基于断裂力学的公路钢桥疲劳寿命可靠度方法研究
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摘要
疲劳寿命预测是钢桥抗疲劳设计和疲劳性能评估的重要任务。本文针对公路钢桥的荷载和结构特点，综合应用断裂力学数值计算理论、裂纹扩展理论、疲劳累积损伤理论和结构可靠度理论，从概率断裂力学的角度系统研究公路钢桥疲劳寿命预测及可靠度计算方法，揭示结构疲劳寿命的变异特性以及考察设计寿命内的疲劳失效概率，为解决工程结构疲劳与断裂问题提供一种具有良好计算精度与效率的数值模拟方法。
本文研究的主要工作包括：
（1）对结构疲劳问题研究进行文献综述。介绍了疲劳问题研究发展简史和现有抗疲劳设计方法；阐述了基于S-N曲线和基于断裂力学的疲劳寿命预测方法；对常用的概率断裂力学方法进行了归纳和分类，并介绍了三种主要的疲劳可靠度分析模型。
（2）开展概率断裂力学方法研究。以基于Erdogan基本解的样条虚边界元法作为确定性断裂数值试验方法，分别结合结构可靠度计算的迭代响应面法和重要抽样蒙特卡罗法，提出了线弹性断裂问题可靠度分析的响应面-样条虚边界元法和重要抽样蒙特卡罗-样条虚边界元法。
（3）开展常幅荷载下疲劳寿命预测及可靠度计算方法研究。综合应用Paris裂纹扩展理论和断裂分析样条虚边界元法，提出了基于样条虚边界元法的常幅荷载下疲劳寿命预测方法；进一步考虑疲劳问题随机因素的影响，联合应用结构可靠度分析响应面法，提出了基于样条虚边界元法的常幅荷载下疲劳寿命可靠度计算方法。
（4）开展变幅荷载下疲劳寿命预测及可靠度计算方法研究。针对公路钢桥疲劳车辆荷载作用的特点，综合应用Miner线性累积损伤理论和常幅荷载下疲劳寿命预测方法，提出了基于样条虚边界元法的变幅荷载下疲劳寿命预测方法；进一步考虑疲劳问题随机因素的影响，联合应用结构随机分析的响应面－蒙特卡罗法，提出了基于样条虚边界元法的变幅荷载下疲劳寿命可靠度分析方法。
（5）开展公路钢桥疲劳寿命可靠度分析工程应用研究。以香港汀九大桥为工程应用背景，采用本文提出的基于样条虚边界元法的变幅荷载下疲劳寿命可靠度分析方法，研究了桥面钢纵梁和钢横梁的疲劳寿命统计规律，以及这些构件在设计寿命内的疲劳失效概率。
研究结果表明，所提出的概率断裂力学方法可以避免复杂的断裂驱动力偏导数列式过程，也可以避免直接蒙特卡罗法中庞大的确定性断裂分析样本试验量，具有良好的计算精度和较高的计算效率；所提出的常幅和变幅荷载下的结构疲劳寿命预测与可靠度计算方法，由于裂纹扩展过程中涉及的大量应力强度因子幅计算均由高效的基于Erdogan基本解的样条虚边界元法完成，因此总体上具有良好的计算精度和较高的计算效率。本文方法在汀九大桥疲劳寿命可靠度分析中的实际应用，充分验证了所提出方法的有效性。
Fatigue life prediction is of great importance to the fatigue design and evaluation ofhighway steel bridges. From the point of view of probabilistic fracture mechanics (PFM), thefatigue life prediction and fatigue reliability evaluation methods for highway steel bridges aresystematically studied in this dissertation by combined applications of fracture mechanicstheory, crack growth theory, cumulative fatigue damage theory and structural reliability theory.Both the variation characteristics of fatigue life and the fatigue failure probability within thedesign period of the structure are obtained by the present approach, indicating the accuracyand efficiency of the proposed method in solving the fatigue and fracture problems ofengineering structures.
The major work in this dissertation is described as follows:
(1) The research history of fatigue problems and the fatigue design methods arepresented first, followed by an introduction to the two major types of approaches for fatiguelife prediction based respectively on S-N curves and fracture mechanics. The tradictionalmethods of PFM are summarized, and three major models of fatigue reliability analysis arealso introduced.
(2) The response surface-spline fictitious boundary element method (SFBEM) and theimpotant sampling Monte Carlo-SFBEM are proposed to assess the fracture probability of alinear-elastic cracked structure. In the above approches, the SFBEM based on the Erdoganfundamental solutions is adopted to perform deterministic fracture analyses for numericaltests.
(3) A fatigue life prediction approach based on SFBEM is proposed for the case ofconstant-amplitude (CA) loading, in which the Paris law for crack growth is used inconjunction with the SFBEM for fracture mechanics. To account for the inherentuncertainties in fatigue problems, a response surface method based on the above approach isfurther applied to the evaluation of the fatigue failure probability of a structure under CAloading.
(4) In consideration of the loading and structural characteristics of highway steel bridges,a fatigue life prediction approach based on SFBEM is proposed for the case ofvariable-amplitude (VA) loading, in which the Miner rule for linear cumulative damage isused in combination with the fatigue life prediction approach for CA loading. To account forthe inherent uncertainties in fatigue problems, a response surface-Monte Carlo method basedon the above approach is further applied to the evaluation of the fatigue failure probability of a structure under VA loading.
(5) Using the proposed fatigue life reliability analysis approach based on SFBEM for VAloading, the statistical characteristics of the fatigue life and the fatigue failure probabilitywithin the design period are obtained for the main steel girder and the cross steel girder of theHong Kong Ting Kau Bridge.
It has been shown that high accuracy and efficiency can be obtained by the present PFMapproach, since the complex formulations for the derivatives of crack-driving forces arecompletely avoided and a much lesser number of numerical tests for deterministic fractureanalyses is required in the proposed method. Good performance can also be observed whenusing the present fatigue life prediction and reliability analysis approaches for CA and VAloading, since repetitive calculation of stress intensity factors during the crack growth isconducted efficiently by SFBEM based on the Erdogan fundamental solutions. Theeffectiveness of the proposed approach is well validated by the successful application of themethod to the fatigue reliability analysis of the Ting Kau Bridge.
本文研究的主要工作包括：
（1）对结构疲劳问题研究进行文献综述。介绍了疲劳问题研究发展简史和现有抗疲劳设计方法；阐述了基于S-N曲线和基于断裂力学的疲劳寿命预测方法；对常用的概率断裂力学方法进行了归纳和分类，并介绍了三种主要的疲劳可靠度分析模型。
（2）开展概率断裂力学方法研究。以基于Erdogan基本解的样条虚边界元法作为确定性断裂数值试验方法，分别结合结构可靠度计算的迭代响应面法和重要抽样蒙特卡罗法，提出了线弹性断裂问题可靠度分析的响应面-样条虚边界元法和重要抽样蒙特卡罗-样条虚边界元法。
（3）开展常幅荷载下疲劳寿命预测及可靠度计算方法研究。综合应用Paris裂纹扩展理论和断裂分析样条虚边界元法，提出了基于样条虚边界元法的常幅荷载下疲劳寿命预测方法；进一步考虑疲劳问题随机因素的影响，联合应用结构可靠度分析响应面法，提出了基于样条虚边界元法的常幅荷载下疲劳寿命可靠度计算方法。
（4）开展变幅荷载下疲劳寿命预测及可靠度计算方法研究。针对公路钢桥疲劳车辆荷载作用的特点，综合应用Miner线性累积损伤理论和常幅荷载下疲劳寿命预测方法，提出了基于样条虚边界元法的变幅荷载下疲劳寿命预测方法；进一步考虑疲劳问题随机因素的影响，联合应用结构随机分析的响应面－蒙特卡罗法，提出了基于样条虚边界元法的变幅荷载下疲劳寿命可靠度分析方法。
（5）开展公路钢桥疲劳寿命可靠度分析工程应用研究。以香港汀九大桥为工程应用背景，采用本文提出的基于样条虚边界元法的变幅荷载下疲劳寿命可靠度分析方法，研究了桥面钢纵梁和钢横梁的疲劳寿命统计规律，以及这些构件在设计寿命内的疲劳失效概率。
研究结果表明，所提出的概率断裂力学方法可以避免复杂的断裂驱动力偏导数列式过程，也可以避免直接蒙特卡罗法中庞大的确定性断裂分析样本试验量，具有良好的计算精度和较高的计算效率；所提出的常幅和变幅荷载下的结构疲劳寿命预测与可靠度计算方法，由于裂纹扩展过程中涉及的大量应力强度因子幅计算均由高效的基于Erdogan基本解的样条虚边界元法完成，因此总体上具有良好的计算精度和较高的计算效率。本文方法在汀九大桥疲劳寿命可靠度分析中的实际应用，充分验证了所提出方法的有效性。
Fatigue life prediction is of great importance to the fatigue design and evaluation ofhighway steel bridges. From the point of view of probabilistic fracture mechanics (PFM), thefatigue life prediction and fatigue reliability evaluation methods for highway steel bridges aresystematically studied in this dissertation by combined applications of fracture mechanicstheory, crack growth theory, cumulative fatigue damage theory and structural reliability theory.Both the variation characteristics of fatigue life and the fatigue failure probability within thedesign period of the structure are obtained by the present approach, indicating the accuracyand efficiency of the proposed method in solving the fatigue and fracture problems ofengineering structures.
The major work in this dissertation is described as follows:
(1) The research history of fatigue problems and the fatigue design methods arepresented first, followed by an introduction to the two major types of approaches for fatiguelife prediction based respectively on S-N curves and fracture mechanics. The tradictionalmethods of PFM are summarized, and three major models of fatigue reliability analysis arealso introduced.
(2) The response surface-spline fictitious boundary element method (SFBEM) and theimpotant sampling Monte Carlo-SFBEM are proposed to assess the fracture probability of alinear-elastic cracked structure. In the above approches, the SFBEM based on the Erdoganfundamental solutions is adopted to perform deterministic fracture analyses for numericaltests.
(3) A fatigue life prediction approach based on SFBEM is proposed for the case ofconstant-amplitude (CA) loading, in which the Paris law for crack growth is used inconjunction with the SFBEM for fracture mechanics. To account for the inherentuncertainties in fatigue problems, a response surface method based on the above approach isfurther applied to the evaluation of the fatigue failure probability of a structure under CAloading.
(4) In consideration of the loading and structural characteristics of highway steel bridges,a fatigue life prediction approach based on SFBEM is proposed for the case ofvariable-amplitude (VA) loading, in which the Miner rule for linear cumulative damage isused in combination with the fatigue life prediction approach for CA loading. To account forthe inherent uncertainties in fatigue problems, a response surface-Monte Carlo method basedon the above approach is further applied to the evaluation of the fatigue failure probability of a structure under VA loading.
(5) Using the proposed fatigue life reliability analysis approach based on SFBEM for VAloading, the statistical characteristics of the fatigue life and the fatigue failure probabilitywithin the design period are obtained for the main steel girder and the cross steel girder of theHong Kong Ting Kau Bridge.
It has been shown that high accuracy and efficiency can be obtained by the present PFMapproach, since the complex formulations for the derivatives of crack-driving forces arecompletely avoided and a much lesser number of numerical tests for deterministic fractureanalyses is required in the proposed method. Good performance can also be observed whenusing the present fatigue life prediction and reliability analysis approaches for CA and VAloading, since repetitive calculation of stress intensity factors during the crack growth isconducted efficiently by SFBEM based on the Erdogan fundamental solutions. Theeffectiveness of the proposed approach is well validated by the successful application of themethod to the fatigue reliability analysis of the Ting Kau Bridge.
引文
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