| 含裂纹平面问题Erdogan基本解的显式表达 |
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| 引用本文： | 许秩,范学明. 含裂纹平面问题Erdogan基本解的显式表达[J]. 应用数学和力学, 2017, 38(9): 1009-1020. DOI: 10.21656/1000-0887.370253 |
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| 作者姓名： | 许秩 范学明 |
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| 作者单位： | 1华南理工大学 土木与交通学院, 广州 510640;2亚热带建筑科学国家重点实验室(华南理工大学), 广州 510640 |
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| 基金项目： | 国家自然科学基金(面上项目)(51378009)，高等学校博士学科点专项科研基金新教师类课题(20110172120038)，中央高校基本科研业务费(2015ZM116)，国家级大学生创新创业训练计划项目(201610561171)本文作者衷心感谢亚热带建筑科学国家重点实验室开放基金(2017ZB32)对本文的资助.The National Natural Science Foundation of China (General Program)(51378009) |
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| 摘 要： | 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.
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| 关 键 词： | 断裂力学 Erdogan基本解 显式表达 样条虚边界元法 |
| 收稿时间： | 2016-08-16 |
The Explicit Expression of Erdogan's Fundamental Solution for Plane Problems With Cracks |
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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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| Authors: | XU Zhi FAN Xue-ming |
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| Affiliation: | 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 |
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| 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 boundarytype 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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| Keywords: | fracture mechanics Erdogan's fundamental solution explicit expression spline fictitious boundary element method |
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