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

LI Xiangyu; ZHOU Delong; YUAN Jianghong

doi:10.21656/1000-0887.460228

Volume 47 Issue 4

Apr. 2026

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LI Xiangyu, ZHOU Delong, YUAN Jianghong. Applications of Complex Analysis in Integral Calculation for 3D Fracture and Contact Problems[J]. Applied Mathematics and Mechanics, 2026, 47(4): 496-504. doi: 10.21656/1000-0887.460228

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

doi: 10.21656/1000-0887.460228

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

Received Date: 2025-12-16
Rev Recd Date: 2025-12-20

Available Online: 2026-04-30

Abstract

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

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References

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