The Explicit Expression of Erdogan’s Fundamental Solution for Plane Problems With Cracks

XU Zhi; FAN Xue-ming

doi:10.21656/1000-0887.370253

Volume 38 Issue 9

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XU Zhi, FAN Xue-ming. The Explicit Expression of Erdogan’s Fundamental Solution for Plane Problems With Cracks[J]. Applied Mathematics and Mechanics, 2017, 38(9): 1009-1020. doi: 10.21656/1000-0887.370253

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The Explicit Expression of Erdogan’s Fundamental Solution for Plane Problems With Cracks

doi: 10.21656/1000-0887.370253

XU Zhi¹,
FAN Xue-ming^1,2

¹School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, P.R.China;²State Key Laboratory of Subtropical Building Science(South China University of Technology), Guangzhou 510640, P.R.China

Funds: The National Natural Science Foundation of China(General Program)(51378009)

Received Date: 2016-08-16
Rev Recd Date: 2017-05-11
Publish Date: 2017-09-15

Abstract

Abstract

The fundamental solution plays an essential role in many numerical methods such as the boundary element method (BEM), the method of fundamental solution and the boundarytype meshless methods. For fracture problems, application of fundamental solutions in domains with cracks can avoid deeming the crack surface as boundary condition and simplify the problems significantly. Based on the complex variable expression of Erdogan’s fundamental solution (EFS) for plane problems, the application conditions for EFS were noted, some faults in EFS were corrected and the explicit expression of the displacement in EFS was obtained. The computer program of the spline fictitious boundary element method (SFBEM) based on EFS was compiled to calculate the numerical solutions to mixed boundary condition problems. Numerical examples prove the correctness and accuracy of the derived explicit expression of EFS.
- fracture mechanics,
- Erdogan’s fundamental solution,
- explicit expression,
- spline fictitious boundary element method

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References(17)

References

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