【作者】 吴德飞；

【导师】 童根树；

【作者基本信息】 浙江大学 ， 结构工程， 2007， 博士

【摘要】 在许多钢结构损伤累积至破坏的工程问题中，各种载荷的随机性和结构材料缺陷是客观存在的。本文从数学方法论角度出发，采用多学科交叉的研究方法，在广泛综合固体力学、流体力学、数学、物理、材料学、传热学等领域的知识和进展的基础上，利用微分方程相似变换理论、函数分析理论、积分方程理论、广义函数理论、随机过程和随机振动和优化设计等，从理论分析、数学模化和数值模拟等多方面对常规与非常规边界条件下的钢结构互联损伤、损伤过程能量相互传递、损伤域扩展、能量遗失和损伤累积至失效问题的解析求解、解的性态及相应的比较行为进行了深入系统研究，目的在于进一步揭示钢结构损伤、破坏、可靠性和服役期限等问题内在的本质联系，并为适当解决一些实际钢结构工程问题给出理论基础和方法依据。大跨度、高层钢结构(钢桥)是一个国家经济的组成部分之一，它们的巨大投资及在国民经济中的重要作用，并且紧系人民生命和财产的安全，使得大跨度钢结构(桥梁)的安全性、耐久性和正常使用功能也越来越受到重视。本文的研究工作为钢结构损伤累积至断裂及损伤负向激励的长期效应的建立给出了部分实用、有效的解决方案，为钢结构安全设防系统的进一步发展应用给出一些理论成果。首先，为分析钢结构损伤累积至断裂的演变过程，从含初始缺陷钢结构的敏感性出发，给出了基于钢结构动态损伤响应分析的断裂数值模拟理论框架，指出该问题的实质是求解钢结构在工作应力低于屈服应力的情况下发生断裂对应于初始缺陷对疲劳寿命增加的百分数。设定初始缺陷为敏感激励参数，并给出疲劳寿命、强度退化以及二者间的数学计算模式。应用确定安全期限的缺陷敏感性理论，运用强度退化方法计算并比较不同初始缺陷情况下钢结构抗断裂韧性和疲劳寿命数值之间的偏差，表明了方法的可行性和有效性。这些结论可为钢结构安全设防提供适当指导和参考。其次，焊接钢桥结构持续损伤至破坏的过程可以从两方面加以分析：一方面要考虑此过程中能量的耗散；另一方面要考虑此过程中焊接部位损伤负向激励。基于格里菲斯能量准则思想，给出了结合动态能量相互传递与遗失理论(TETL)和损伤负向激励机制(MDPE)并考虑焊接钢桥结构剩余寿命的综合评估方法。将给出的综合评估标准拟合到钢桥结构中，耦合了损伤负向激励机制与焊接结构参数之间的一些关系。从而有机地促进了能量相互传递与遗失理论和损伤负向激励两个方向的整体结合。在说明方法的有效性时，给出悬臂梁和X形框墩二者的焊接连接的简单算例，并与基于S-N曲线的CD法和检测评估方法进行了分析比较，为钢桥结构安全寿命给出了一种较为朴实、简单的预测方法。此外，互联损伤网络存在能量消耗的过程，能量传递优化是利用损伤累积过程的时差，能适当调整损伤累积的开始和结束时间段，以达到减少峰期的耗散量，增加低谷期的耗散量，使各局部能量相互传递趋于均衡。在互联损伤传递网络的实际问题中，对于损伤量有两个方面的要求：一是每个途上的损伤量不能超过该途的最大通过能力；二是途点的传递量认为为零。损伤稳定时间域是一类统计特性不随时间推移而变的时间域。将这类时间域拟合到工程技术中，并介绍损伤稳定时间域的一些理论及其简单应用，包括损伤稳定时间域及其相关函数、各态历经性、谱密度、时间域谱分解、能量系统中的损伤稳定时间域等。同时，客观地评价持续损伤至结构的破坏行为是确保实现钢结构安全设防的因素之一。对于工程中钢结构的疲劳(累积)损伤给出了一些新思维：如钢结构能量的传递和释放过程、损伤稳定时间域推理、钢结构Runge-Kutta裂纹扩展、互联损伤传递网络、钢结构耐久性和综合评估并考虑钢结构服役期限的建模预测方法。基于钢结构损伤的各种关系和Irwin—Orowan的能量准则，并给出了模型参数的度量及计算方法。表述了互联多维损伤和耗能之间同步变化与协调发展的内在微薄规律。之后，给出了一些理论和工程中的例子，并做出计算分析。数值分析的结果对钢桥结构的安全设防会有适当的实践指导意义。最后，交通载荷、风载荷、地震、海浪载荷等作用下钢结构破坏机理的研究，将有助于钢结构建造物安全设防能力水平及服役期限的提高。同时，材料缺陷、损伤、破坏、断裂、残余应力、能量准则、优化规划和可靠性评估相互之间的交叉研究将会促进钢结构建筑物向经济型、安全型、适用型发展，为钢结构工程的应用展开广阔的前景。更多还原

【Abstract】 In many structure-engineering accidents, each kind of loading and the structural material flaw is the objective existence. This paper embarks from the mathematics methodology, and makes use of the multi-subjects overlapping research technique. On the base of widespread synthesis of the domain about solid mechanics, hydromechanics, mathematics, physics, material science, heat transfer science, using the theory of differential equation of similarity transformation, function analysis, integral equation, generalized function, stochastic process, stochastic vibration and optimized design. Based on the theory of the mathematics simulation and the value simulation, the paper concerned with the conventional and the non-conventional boundary condition about the steel structures of inter-damage, the damage process of energy inter-transmission, the expansion of damage domain, the energy dissipation and the destruction, which is the problems of the analytical solutions, the solution condition and the behavior of corresponding comparison under the system of research in every way. The goal is thoroughly revealing the problems of intrinsic essence about the steel structures damage, the destruction, the reliability, the service deadline and so on, and provided the method basis and the rationale for the solution of actual project.The great span, the high level steel structure (steel bridge) is one of ingredient in national economy, their huge investment, the vital role in national economy, which links security to the people life and the property. The great span of steel structures have some characteristics in the security, the durability and the normal using function, which become more and more to be valued.The researches is steel structures damage accumulated to fracture and the long-term effect of damage passive encouragement, which establish a series of practical, effective solution for the steel structures engineering, and provided the rich theory for further development and application of the system of security defense.First, the numerical simulation method that is based on the dynamic damage responses of initially flawed steel structures is proposed. It is pointed out that the critical step is to solve the fractures of steel structures with working stress lower than yield stress. In order to analyze the developing process from damaging to fracturing of steel structure, the sensitivity of the initially flawed structures used to predict the damage accumulation is presented. The initial crack is regarded as the sensitivity parameters, and the mathematical models are provided for the fatigue damage of steel structures. Numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method for the fracture toughness and fatigue life of steel structures with different initial flaws. The conclusions can offer guidelines for the security design of steel structures.Second, for the behavior of structure fracture, the dissipation of energy and the damage of passive encourage should be taken into consideration in the course of dynamic damage. The paper presents a comprehensive assessment method which combines the theory of energy transmission and loss (TETL) and the mechanism of the damage of passive encouragement (MDPE). The comprehensive assessment standard has been applied to the case of steel bridge, which defined the relation between the mechanism of the damage of passive encourage and welded structure parameters. These tremendously improve the combination of TETL and MDPE. The results are compared with the method of CD and target reliability, numerical simulation about steel bridge demonstrates that method the paper presented is reasonable and effective. There are certain application prospects in the security design of the steel bridge.Besides, the network of damage exists in the process of energy dissipation. The optimizes of energy delivery can be make use of the time difference in the process of damage accumulation mainly, adjusts the damage accumulation about the beginning of loss and end of time section, to reaching the amounts of consumption and cutting down peak-hour, the delivery increases the amounts of dissipation that lowers the point of expectation, making every part of energy tends to balance.In actual problem of interconnection damage, it can be seen, damage amounts have obvious two requests. One is that the damage amounts on every way cannot exceed the maximal of the capacity. Two is that the amounts of delivery in the process are zero. The time region of damage stable is a kind of time region that not following time to develop. This kind of time region is comparatively common in the engineering. Article introduce that the time region of damage stable about a few concepts and project applies, include time region and their relevance function, every state of time, spectral density, spectral decomposition, the time region of damage stable in the energy system and so on.Meanwhile, the behavior of structure fracture because of dynamic damage, which need appraise correctly, is the key to realizing the security defense of steel structures. The paper concerned with the damage of steel structures in engineering application and put forward some new thought, such as, energy transmission and its dissipation, the speculation of time region of damage stable, Runge-Kutta crack development, the network of damage transmission, durability and life assessment, and considered the model of comprehensive assessment for the service deadline of steel structures. Based on the damage of constitutive relations and the energy criterion of Irwin—Orowan, expounded the inherent laws of multi-dimensional damage and energy dissipation between the synchronized change and the coordination development, and set the method of the model of parameters. The case of comparative computation demonstrates that the precision and numerical efficiency that the paper given is parallel to the traditional assessment, which offers some value applications in the multi-security defenses of steel structures.At last, the researches of the mechanism of steel structural destroys under the function of the traffic loading, wind loading, earthquake loading, waves loading is an enhancement for the ability of security defense and service deadline of the building. At the same time, the mutually studies among the material flaw, the damage, the destruction, the fracture, the residual stress, the energy criterion, the optimized plan and the reliability appraises, which will promote structural building to the development of the economy, safety and suitability, launches the broaden prospect for the steel structures of project applications.更多还原