复分析在三维断裂和接触问题积分计算中的应用

李翔宇; 周德龙; 袁江宏

doi:10.21656/1000-0887.460228

复分析在三维断裂和接触问题积分计算中的应用

doi: 10.21656/1000-0887.460228

西南交通大学力学与航空航天学院，成都 611756

基金项目:

中国交通教育研究会交通教育科学研究重点课题 JT2024ZD051

四川省研究生教育教学改革重点项目 YJGXM24-B003

四川省高等教育人才培养质量和教学改革重点项目 JG2024-0265

详细信息

通讯作者:
李翔宇(1979—)，男，教授，博士，博士生导师(通信作者. E-mail: lixiangyu@swjtu.edu.cn)

中图分类号: O302
计量
- 文章访问数: 149
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- 被引次数: 0
出版历程
- 收稿日期: 2025-12-16
- 修回日期: 2025-12-20
- 刊出日期: 2026-04-01

Applications of Complex Analysis in Integral Calculation for 3D Fracture and Contact Problems

School of Mechanics and Aerospace, Southwest Jiaotong University, Chengdu 611756, P.R.China

摘要

摘要: 本文旨在利用复分析计算现代势理论方法基础理论中的两个典型积分.在高等数学框架下，这些定积分较难计算，它们通常作为结论直接应用于三维断裂和接触问题中.综合利用复分析中的留数定理、大圆弧引理和小圆弧引理，获得定积分的显式表达式.该工作进一步完善了三维断裂和接触问题的理论基础，彰显了复分析在计算定积分方面的独特优势.
- 复分析 /
- 现代势理论方法 /
- 定积分 /
- 断裂 /
- 接触
Abstract: Two typical definite integrals are calculated with the method of modern potential theory by virtue of complex analysis. In the context of calculus, the integrals in consideration are difficult to calculate and are usually directly applied as established results in fracture and contact problems. However, they may be expressed explicitly by means of the residue theorem, the infinite arc lemma and the infinitesimal arc lemma in the context of complex analysis. This work perfects the theoretical fundamentals of 3D fracture and contact problems, and further demonstrates the intrinsic advantages of complex analysis in calculation of definite integrals.
- complex analysis /
- method of modern potential theory /
- definite integral /
- fracture /
- contact

HTML全文

图 1 式(8)对应的复平面、围道积分路径和奇点示意图

Figure 1. The schematic diagram of the complex plane, the contour integral path and the singularities of the integrand in eq.(8)

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图 2 围道为单位圆的复变积分(式(24))示意图

Figure 2. The schematic diagram of the complex integral of the unit circular contour (eq.(24))

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A1 式(A3)对应的复平面、围道积分路径和奇点示意图

A1. The schematic diagram of the complex plane, the contour integral path and the singularity of the integrand in eq.(A3)

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B1 围道为单位圆的复变积分(式(B6))示意图

B1. The schematic diagram of the complex integral of the unit circular contour (eq.(B6))

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