基于区间理论的不确定结构随机疲劳损伤估计方法

将结构体系中不确定参数定义为区间变量,在随机疲劳谱分析方法的基础上,提出一种计算平稳高斯荷载作用下不确定结构疲劳损伤的新方法。该方法采用区间参数模型定义结构的不确定性,应用功率谱密度描述外荷载的随机性;利用有理级数和单位对称区间显式表达结构区间频响函数和不确定结构在平稳高斯荷载作用下的动力响应区间;根据Tovo-Benasciutti疲劳损伤预测模型,计算不确定结构在随机荷载作用下的疲劳损伤区间期望率;并可通过调整相应不确定参数的单位对称区间近似估计该不确定参数不同不确定半径的疲劳损伤区间期望率。通过数值算例,将该文提出的随机疲劳区间分析方法与顶点法进行比较,验证了该方法的准确性和适用性。     

基于非概率集合理论的屋面板风致疲劳寿命估计

现有疲劳分析中,通常将结构材料参数、几何尺寸等定义为确定性参数;实际结构中,相关参数均为有界但不确定变量,如按确定性参数估计结构的疲劳寿命是偏于不安全的。该文将结构体系中不确定参数定义为区间变量,在线性疲劳损伤累积理论基础上,提出一种仅需一次动力响应分析即可计算不确定结构在动力荷载作用下疲劳损伤的新方法。该方法将金属屋面板弹性模量和屋面板板厚等由于施工误差等因素引起的不确定参数定义为区间变量,通过摄动法和区间动力响应分析,计算屋面板在脉动风荷载作用下的应力响应区间;结合屋面板材料的S-N曲线,采用修正Miner疲劳线性累积准则对屋面板的疲劳损伤和寿命区间进行估计。结果表明:该文方法可有效计算考虑结构参数不确定条件下金属屋面板的疲劳损伤和寿命区间;与顶点法比较,该文方法仅需一次动力响应分析就可计算金属屋面板风致疲劳损伤和寿命区间。     

模糊有限元法在桥梁结构中的应用

本文简要地论述了桥梁结构分析计算中的模糊性,采用区间方法表示荷载及性质模糊性的上、下限。对不确定荷载矢量和单元刚度矩有限元法（ＦＦＥＭ）计算结构的响应。在荷载不确定的情况下,仅在右端项的矢量中包含有模糊值,通过一次计算,可以获得一组相应于所有的荷载工况我可能的位移值。算例表明：针对所有可能的荷载组合,采用模糊有限元法可以计算出相应的单元内力极值界限：与通过设计荷载方案比较,该方案可以利用现有的有限     

区间桁架结构有限元分析的区间因子法

研究了具有区间参数的桁架结构在区间力作用下的有限元分析方法。利用区间因子法,桁架结构材料物理参数、几何尺寸和外荷载均可表达为其区间因子和其确定性量的乘积,进而结构的位移和应力响应也可表达成区间因子们的函数。利用区间算法,推导出了结构位移和应力响应的上、下限和均值的计算表达式。通过算例,分析了结构参数和外荷载的不确定性对结构响应的影响,并验证了模型和方法的合理性与可行性。该方法的优点是能够反映结构某一参数的不确定性对结构响应的影响。     

基于平稳非高斯结构响应前四阶矩的首次穿越概率计算

发展了一个平稳非高斯结构响应的首次穿越概率解析方法。在该方法中,基于已得到的平稳非高斯结构响应的前四阶矩(均值、标准差、偏度和峰度),分别利用Winterstein(1994)模型与Ding和Chen模型的等效高斯分位数,以及平稳非高斯结构响应的界限水平,将软化与硬化非高斯结构响应映射为标准高斯过程;进而利用考虑初始条件与群超效应的平稳高斯结构响应的Poisson模型来实现平稳非高斯结构响应的首次穿越概率计算。算例对比分析验证了该修正方法的有效性和准确性,同时相比蒙特卡洛模拟提高了计算效率,为计算平稳非高斯结构响应的首次穿越概率提供了高效合理的工具。     

随机声载荷作用下的复杂薄壁结构Von Mises应力概率分布研究

随机声载荷作用下的某些复杂薄壁结构的振动疲劳属于多轴疲劳,Von Mises 应力准则是多轴疲劳损伤分析的一条有效途径。本文通过对有限带宽高斯白噪声载荷作用下结构Von Mises应力概率分布研究,分析提出Von Mises应力服从双参数Weibull分布或Lognormal分布,并且给出了估算这两种概率分布参数的方法,进而得到了Von Mises应力峰值概率密度函数,从而为结构的疲劳损伤寿命估算提供依据。在工程应用中采用耦合的有限元和边界元方法计算了某型航空发动机燃烧室火焰筒薄壁结构在随机声载荷作用下的振动应力响应功率谱密度,着重分析了Von Mises应力响应的概率分布特征,并对分析结果采用Kolmogorov-Smirnov (K-S)检验进行了比较验证。     

基岩软化条件下仰拱结构疲劳寿命的预测分析

由于隧道施工期间扰动及重载列车荷载的长期循环作用,造成底部基岩出现一定范围的软化和围岩力学参数降低,引起拱底围压的不均匀分布,并影响基底结构的疲劳寿命。通过引入重载列车振动荷载函数和Miner线性累积损伤理论,建立了考虑基底软化仰拱结构疲劳寿命的预测方法,研究列车振动荷载作用下基底软化因素对铁路隧道底部结构疲劳寿命的影响。计算结果表明:在基岩不同软化条件下,隧道底部结构动应力响应分布规律相似,隧道底部结构各部位动拉应力和动压应力增幅较大,仰拱结构疲劳寿命明显减小。隧道底部结构仰拱中心处出现拉应力最大值,仰拱与边墙连接处出现压应力最大值。在仰拱结构的应力计算结果的基础上,结合混凝土疲劳寿命原理,论述了基底软化条件下隧道底部结构疲劳寿命预测值。     

阵风响应问题的区间分析方法

研究弹性飞机在大气中飞行时受到阵风干扰后产生的结构响应,考虑飞机阵风响应问题分析中存在的不确定性参数,将其用区间向量定量化,基于区间扩张理论和Taylor级数展开,并结合有限元计算方法,提出了区间分析的方法来估计结构阵风响应的变化区间.该方法只需要知道不确定参数的所在范围界限,为解决含有不确定参数的阵风响应这类复杂的气动弹性动力学问题提供了一个途径.通过数值算例,将区间分析方法与概率方法的结果进行了比较,显示了区间分析方法的有效性.     

热弹耦合梁结构动力响应的区间数值分析

研究了含有区间参数梁结构在温度载荷和力载荷共同作用下的动力响应问题,考虑材料变形与传热的相互影响,建立了梁在热弹耦合下的动力学有限元模型,并给出了对结构瞬态热传导方程与动力学方程进行相互交替迭代求解的计算方法。针对结构响应不确定性问题,以不确定参数作为约束变量,通过寻求结构响应函数的区间范围,将区间问题转化为优化问题,并利用遗传算法给出了结构响应函数的区间界限。通过算例及与概率有限元方法的计算结果比较,表明文中所提出方法的可行性和有效性,并获得在热弹耦合作用下梁结构的固有振动频率有所增加,而振动响应振幅则逐渐减弱的结论。该方法只需已知不确定参数所在范围的界限,而无需其他统计信息,为解决区间参数热弹耦合梁问题提供了一种途径。     

结构静力分析的区间摄动有限元法

基于新的区间参数系统响应界值的评估方法,推导了基于Taylor展开的区间摄动有限元法和区间参数摄动有限元法的高阶求解方法。并提出了一种新的区间摄动有限元法,该方法将刚度矩阵的逆矩阵用一系列Neumann展开级数来表示,最终得到结构响应摄动量的上下界限,是对结构响应鲁棒性的一种直接评估,因此称之为区间鲁棒摄动有限元法。比较了三种区间摄动有限元法的计算精度和计算效率。算例结果表明:区间鲁棒摄动有限元法具有较好的精度,能够适用于大型航空航天结构的不确定分析和优化。     

Wiener chaos expansions for estimating rain-flow fatigue damage in randomly vibrating structures with uncertain parameters

The problem of estimating the fatigue damage in randomly vibrating structures with uncertain parameters is considered. The loadings are assumed to be stationary and Gaussian. The corresponding accumulated fatigue damage is described through the rain-flow cycle counting algorithm. For stationary and ergodic loads, the accumulated rain-flow fatigue damage can be estimated if the system and the load spectrum are known. However, these estimates would be erroneous if the structure properties and/or the spectrum parameters of the loading are significantly uncertain. Corrections to account for the parameter uncertainties is usually obtained using the Gauss error propagation formula, and is accurate for small parameter variations. An alternative approach based on Wiener chaos expansions is employed to estimate the rain-flow fatigue damage in linear/nonlinear structural systems with parameter uncertainties. The performance of the proposed approach is compared with the Gauss error propagation formula. The proposed method is illustrated through fatigue damage estimation of three simplified examples involving a moving vehicle on a rough road, Morison’s force due to random sea waves and the blade of a wind turbine.     

On fatigue life under stationary Gaussian random loads

Load parameters for a stationary Gaussian random load are taken as the location, scale and shape parameters of its power spectrum. The centre frequency of a power spectrum is proposed as a measure of fatigue life. A fatigue life function, formulated in terms of the load parameters, is evaluated from the test results obtained by fatigue testing a structural steel under six different power spectral shapes. The concept of a shape operator is employed to correlate fatigue lives under different power spectral shapes.     

Cycle counting methods for bi-modal stationary Gaussian processes

The cycle counting procedure is a fundamental step in the fatigue analysis of structures. This paper is devoted to cycle counting methods, starting from the spectral properties of the loading process. Cycle counting methods for stationary Gaussian narrow-band and broad-band processes proposed in literature are discussed. Focusing attention on bi-modal processes, which are usual in dynamic response of structures, the cycles histograms obtained by the Peak and Peak-Valley Counting methods are expressed in closed form. From these, a couple of upper and lower bounds for the mean total damage and for the mean fatigue life are obtained. Then, an advanced formulation of the cycle counting is developed, obtaining a new closed form solution of the cycles histogram which better approximate the Rainflow Counting results. The proposed method is finally applied to several different bi-modal processes, comparing the results with other criteria and with solutions based on simulated time-histories.     

Bearing dynamic parameters identification for a sliding bearing-rotor system with uncertainty

Bearing dynamic parameters of a sliding bearing-rotor system are important factors to the vibration absorbing characteristics. It is a valuable method to identify bearing dynamic parameters based on the unbalance response. Nevertheless, in Engineer, the unbalance parameters are uncertain due to the structural complexity and manufacturing or measuring error. Thus, developing an efficient method to estimate the bearing dynamic parameters for the uncertain unbalance parameters seems more important and necessary. This paper presented an inverse method for identifying stably the bounds of bearing dynamic parameters with uncertain unbalance parameters based on dynamic load identification method and the interval analysis .In the method, bearing dynamic parameters identification problem is formulated as the oil film force reconstruction by considering the oil film supports as rotor load boundary conditions; the midpoint oil film force and the first derivative to each uncertain unbalance parameter need be calculated with the interval analysis; the bounds of bearing dynamic parameters can be finally identified based on the interval mathematics. Finally, the efficiency and robustness of the proposed method are verified by a numerical example.     

Robust stability analysis of structures with uncertain parameters using mathematical programming approach

This paper presents a novel mathematical programming approach for the static stability analysis of structures with uncertainties within the framework of FEM. The considered uncertain parameters are material properties, geometry of element cross section, and loading conditions, all of which are described by an interval model. The proposed method formulates the two cases of interest, namely, worst and best buckling load calculation, into a pair of mathematical programming problems. Two straightforward advantages are exhibited by such formulations. The first advantage is that the proposed formulation can overcome the interference on the sharpness of bounds of the buckling load due to the interval dependence issue. The second benefit is that the information of uncertain parameters causing the extremities of buckling load can always be retrieved as by‐products of the uncertain stability analysis. Some numerical examples are presented to illustrate the capability of the proposed method on various structures and the sharpness of the bounds of the buckling load factors. The efficiency and effectiveness of the proposed method are also demonstrated through comparison with the classical Monte Carlo simulation method. Copyright © 2014 John Wiley & Sons, Ltd.     

A new frequency domain method for random fatigue life estimation in a wide‐band stationary Gaussian random process

A new frequency domain method for random fatigue life estimation in a wide‐band stationary Gaussian random process was proposed for application in fatigue analysis. Simulations of the power spectral densities of different types were firstly performed; the simulated results showed that the accuracy and applicability for the current frequency domain methods are not only related to the spectral type but also associated with the types of the analysed materials. Compared with the current methods, the proposed method, in which the rain‐flow amplitude obeys Nakagami distribution, has better universality and could significantly reduce the error for the random fatigue life estimation with simulated and actual spectra. Verified application in cast‐steel fatigue life analysis were performed between random fatigue life and constant amplitude fatigue life. It is shown that the fatigue life analysis under random load cannot be ignored and the proposed new method can serve as a recommended method.     

城市轨道交通钢桥疲劳损伤等效系数研究

为研究城市轨道交通钢桥疲劳损伤等效系数,根据Eurocode中S-N曲线和损伤等效系数法,对中国城市轨道交通钢桥疲劳损伤等效系数进行求解分析。提出6种适用于中国城市轨道交通钢桥的列车编组,选取ZC、ZK和LM71这3种荷载图式作为疲劳荷载模型。根据中国城市轨道交通的实际交通量,提出1种采用双斜率S-N曲线的简化算法,与采用单斜率S-N曲线求解方法进行对比分析。求解分析各项疲劳损伤等效系数,并针对中国城市轨道交通钢桥列车编组的特点提出考虑列车最大容许速度影响的损伤等效系数λ_v。结果表明:以ZC图式作为疲劳荷载模型,考虑列车最大容许速度的影响,依据双斜率S-N曲线简化算法求得的损伤等效系数较能合理地对中国轨道交通钢桥进行疲劳验算。     

Frequency based fatigue analysis and temperature effect

This paper proposes a temperature modified Dirlik method to estimate the high cycle fatigue damage for uniaxial loadings caused by random vibrations directly from a power spectral analysis. Besides, the methodology for combining the frequency based fatigue analysis with the temperature effect is represented. This approach is based on a new definition of loading as a random Gaussian process. The fatigue damage estimation of the high pressure die-cast aluminium alloy AlSi₉Cu₃ is investigated at elevated temperatures. Finally, numerical simulations on the known power spectral densities with different shapes at different temperatures are performed in order to establish proper dependence between the temperature modified Dirlik method, the rainflow cycle counting, the linear cumulative fatigue damage and the spectral bandwidth parameters. The proposed method enables computationally fast fatigue damage estimation for the random loadings and the temperature histories.