引用本文: 汤轶丰, 顾敏明, 程洪福等. 差异沉降下的拱形门径向裂纹应力强度因子解析解研究. 力学与实践, 2023, 45(5): 1117-1127.
Tang Yifeng, Gu Minming, Cheng Hongfu, et al. Analytical solution of stress intensity factor of arch door radial crack under differential settlement. Mechanics in Engineering, 2023, 45(5): 1117-1127.
 Citation: Tang Yifeng, Gu Minming, Cheng Hongfu, et al. Analytical solution of stress intensity factor of arch door radial crack under differential settlement. Mechanics in Engineering, 2023, 45(5): 1117-1127.

## ANALYTICAL SOLUTION OF STRESS INTENSITY FACTOR OF ARCH DOOR RADIAL CRACK UNDER DIFFERENTIAL SETTLEMENT

• 摘要: 拱形门结构的裂纹应力强度因子是表征径向裂纹尖端应力场强弱的重要参数，但是差异沉降下拱形门结构的径向裂纹应力强度因子面临着难以模式化计算的问题。为此，本文推导了差异沉降作用下的拱形门径向裂纹应力强度因子解析解公式。首先，根据拱形门的对称性，将其分解为正、反对称状态的叠加形式，利用力法对拱形门内力分布进行分析；然后，依据内力情况采用截面法对拱形门径向裂纹截面上的应力分布沿厚度方向进行表达；最后，利用权函数法将权重函数和裂纹表面应力分布的乘积进行积分，得到差异沉降下的拱形门径向裂纹应力强度因子解析解。解析解推导结果与ANSYS数值仿真结果一致，即Ⅰ型、Ⅱ型应力强度因子对差异沉降值与径向裂纹倾角均有显著的线性响应趋势。实验结果表明，本文解析解可以准确有效地将差异沉降下的拱形门径向裂纹应力强度因子进行模式化计算，为裂纹的扩展延伸提供参考。

Abstract: The stress intensity factor (SIF) of an arch door structure is a crucial parameter for characterizing the strength of stress field at the tip of a radial crack. However, calculating the SIF of an arch door structure under differential settlement remains challenging. In this paper, we derive an analytical formula for the SIF of an arch door's radial crack subjected to differential settlement. First, considering the arch door's symmetry, we decompose it into a superimposed form of positive and antisymmetric states, using the force method to analyze the internal force distribution within the structure. Next, we express the stress distribution along the thickness direction on the arch door's crack section using the section method, based on the internal force situation. Finally, we integrate the product of the weight function and the stress distribution on the crack surface using the weight function method, obtaining an analytical solution for the SIF of the arch door under differential settlement. Our analytical results align with the findings of ANSYS numerical simulations, demonstrating that both mode-I and mode-II SIF exhibit a significant linear response trend with respect to the differential settlement value and radial crack angle. These experimental results suggest that the analytical solution presented in this paper can accurately and effectively model the SIF of arch door cracks under differential settlement, providing valuable insights for crack propagation analysis.

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