Acta Mechanica Sinica

, Volume 35, Issue 1, pp 212–227

# Numerical solutions for cracks in an elastic half-plane

• N. R. F. Elfakhakhre
• N. M. A. Nik Long
• Z. K. Eshkuvatov
Research Paper

## Abstract

The behavior of the stress intensity factor at the tips of cracks subjected to uniaxial tension $$\sigma ^{\infty }_{x}=p$$ with traction-free boundary condition in half-plane elasticity is investigated. The problem is formulated into singular integral equations with the distribution dislocation function as unknown. In the formulation, we make used of a modified complex potential. Based on the appropriate quadrature formulas together with a suitable choice of collocation points, the singular integral equations are reduced to a system of linear equations for the unknown coefficients. Numerical examples show that the values of the stress intensity factor are influenced by the distance from the cracks to the boundary of the half-plane and the configuration of the cracks.

## Keywords

Elastic half-plane Multiple cracks Singular integral equation Sine-shaped crack

## Notes

### Acknowledgements

The author would like to thank University Putra Malaysia for Putra Grant (9442300).

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© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

## Authors and Affiliations

• N. R. F. Elfakhakhre
• 1
• N. M. A. Nik Long
• 1
• 2
Email author
• Z. K. Eshkuvatov
• 2
• 3
1. 1.Mathematics Department, Faculty of ScienceUniversiti Putra MalaysiaSerdangMalaysia
2. 2.Institute for Mathematical ResearchUniversiti Putra MalaysiaSerdangMalaysia
3. 3.Faculty of Science and TechnologyUniversiti Sains Islam MalaysiaNilaiMalaysia