| 基于比例边界有限元法和灰狼优化算法的裂纹尖端位置识别 |
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| 引用本文： | 余波,孙文涧.基于比例边界有限元法和灰狼优化算法的裂纹尖端位置识别[J].应用数学和力学,2021,42(11):1177-1189. |
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| 作者姓名： | 余波 孙文涧 |
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| 作者单位： | 合肥工业大学 土木与水利工程学院, 合肥 230009 |
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| 基金项目： | 国家自然科学基金(面上项目)（11872166） |
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| 摘 要： | 基于比例边界有限元法(SBFEM)和灰狼优化(GWO)算法，提出了一种裂纹尖端识别方法。首先，借助SBFEM解决断裂力学问题特有的优势，快速准确地计算出反演所需的测点位移，并验证了正问题求解的正确性。其次，建立与裂纹尖端位置有关的目标函数，将求解裂纹尖端位置转换为求解目标函数最小值的优化问题。最后，采用GWO算法对目标函数进行了优化，进而搜索裂纹尖端的最佳位置。数值算例结果表明:利用SBFEM的高精度、半解析的优点，在反演过程中采用其求解正问题是非常有效的；GWO算法具有良好的全局收敛性，且相比经典的粒子群算法，能够更快速准确地搜索出裂纹尖端的位置；GWO算法具有较好的抗噪性。
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| 关 键 词： | 裂纹尖端识别 比例边界有限元法 灰狼优化算法 粒子群优化算法 |
| 收稿时间： | 2020-12-14 |
Identification of Crack Tip Positions Based on the Scaled Boundary Finite Element Method and the Grey Wolf Optimization Algorithm |
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| Affiliation: | College of Civil Engineering, Hefei University of Technology, Hefei 230009, P.R.China |
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| Abstract: | Based on the scaled boundary finite element method (SBFEM) and the grey wolf optimization algorithm (GWO), an identification method for crack tips was proposed. Firstly, the special advantages of the SBFEM were used to solve the fracture mechanics problem, the displacements of measurement points required in the inversion process were quickly and accurately calculated, and the correctness of the solution to the forward problem was verified in advance. Then, the objective function related to the crack tip position was established, and the identification of the crack tip position was converted to the optimization problem of solving the minimum value of the objective function. Finally, the GWO was used to optimize the objective function, that is, to search for the optimal position of the crack tip. The numerical example results show that, it is very effective to solve forward problems in the inversion process with the high precision and semi-analytical advantages of the SBFEM. The grey wolf optimization algorithm has good global convergence property, and can search for the crack tip position more quickly and accurately compared with the classical particle swarm optimization. The grey wolf optimization algorithm has good noise resistance. |
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