Probabilistic analysis of multi-step failure process of a laminated composite in bending

This paper presents results of a theoretical and experimental analysis of the random bending strength of laminated composites. Multi-layered composites with a periodic structure of sublaminates are considered in a combined loading (bending action and plane stress) state. The random strength response of the composites is analyzed on the basis of a multi-step failure probabilistic model. Here, the multi-step failure is considered as a process in which the failure of some single structural elements (sublaminates, laminae) leads to load redistribution onto other intact elements. A numerical algorithm based on the Monte Carlo technique and respective computer code are offered. The effect of scatter of structure parameters and number of sublaminates on the bending strength distribution is analyzed in detail. Experimental confirmation is considered on an example of uniaxial bending of laminated carbon-fiber-reinforced plastics. A method for evaluation of reliability in a random combined loading is also suggested.     

A stochastic finite element method for real eigenvalue problems

A stochastic finite element method (SFEM) based on local averages of a random vector field is developed for both distinct and repeated eigenvalues. Formulae for the variances and covariances of the eigenvalues and eigenvectors are derived. It is shown in a numerical example that, as the number of elements increases, solutions obtained from the present SFEM formulation converge much faster than those obtained from the SFEM formulation based on mid-point discretization.     

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.     

Stochastic finite element analysis of a cable-stayed bridge system with varying material properties

Stochastic seismic finite element analysis of a cable-stayed bridge whose material properties are described by random fields is presented in this paper. The stochastic perturbation technique and Monte Carlo simulation (MCS) method are used in the analyses. A summary of MCS and perturbation based stochastic finite element dynamic analysis formulation of structural system is given. The Jindo Bridge, constructed in South Korea, is chosen as a numerical example. The Kocaeli earthquake in 1999 is considered as a ground motion. During the stochastic analysis, displacements and internal forces of the considered bridge are obtained from perturbation based stochastic finite element method (SFEM) and MCS method by changing elastic modulus and mass density as random variable. The efficiency and accuracy of the proposed SFEM algorithm are evaluated by comparison with results of MCS method. The results imply that perturbation based SFEM method gives close results to MCS method and it can be used instead of MCS method, especially, if computational cost is taken into consideration.     

Efficient structural reliability analysis via a weak-intrusive stochastic finite element method

This paper presents a novel methodology for structural reliability analysis by means of the stochastic finite element method (SFEM). The key issue of structural reliability analysis is to determine the limit state function and corresponding multidimensional integral that are usually related to the structural stochastic displacement and/or its derivative, e.g., the stress and strain. In this paper, a novel weak-intrusive SFEM is first used to calculate structural stochastic displacements of all spatial positions. In this method, the stochastic displacement is decoupled into a combination of a series of deterministic displacements with random variable coefficients. An iterative algorithm is then given to solve the deterministic displacements and the corresponding random variables. Based on the stochastic displacement obtained by the SFEM, the limit state function described by the stochastic displacement (and/or its derivative) and the corresponding multidimensional integral encountered in reliability analysis can be calculated in a straightforward way. Failure probabilities of all spatial positions can be obtained at once since the stochastic displacements of all spatial points have been known by using the proposed SFEM. Furthermore, the proposed method can be applied to high-dimensional stochastic problems without any modification. One of the most challenging problems encountered in high-dimensional reliability analysis, known as the curse of dimensionality, can be circumvented with great success. Three numerical examples, including low- and high-dimensional reliability analysis, are given to demonstrate the good accuracy and the high efficiency of the proposed method.     

弹塑性随机有限元在低周疲劳分析中的应用

推导了交变载荷下弹塑性随机有限元的迭代格式,计算了局部多轴应力应变的随机响应。迭代格式中,针对复杂的交变载荷,采用运动强化模型反映塑性变形引起的各向异性和包辛格效应,运用Jhansale模型描述材料的瞬态应力应变关系。弹塑性有限元分析,克服了以往近似方法只能计算单轴局部应力应变响应的缺陷,为多轴疲劳分析奠定了基础。考虑零构件的随机因素,将随机有限元方法引入到交变载荷下弹塑性有限元的迭代格式中,得到局部应力应变的随机响应,为低周疲劳可靠性分析提供了更精确的依据。MontCarlo模拟结果证实了提出的弹塑性随机有限元方法是可靠的。     

On probabilistic fatigue models for composite materials

The general purpose of this article is to review the main ideas in fatigue analysis of composites in the context of the application of probabilistic methods, both theoretical and computational. That is why most deterministic concepts of composite materials fatigue are summarized together with stochastic approaches. The application of the perturbation based Stochastic Finite Element Method (SFEM) to fatigue analysis of homogeneous and heterogeneous media is shown. Further, homogenization method in its effective modules approach is proposed below for application in fatigue processes modeling of linear elastic periodic random composites. Considering stochastic character of the analysis, the reliability tools appropriate to multicomponent materials are presented together with the specially adopted brittle and ductile fracture criteria.     

Modeling the flexural fatigue behavior of glass-fiber-reinforced thermoplastic matrices

A two-parameter model explicitly accounting for the cyclic as well as the mean stress was proposed and tested on the basis of static and fatigue data obtained in four-point bending on a random continuous glass-fiber-reinforced polypropylene. The model is based on residual strength degradation and captures the effect of stress ratio (i.e. the ratio between the minimal and the maximal stress). The experimental data were in excellent agreement with the theoretical predictions, indicating that a fatigue characterization can be achieved with a minimum of experimental tests. Further, the reasonable agreement between the static strength data and the theoretical predictions highlighted the potential and reliability of the model in view of its statistical implementation     

On the assessment of fatigue life of marine diesel engine crankshafts

The fatigue strength and its correct assessment play an important role in design and maintenance of marine crankshafts to obtain operational safety and reliability. Crankshafts are under alternating bending on crankpins and rotating bending combined with torsion on main journals, which mostly are responsible for fatigue failure. The commercial management success substantially depends on the main engine in service and of its design crankshaft, in particular. The crankshaft design strictly follows the rules of classification societies. The present study provides an overview on the assessment of fatigue life of marine engine crankshafts and its maintenance taking into account the design improving in the last decades, considering that accurate estimation of fatigue life is very important to ensure safety of components and its reliability. An example of a semi-built crankshaft failure is also presented and the probable root case of damage, and at the end some final remarks are presented.     

失效相关的齿轮一次四阶矩可靠性分析

齿轮是机械传动的关键零件之一,为了分析其可靠性,在改进的验算点一次二阶矩可靠性方法基础上,应用Taylor级数展开和Hermite多项式近似等方法,推导了齿轮功能函数的验算点前四阶矩,分析了具有齿根断裂和齿面点蚀两种主要相关失效模式的齿轮传动可靠性,给出了其相关系数和齿轮的可靠度。另一方面,因影响齿轮失效的因素繁杂众多,计算齿轮的可靠度时,不管是用一次二阶矩可靠性方法还是四阶矩可靠性方法,其计算量均偏大,且容易出错。针对该问题,提出了一种分类变差系数验算点一次四阶矩可靠性分析方法,该方法对齿轮功能函数的不同基本随机变量进行分类综合,减少了设计变量,使计算量明显减小,解决了用矩方法分析结构可靠性时计算量偏大且易出错的难题。最后应用所提分类变差系数验算点一次四阶矩可靠性分析法估计了某车床主轴箱一对传动齿轮的可靠性,计算结果显示该对齿轮齿根弯曲疲劳强度和齿面接触疲劳强度有一定的相关性,所用一次四阶矩方法因包含偏度、峰度等更高阶的统计信息可进一步提高估计精度。     

有机玻璃边缘连接结构疲劳寿命可靠性分析

针对有机玻璃边缘连接结构弯曲疲劳实验结果,提出了结构低周疲劳寿命模型,对有机玻璃边缘连接结构可靠性进行分析.考虑材料属性、疲劳幅值载荷的随机性,分别采用Monte-Carlo法和四阶矩法,借助有限元分析软件Marc对结构进行了可靠性分析,得到低周疲劳载荷作用下结构疲劳寿命的可靠度,比较两种计算结果,发现四阶矩法计算结果与Monte-Carlo法计算偏差很小,适用于有机玻璃边缘连接结构疲劳可靠性分析;同时分析了基本变量均值与标准差影响结构可靠性的灵敏度,得到载荷为影响结构疲劳寿命可靠性的主要因素.     

Stochastic finite element method applied to non-linear analysis of embankments

The deterministic Finite Element Method (FEM) is a valuable tool for understanding and predicting the mechanical behaviour of earth structures. The main difficulty in the application of this technique generally arises from the large uncertainties affecting the mechanical properties of materials to be introduced in the analysis. In many instances, these parameters should actually be considered as random variables or random fields. The Stochastic Finite Element Method (SFEM) should then be used to assess the results of the analyses in probabilistic terms.In this paper, the usefulness of the SFEM approach for engineering purposes is discussed and illustrated by analyses of embankments constructed by placing successive lifts of compacted soil. Construction materials are assumed to follow a simple non-linear constitutive law (Duncan JM, Chang CY. Non-linear analysis of stress and strain in soils, Journal of the Soils Mechanics and Foundation Division, ASCE 1970;96(5):1629–1653). Stochastic finite element analyses are performed using both the First Order-Second Moment method (FOSM) and Monte Carlo simulations (MC). A simple example shows that SFEM analyses can be useful to evaluate the relative influence of each of the parameters of the constitutive model on the results. Uncertainties affecting displacements, strains and stresses predictions for a large earth dam are also presented.     

A new approach to the estimation of fatigue reliability at a single stress level

Based on a probabilistic model of strength-lifetime, an approach to estimating simple fatigue reliability by using first-order reliability techniques is presented. By this approach the results of life testing at two stress levels can be used directly to estimate simple fatigue reliability corresponding to any lifetime and applied stress ratio. Using the approach does not need the data of a fatigue strength staircase test which are not exact enough for describing the distribution of fatigue strength and can only be used for a specific lifetime. A numerical example is given to show the application of the approach.     

Quasi-weak and weak formulation of stochastic finite elements on static and dynamic problems—a unifying framework

To model uncertainty of spatial and/or temporal variations widely present in synthetic and natural media, a variety of displacement-based stochastic finite element methods (SFEMs) have been formulated using the standard displacement-based finite elements. In this paper, by distinguishing a quasi-weak form from a weak form in both real and random space, a unifying framework of variational formulation is presented covering both the displacement-based SFEMs and the recently proposed Green-function-based (GFB) SFEM. The study shows that Monte Carlo, perturbation, and weighted integral SFEMs correspond to the quasi-weak form, while the weak form results in spectral SFEM, pseudo-spectral SFEM, and GFB-SFEM. Within the unifying framework, dynamic problems are further addressed especially to demonstrate the unique feature of GFB-SFEM on problems with inputs characterized as random fields or random processes.     

基于车桥耦合随机振动分析的钢桥疲劳可靠度评估

发展了一种基于车桥耦合系统随机振动分析的铁路钢桥疲劳可靠度评估方法,建立车桥耦合系统模型,选取车速和轨道不平顺作为基本随机变量进行随机振动分析,以此确定桥梁构件等效疲劳应力幅及其循环次数的概率模型。在此基础上,建立基于S-N曲线法的疲劳极限状态函数并进行疲劳可靠度分析。以一座铁路下承式钢桁梁桥为例进行了疲劳可靠度评估,并讨论了车速及轨道平顺性对构件疲劳可靠性的影响。结果表明:该文方法可有效用于铁路钢桥疲劳可靠度评估;受车速及轨道不平顺随机性的影响,列车引起的桥梁构件等效疲劳应力幅及其循环次数均具有一定的不确定性,应视为随机变量,二者可采用对数正态分布表示;车速和轨道不平顺可显著影响桥梁构件的疲劳可靠性,疲劳关键构件的可靠度指标随着轨道平顺性增强而提高。     

既有钢筋混凝土桥梁构件抗力模糊随机时变概率模型研究

构件的抗力概率模型是进行桥梁结构时变可靠性研究的基础之一。既有钢筋混凝土桥梁材料的老化与损伤情况复杂使其抗力同时具有随机性、模糊性和时变性是一个模糊随机过程。在分析影响既有钢筋混凝土桥梁构件抗力不确定性因素的基础上,考虑桥梁在服役过程中的耐久性损伤对构件抗力的影响,在常规方法只能考虑抗力随机时变性基础上,进一步考虑模糊性,结合实测数据和现有资料建立了既有钢筋混凝土桥梁中混凝土强度、钢筋截面积和钢筋强度模糊随机时变模型,进而研究了在不修复情况下桥梁构件抗力模糊时变概率模型,分析了抗力平均值和标准差随时间和阈值变化的规律,并以受弯构件为例给出了具体分析过程和结果。     

三维结构可靠度对随机变量的敏感性研究

本文基于三维随机有限元提出了结构点可靠度、失效模式的可靠度及整个结构体系的可靠度分别对随机变量的＂分布参数＂和＂极限状态方程参数＂的敏感性计算方法，并以一典型重力坝为例进行了计算，得出了若干有益的结论。     

一般尺度法的振动疲劳强化系数分析

在Dirlik模型的基础之上,结合一般尺度法（General scaling law）提出适用于平稳宽带随机过程的疲劳强化系数模型。一般尺度法认为结构在原始载荷和强化后载荷下的应力响应功率谱各阶谱矩成简单的线性关系;与Dirlik宽带疲劳损伤模型结合,便得到适用于平稳宽带随机过程的疲劳强化系数模型。为了验证模型的有效性,分别在原始加速度功率谱和经一般尺度法强化后的加速度功率谱载荷下;对悬臂梁采用雨流计数(Rainflow counting)和Miner损伤准则进行疲劳寿命预测,得到它们的疲劳强化系数,并与疲劳强化系数模型得到的疲劳强化系数进行对比。结果表明：提出的疲劳强化系数模型精度为99.7 %,由此可验证疲劳强化系数模型的有效性。