Calculation results of dimensionless SIFs with varying size

    表  1  模型参数(λ=0)

    Table  1.   Model parameter (λ=0)

    a/W$\displaystyle \int_{a - c}^a {\sigma \left( X \right){\text{d} }X}$PQ
    0.050.51.960.982
    0.100.51.980.991
    0.200.51.990.997
    0.300.51.980.988
    0.400.51.930.963
    0.500.51.850.924
    0.600.51.740.869
    0.700.51.600.800
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-10-25
  • 录用日期:  2021-10-25
  • 修回日期:  2021-12-20
  • 网络出版日期:  2022-06-01

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