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变厚度各向异性功能梯度转动圆盘的弹性分析

彭旭龙 黄海平 李进宝 陈央 陈子光

彭旭龙,黄海平,李进宝,陈央,陈子光. 变厚度各向异性功能梯度转动圆盘的弹性分析 [J]. 应用数学和力学,2022,43(10):1146-1154 doi: 10.21656/1000-0887.430032
引用本文: 彭旭龙,黄海平,李进宝,陈央,陈子光. 变厚度各向异性功能梯度转动圆盘的弹性分析 [J]. 应用数学和力学,2022,43(10):1146-1154 doi: 10.21656/1000-0887.430032
PENG Xulong, HUANG Haiping, LI Jinbao, CHEN Yang, CHEN Ziguang. Elastic Analysis of Anisotropic Functionally Graded Rotating Disks With Non-Uniform Thicknesses[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1146-1154. doi: 10.21656/1000-0887.430032
Citation: PENG Xulong, HUANG Haiping, LI Jinbao, CHEN Yang, CHEN Ziguang. Elastic Analysis of Anisotropic Functionally Graded Rotating Disks With Non-Uniform Thicknesses[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1146-1154. doi: 10.21656/1000-0887.430032

变厚度各向异性功能梯度转动圆盘的弹性分析

doi: 10.21656/1000-0887.430032
基金项目: 湖南省教育厅自然科学研究基金(21B0315;18C0243);湖南省大学生创新创业训练计划项目(S2021105360050)
详细信息
    作者简介:

    彭旭龙(1983—),女,副教授,博士,硕士生导师(通讯作者. E-mail:peng_xulong@csust.edu.cn

  • 中图分类号: O343.6; O343.8

Elastic Analysis of Anisotropic Functionally Graded Rotating Disks With Non-Uniform Thicknesses

  • 摘要:

    研究了任意梯度变化的变厚度各向异性转动圆盘的弹性问题。假设圆盘绕刚性轴匀速转动,其材料性能和厚度沿径向任意梯度变化。考虑圆盘在中心转轴处受位移约束,外侧自由,根据各向异性转动圆盘的平衡微分方程,得到关于径向应力的Fredholm积分方程,继而通过对Fredholm积分方程进行数值求解,得到结构的位移场和应力场。对具体梯度变化情况仅需代入相应梯度变化进行求解即可。数值算例部分,通过假设厚度、弹性模量等参数为特殊的幂函数形式,将由Fredholm积分方程求出的数值解与对应的精确解进行对比,以及针对常见的Voigt模型,将由该方法算得的数值解和ANSYS有限元计算结果进行对比,验证了该方法的准确性和精度。其次,针对Voigt模型,重点分析了厚度变化、材料性能梯度参数、各向异性度等对应力场和位移场的影响。提出了针对材料性能和厚度沿径向呈任意梯度变化的圆盘结构弹性分析方法,将为优化功能梯度圆盘的结构和材料参数、有效调整构件应力分布、提高结构安全性,提供强有力的工具;算例分析结果对功能梯度圆盘在复杂条件下的结构安全设计有重要的理论指导意义。

  • 图  1  模型剖切示意图(左)与俯视示意图(右)

    Figure  1.  Schematic diagram of the model: profile (left); top view (right)

    图  2  幂函数时数值解和解析解的比较($\alpha = \delta = {\beta _1} = {\beta _2}$

    Figure  2.  A comparison of the exact and numerical results of the power law function ($\alpha = \delta = {\beta _1} = {\beta _2}$

    图  3  Voigt函数时本文解和有限元解的比较($\alpha = \delta = {\beta _1} = {\beta _2}$

    Figure  3.  A comparison of the present method results and the FEM solutions for the Voigt model ($\alpha = \delta = {\beta _1} = {\beta _2}$

    图  4  厚度梯度参数δ对应力场和位移场的影响

    Figure  4.  The effects of δ on the stress and radial displacement components

    图  5  弹性模量梯度参数β1对应力场和位移场的影响

    Figure  5.  The effects of β1 on the stress and radial displacement components

    图  6  密度梯度参数β2对应力场和位移场的影响

    Figure  6.  The effects of β2 on the stress and radial displacement components

    图  7  各向异性度参数λ对应力场和位移场的影响

    Figure  7.  The effects of λ on the stress and radial displacement components

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出版历程
  • 收稿日期:  2022-02-11
  • 录用日期:  2022-04-05
  • 修回日期:  2022-03-17
  • 网络出版日期:  2022-09-19
  • 刊出日期:  2022-10-31

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