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
Citation: 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

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

doi: 10.21656/1000-0887.370253
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
  • 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.
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