综合考虑静强度、疲劳和稳定的结构系统可靠性分析
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摘要
对于一个承受多种载荷作用的结构系统来说,它的失效存在着多种模式,主要有静强度失效、疲劳失效以及受压细长杆件或细长结构的失稳失效等。每一种失效模式都对系统的安全存在着巨大的影响。然而,在目前的结构可靠性分析中,失稳失效可靠性的研究较少,这样可能带来严重的后果,特别是结构系统的整体失稳隐蔽性很强,一将发生,就会造成巨大破坏。而且,目前结构系统在静载荷和疲劳载荷作用下失效的可靠性大多是分别予以考虑的,但是对于结构系统来说,非常有可能出现几种失效模式的混合情况。例如:因较小的疲劳载荷引起一定的疲劳损伤并造成极限承载能力的下降,又因极限载荷而引起结构的完全破坏。由于疲劳载荷的作用,在结构可靠性分析中,还要考虑元件不同失效形式对后面元件累积损伤的影响。再加之失效模式之间存在相关性,这就使得结构的失效机理比较复杂,给结构系统可靠性分析带来了较大难度。针对上述问题,本文开展以下研究,主要如下:
1)为了精确的计算非线性安全余量的可靠性指标,文中提出了一种在验算点和中心点法基础上的新方法—联合法,简便了计算且提高了计算精度。
2)以裂纹扩展为基础,具体分析了在静载和疲劳载荷作用下的结构系统失效机理,给出了在这两种载荷作用下结构系统综合考虑静强度和疲劳的可靠性分析方法。
3)给出了细长运动杆件及结构系统稳定可靠性的分析方法。首先针对细长运动杆件的稳定性问题,建立了力学模型。基于小挠度下杆所承受载荷的微分方程,确定了细长运动杆的失稳临界载荷。在此基础上进行了结构的可靠性分析,计算了结构的可靠性指标和失效概率,并分析了初偏心影响下杆件的临界载荷及可靠性指标。其次,推导了结构系统的稳定性特征方程,计算了结构系统整体失稳的临界载荷,从而建立了结构系统整体失稳的安全余量,分析了结构系统稳定可靠性。
4)给出了同时考虑静载、疲劳和失稳失效模式下,结构系统可靠性分析方法。对于一个承受静载和疲劳载荷作用的结构系统,由于疲劳损伤的影响,元件的抗力、弹性模量等力学特性将会随时间的增长而衰减,结构整体稳定性也会随着元件的失效、弹性模量的衰减等因素而下降。因此,文中结合累积损伤理论,给出元件不同失效形式的失效时刻,并考虑到失效路径中残余结构整体失稳,采用系统可靠性理论,完成了结构系统的可靠性分析。
Several kinds of failure modes take place when various loads act on the structural system, mainly including static strength failure, fatigue failure, and the stability failure of the vimineous bar or the vimineous structure under pressure etc., and each failure mode has a large influence on the system safety. However, within the present analysis of structural reliability, the reliability research of stability failure is less. But that can bring the serious aftermath, especially, the concealment of the whole structure system's stability failure is strong. Once it happens, tremendous destruction will be caused. Moreover, the present reliability analysis of the structural system under static load or fatigue load is mostly considered respectively. But the mixed case of several failure modes is very likely to occur for the structure system. For example, certain fatigue damage, caused by the lesser fatigue load, makes the ultimate carrying capacity of the structure decreasing. And the structure may even destroy completely because of the ultimate load. When analyzing the structural reliability, the influence of different failure modes on the cumulative damage of the hinder elements should be considered due to the effect of fatigue load. And besides the relativity among those failure modes, it makes the failure mechanism of the structure more complicated and the reliability analysis of the structure system more difficult. For the above problems, the research has been done in this thesis, such as follows:
1) In order to calculate the reliability index of the non-linear safety margin accurately, a new method-the Joint Method is introduced based on the Design Point Method and the Mean Point Method, which not only simplifies calculation but also improves accuracy of the calculation.
2) Based on the crack propagation, the failure mechanism of structure system under static load and fatigue load is analyzed concretely. And considering the static strength and the fatigue synthetically, the method of reliability analysis under the two kinds of loads is given.
3) The methods of reliability analysis for the moving vimineous bar and structure system stability are given. First, aiming at the problem of stability for the elastic vimineous bar, the mechanical models are established. Based on the differential equation of the bar with small defection, the buckling critical load of vimineous bar is confirmed. And then the reliability analysis of the structure is carried out. The reliability index and failure probability are calculated. The critical load and the reliability index of the bar are analyzed under the influence of initial eccentricity. Secondly, the stability characteristic equation of the structure system is deduced. The critical load of the whole structure system's stability failure is calculated. Thereby, the safety margin of that is established, and the stability reliability of the structure system is analyzed.
4) Considering the failure modes of static load, fatigue and stability failure simultaneously, the method of reliability analysis of the structure system is given. For a structure system under static load and fatigue load, because of the influence of fatigue damage, the mechanical characteristics of resistance and elastic module of the element will decrease along with the increase of time. The whole structural reliability will decrease along with the failure of element and the attenuation of module. Thus, combine with the cumulative damage theory, the time of failure for different failure modes is given. Furthermore, considering the remnant structure's stability failure in the failure route, the reliability analysis of the structure system is done by the theory of system reliability.
1)为了精确的计算非线性安全余量的可靠性指标,文中提出了一种在验算点和中心点法基础上的新方法—联合法,简便了计算且提高了计算精度。
2)以裂纹扩展为基础,具体分析了在静载和疲劳载荷作用下的结构系统失效机理,给出了在这两种载荷作用下结构系统综合考虑静强度和疲劳的可靠性分析方法。
3)给出了细长运动杆件及结构系统稳定可靠性的分析方法。首先针对细长运动杆件的稳定性问题,建立了力学模型。基于小挠度下杆所承受载荷的微分方程,确定了细长运动杆的失稳临界载荷。在此基础上进行了结构的可靠性分析,计算了结构的可靠性指标和失效概率,并分析了初偏心影响下杆件的临界载荷及可靠性指标。其次,推导了结构系统的稳定性特征方程,计算了结构系统整体失稳的临界载荷,从而建立了结构系统整体失稳的安全余量,分析了结构系统稳定可靠性。
4)给出了同时考虑静载、疲劳和失稳失效模式下,结构系统可靠性分析方法。对于一个承受静载和疲劳载荷作用的结构系统,由于疲劳损伤的影响,元件的抗力、弹性模量等力学特性将会随时间的增长而衰减,结构整体稳定性也会随着元件的失效、弹性模量的衰减等因素而下降。因此,文中结合累积损伤理论,给出元件不同失效形式的失效时刻,并考虑到失效路径中残余结构整体失稳,采用系统可靠性理论,完成了结构系统的可靠性分析。
Several kinds of failure modes take place when various loads act on the structural system, mainly including static strength failure, fatigue failure, and the stability failure of the vimineous bar or the vimineous structure under pressure etc., and each failure mode has a large influence on the system safety. However, within the present analysis of structural reliability, the reliability research of stability failure is less. But that can bring the serious aftermath, especially, the concealment of the whole structure system's stability failure is strong. Once it happens, tremendous destruction will be caused. Moreover, the present reliability analysis of the structural system under static load or fatigue load is mostly considered respectively. But the mixed case of several failure modes is very likely to occur for the structure system. For example, certain fatigue damage, caused by the lesser fatigue load, makes the ultimate carrying capacity of the structure decreasing. And the structure may even destroy completely because of the ultimate load. When analyzing the structural reliability, the influence of different failure modes on the cumulative damage of the hinder elements should be considered due to the effect of fatigue load. And besides the relativity among those failure modes, it makes the failure mechanism of the structure more complicated and the reliability analysis of the structure system more difficult. For the above problems, the research has been done in this thesis, such as follows:
1) In order to calculate the reliability index of the non-linear safety margin accurately, a new method-the Joint Method is introduced based on the Design Point Method and the Mean Point Method, which not only simplifies calculation but also improves accuracy of the calculation.
2) Based on the crack propagation, the failure mechanism of structure system under static load and fatigue load is analyzed concretely. And considering the static strength and the fatigue synthetically, the method of reliability analysis under the two kinds of loads is given.
3) The methods of reliability analysis for the moving vimineous bar and structure system stability are given. First, aiming at the problem of stability for the elastic vimineous bar, the mechanical models are established. Based on the differential equation of the bar with small defection, the buckling critical load of vimineous bar is confirmed. And then the reliability analysis of the structure is carried out. The reliability index and failure probability are calculated. The critical load and the reliability index of the bar are analyzed under the influence of initial eccentricity. Secondly, the stability characteristic equation of the structure system is deduced. The critical load of the whole structure system's stability failure is calculated. Thereby, the safety margin of that is established, and the stability reliability of the structure system is analyzed.
4) Considering the failure modes of static load, fatigue and stability failure simultaneously, the method of reliability analysis of the structure system is given. For a structure system under static load and fatigue load, because of the influence of fatigue damage, the mechanical characteristics of resistance and elastic module of the element will decrease along with the increase of time. The whole structural reliability will decrease along with the failure of element and the attenuation of module. Thus, combine with the cumulative damage theory, the time of failure for different failure modes is given. Furthermore, considering the remnant structure's stability failure in the failure route, the reliability analysis of the structure system is done by the theory of system reliability.
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