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隧洞围岩应力复变函数分析法中的解析函数求解

祝江鸿

祝江鸿. 隧洞围岩应力复变函数分析法中的解析函数求解[J]. 应用数学和力学, 2013, 34(4): 345-354. doi: 10.3879/j.issn.1000-0887.2013.04.003
引用本文: 祝江鸿. 隧洞围岩应力复变函数分析法中的解析函数求解[J]. 应用数学和力学, 2013, 34(4): 345-354. doi: 10.3879/j.issn.1000-0887.2013.04.003
ZHU Jiang-hong. Analytic Functions in Stress Analysis of the Surrounding Rock for Caverns With the Complex Variable Theory[J]. Applied Mathematics and Mechanics, 2013, 34(4): 345-354. doi: 10.3879/j.issn.1000-0887.2013.04.003
Citation: ZHU Jiang-hong. Analytic Functions in Stress Analysis of the Surrounding Rock for Caverns With the Complex Variable Theory[J]. Applied Mathematics and Mechanics, 2013, 34(4): 345-354. doi: 10.3879/j.issn.1000-0887.2013.04.003

隧洞围岩应力复变函数分析法中的解析函数求解

doi: 10.3879/j.issn.1000-0887.2013.04.003
基金项目: 浙江省科技厅面上基金资助项目(2008C23G2130013)
详细信息
    作者简介:

    祝江鸿(1974—),男,浙江江山人,高级工程师(Tel:+86-571-85070856; E-mail;zhujianghong@zust.edu.cn).

  • 中图分类号: U451;O302

Analytic Functions in Stress Analysis of the Surrounding Rock for Caverns With the Complex Variable Theory

  • 摘要: 利用复变函数理论进行地下任意开挖断面隧洞围岩应力分析的前提,是根据围岩应力边界条件方程推导出两个解析函数.从Harnack定理出发,将隧洞围岩应力边界条件方程转化成积分方程;把Laurent级数有限项表示的映射函数引入积分方程中,将以任意开挖断面为边界条件的解析函数求解转化成以单位圆周线为边界条件的求解问题.对积分方程中各被积函数在讨论域内的解析性进行了分析,在此基础上利用留数理论求解了方程中各项积分值,并获得了用来表示任意开挖断面隧道围岩应力的两个解析函数通式.给出了圆形和椭圆形隧道的两个解析函数求解算例,所获得的结果与文献中的结果一致.利用留数理论推导出的两个解析函数通式,适用于任意开挖断面隧洞的围岩应力解析解的计算,且计算过程更为简单,计算结果更为精确.
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出版历程
  • 收稿日期:  2012-02-22
  • 修回日期:  2013-04-03
  • 刊出日期:  2013-04-15

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