含裂纹平面问题Erdogan基本解的显式表达

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

基本解是边界元法、基本解法和无网格法等数值方法的重要理论基础.在断裂问题中,采用含裂纹的基本解可以避免将裂纹表面作为边界条件,从而大大简化问题的求解.在复变函数表示的含裂纹平面问题Erdogan基本解的基础上,对Erdogan基本解的使用条件进行了注解,修正了Erdogan基本解的一些错误,并推导出Erdogan基本解中位移函数解答的显式表达形式.编写了基于Erdogan基本解显式表达的样条虚边界元法(spline fictitious boundary element method,SFBEM)计算程序,计算了具有复合边界条件平面问题的位移、应力和应力强度因子.数值算例结果表明了该文提出的Erdogan基本解显式表达形式的正确性.

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.