随机荷载作用下参数不确定结构的疲劳损伤估计

基于改进区间分析和频域疲劳计算方法,对参数不确定结构在平稳高斯荷载作用下的疲劳损伤进行研究,提出完全混合和简化计算两种方法。采用区间变量模型定义结构的不确定参数,功率谱密度描述外荷载的随机性;利用有理级数显式表示结构区间频响函数及在平稳高斯荷载作用下不确定结构的应力响应区间。通过数值方法验证疲劳损伤期望率关于不确定参数的单调性后,将应力响应中不确定参数的界限完全组合提出完全混合方法,准确估计参数不确定结构的疲劳损伤期望率区间;简化计算方法则将不确定参数的界限适当组合,由显式表达式近似计算结构的疲劳损伤期望率区间。算例表明,两种方法均具有较高计算精度,且大幅减少计算量。     

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。     

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。     

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。     

区间随机桁架结构动力特性分析方法研究

摘 要：针对区间随机桁架结构的动力特性分析,提出了一种区间随机有限元方法。当结构的物理参数和几何尺寸同时具有区间随机性时,利用区间因子法和随机因子法建立了结构的刚度矩阵和质量矩阵;从结构振动的瑞利商表达式出发,利用区间运算推导了结构动力特性区间随机变量的计算式;进而利用随机变量的矩法和代数综合法,推导出了结构特征值的数字特征的计算式。最后通过算例分析了区间随机桁架结构参数的区间随机性对其动力特性的影响,计算结果表明该方法是可行和有效的。
     

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。     

具有区间参数的智能桁架结构自振特性分析

研究了具有区间参数压电智能桁架结构的动力特性分析问题,在压电主动杆和被动杆的物理参数和几何尺寸同时为区间变量时,利用区间因子法建立了结构的刚度矩阵和质量矩阵;从结构振动的Rayleigh商表达式出发,利用区间运算推导出结构特征值不确定变量的计算表达式。通过算例分析了不确定性智能桁架结构参数的区间分散性对其动力特性的影响,并获得了一些有意义的结论。     

混凝土拉-压疲劳损伤模型及其验证

基于连续损伤力学理论,提出了混凝土单轴拉-压疲劳损伤模型。模型中采用了拉和压两个边界面。加载面、边界面方程均以损伤能量释放率表示。在能量释放率空间内,由加载面与初始损伤面、边界面之间的位置描述损伤状态。通过建立累积损伤与相应循环损伤能量释放率阈值之间的关系,确定了疲劳加载中极限断裂面尺寸的变化规律,由此模拟混凝土在循环荷载作用下的刚度退化过程。结合作者完成的疲劳试验结果,确定了理论模型中的计算参数。经比较,理论模型预测的应力-应变数值、疲劳寿命和试验结果吻合较好。     

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.     

基于区间扩阶系统方法的结构静力分析

基于函数的正交分解、次序正交分解与区间数学理论,推导出区间扩阶系统方程,并利用不确定性结构分析的扩阶系统方程对具有不确定性参数的结构系统进行静力分析。将不确定参数处理为有界区间数,基于有限元模型和区间结构力学矩阵的线性分解形式,通过区间扩阶系统方程和有约束的非线性优化方法,对具有区间参数的结构静力响应进行计算。通过数值算例,对区间扩阶系统方法的结果与解析结果进行对比,分析了区间扩阶系统的展开阶数和不确定度对计算结果的影响,数值结果表明了区间扩阶系统方法的可行性与有效性。     

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.     

Reliability analysis of excavator boom considering mixed uncertain variables

There are differences among sampling data and representation types of uncertain interval, fuzzy and random variables, which increases the complexity of structure reliability analysis. A α, β-Cut-FORM is proposed to analyze structure reliability considering the mixed uncertain variables. Fuzzy variables are optimized on the interval under two cut sets (α, β) based on the theory of cut set optimization. Interval variables are modeled with probability using a uniformity method. The proposed method involves the nested probabilistic analysis and interval analysis. The first-order reliability method (FORM) is used for probabilistic analysis and nonlinear optimization is used for interval analysis. The excavator boom performance function is established for reliability analysis considering the mixed uncertain input variables, which verifies the effectiveness and advantages of the proposed method. And it has great application for safe and reliable design of excavator boom.     

Level-set topology optimization for robust design of structures under hybrid uncertainties

This paper will develop a new robust topology optimization (RTO) method based on level sets for structures subject to hybrid uncertainties, with a more efficient Karhunen-Loève hyperbolic Polynomial Chaos–Chebyshev Interval method to conduct the hybrid uncertain analysis. The loadings and material properties are considered hybrid uncertainties in structures. The parameters with sufficient information are regarded as random fields, while the parameters without sufficient information are treated as intervals. The Karhunen-Loève expansion is applied to discretize random fields into a finite number of random variables, and then, the original hybrid uncertainty analysis is transformed into a new process with random and interval parameters, to which the hyperbolic Polynomial Chaos–Chebyshev Interval is employed for the uncertainty analysis. RTO is formulated to minimize a weighted sum of the mean and standard variance of the structural objective function under the worst-case scenario. Several numerical examples are employed to demonstrate the effectiveness of the proposed RTO, and Monte Carlo simulation is used to validate the numerical accuracy of our proposed method.     

RAINFLOW CYCLES IN GAUSSIAN LOADS†

We present a new approximation of the expected damage for Gaussian loads. The approximation is based on an exact relationship between the rainflow cycle count and the range-pair exceedances count. This relationship links the intensity of rainflow amplitudes to expectations of marked crossings of the random load. The method is best suited for the fatigue life prediction for locally stationary Gaussian loads with slowly varying means and covariance functions. These results are illustrated with numerical examples.     

梁结构刚度动态非概率可靠性分析

 为了定量分析在疲劳载荷作用下梁在不同寿命期内刚度的可靠性,建立梁结构物理性能退化的精确公式就十分重要.依据疲劳载荷造成的累积损伤对材料极限应力的影响,基于材料剩余强度模型,利用材料强度与弹性模量之间的关系,推导出结构弹性模量的退化表达式,并在此基础上,提出梁弹性模量退化系数的递推表达式,推导出圆截面梁剩余抗弯刚度的表达式.在对结构可靠性分析时,概率可靠性模型和模糊可靠性模型对于原始数据信息要求较高.为了充分利用结构的不确定性信息弥补原始数据的不足,将梁的初始弹性模量及所受的疲劳载荷等看作区间变量,利用区间模型建立基于刚度退化的梁刚度动态非概率可靠性模型.最后,结合工程实例的计算表明了该方法对梁的刚度退化分析及其刚度动态可靠性分析是可行、有效和合理的.     

基于类桁架材料模型的不确定荷载下结构拓扑优化

用区间分析方法研究了不确定荷载下结构拓扑优化方法。采用类桁架材料模型建立拓扑优化类桁架连续体结构。根据区间变量运算法则推导出不确定荷载下应力约束体积最小类桁架结构的拓扑优化方法。首先采用区间分析方法得到任一点的最不利荷载工况下应变状态。在此应变状态下,利用满应力准则优化类桁架材料中杆件的方向和密度。如此反复分析和优化,直至迭代收敛。最后由类桁架中杆件分布场可以近似离散得到桁架结构。通过几个数值算例验证了方法的有效性。数值算例显示了不确定荷载下的结构拓扑优化布局更合理。     

An interval random perturbation method for structural‐acoustic system with hybrid uncertain parameters

An interval random model is introduced for the response analysis of structural‐acoustic systems that lack sufficient information to construct the precise probability distributions of uncertain parameters. In the interval random model, the uncertain parameters are treated as random variables, whereas some distribution parameters of random variables with limited information are expressed as interval variables instead of precise values. On the basis of the interval random model, the interval random structural‐acoustic finite element equation is constructed, and an interval random perturbation method for solving this interval random equation is proposed. In the proposed method, the interval random matrix and vector are expanded by the first‐order Taylor series, and the response vector of the structural‐acoustic system is calculated by the matrix perturbation method. According to the linear monotonicity of the response vector, the lower and upper bounds of the response vector are calculated by the vertex method. On the basis of the lower and upper bounds, the intervals of expectation and standard variance of the response vector are obtained by the random interval moment method. The numerical results on a shell structural‐acoustic model and an automobile passenger compartment with flexible front panel demonstrate the effectiveness and efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

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.