模糊随机桁架结构可靠性指标的灵敏度分析

在结构有限元分析基础之上研究了模糊随机桁架的可靠性指标对设计变量的灵敏度问题.同时考虑结构参数和荷载的模糊随机性,在利用双因子法得出结构模糊随机响应及其模糊数字特征的基础之上,推导了结构的可靠性指标对设计变量的灵敏度.通过算例验证了该方法的可行性,得出了若干有意义的结论.     

模糊随机桁架结构的非平稳随机振动分析

利用一种新的双因子法研究了模糊随机桁架结构的非平稳随机振动问题。同时考虑结构物理参数和几何尺寸的模糊随机性,首先从时域上推导出了位移响应的模糊随机相关函数矩阵;进而得出了位移和应力响应在频域上的模糊随机均方值,并用随机变量的矩法得到了结构响应均方值模糊随机变量的模糊数字特征。最后用算例验证了该方法的可行性。     

随机参数结构在随机荷载激励下的动力响应分析

研究了基于概率的工程结构动力响应分析方法。利用振型迭加法导出了结构物理参数和作用荷载幅值同时具有随机性时结构动力响应随机变量的数字特征计算表达式，并提出了求解方法。通过算例考察了结构物理参数和作用荷载的随机性对结构动力响应的影响，表明文中提出的计算模型和方法是正确与可行的。     

基于完全概率的随机桁架结构动力响应分析

提出了一种求解随机桁架结构在随机荷载作用下动力响应概率密度函数的方法.通过对随机参数桁架结构的有限元分析,获得了结构的质量阵与刚度阵,利用振型迭加法导出了结构的物理参数、几何参数、外荷载幅值及频率同时具有随机性时,结构动力响应随机变量的表达式,应用随机向量函数的概率分布函数表达式,通过逐步求解的策略,获得结构动力响应的概率密度函数.算例结果与Monte-Carlo模拟法结果比较表明,该方法具有较高的精度及效率.     

随机刚架结构在平稳随机激励下的动力响应分析

文中研究了随机刚架结构的平稳随机响应问题。考虑结构物理参数的随机性，导出了结构在平稳随机激励下位移响应均方值和应力响应均方值的均值、方差和变异系数的计算表达式。通过算例考察了结构物理参数的随机性对结构动力响应均方值随机性的影响，并获得了若干有意义的结论。     

随机行人荷载下结构动力可靠度分析

基于概率密度演化理论(PDEM),提出一种通过动力可靠度对简支梁在随机行人荷载下的响应进行评估的方法。选取步频、步长、体重以及各行人的到达时间为随机变量,确定性结构动力响应由显式Newmark法计算给出,通过PDEM理论可以方便地计算出行人通过简支梁时任意时刻响应的概率信息,以及不同舒适度阈值水平下跨中加速度的动力可靠度。算例验证表明,简谐荷载下分布参数体系的概率密度演化分析结果与统计结果吻合良好。通过对单人以及多人荷载下响应随机演化过程的分析表明,行人荷载随机性对结构响应具有显著影响,建议利用动力可靠度对结构进行振动响应分析以及人致振动舒适度评价。     

随机参数智能梁结构闭环控制系统动力响应分析

针对随机智能梁结构参数的不确定性建立了其闭环控制动力响应随机模型.从结构动力响应的Duhamel积分出发,利用求解随机变量函数矩法导出了在三种情况下横向位移、转角位移和应力响应的数字特征表达式.并通过算例分析了在随机荷载作用下控制前后其物理参数、几何参数和控制力对闭环结构系统动力响应的影响.结果表明基于随机方法处理压电...     

抗震结构模糊随机动力可靠性分析

本文对在考虑地震烈度和场地土分类的模糊性的基础上所建立的含模糊参数的地震地面运动随机过程模型,采用分步等效线性化及状态方程法,求出了结构模糊随机变形和能量反应的统计矩;基于单参数(变形或能量)及双参数(变形和能量)的模糊破坏准则,分析了抗震结构的模糊随机动力可靠性。最后给出了两个自由度结构的数值算例,表明双参数准则更为合理和安全。     

刚架结构物理参数的随机性对其非平稳随机响应的影响

文中研究了随机刚架结构的非平稳随机响应问题。考虑结构在非平稳随机激励下其物理参数的随机性,从结构非平稳随机响应的表达式出发,利用求解随机变量函数矩的方法和求解随机变量数字特征的代数综合法,导出了结构位移响应均方值和应力响应均方值的均值、方差和变异系数的计算表达式。通过算例,考察了结构物理参数的随机性对结构动力响应均方值随机性的影响,获得了若干有意义的结论。     

随机结构在随机载荷下的动力可靠度分析

提出了综合考虑动载荷和结构参数双重随机性的动力可靠度分析方法.首先基于随机振动的首次超越破坏准则,参照随机变量功能函数模式,建立了随机结构动力可靠度功能函数;然后引入序列响应面法,对功能函数进行拟合;最后用JC法求解可靠指标.算例分析验证了本文方法具有较好的计算精度和计算效率,尤其在复杂工程结构的动力可靠度分析中有广阔的应用前景.     

Dynamic Response Analysis of Fuzzy Stochastic Truss Structures under Fuzzy Stochastic Excitation

A novel method (Fuzzy factor method) is presented, which is used in the dynamic response analysis of fuzzy stochastic truss structures under fuzzy stochastic step loads. Considering the fuzzy randomness of structural physical parameters, geometric dimensions and the amplitudes of step loads simultaneously, fuzzy stochastic dynamic response of the truss structures is developed using the mode superposition method and fuzzy factor method. The fuzzy numerical characteristics of dynamic response are then obtained by using the random variable’s moment method and the algebra synthesis method. The influences of the fuzzy randomness of structural physical parameters, geometric dimensions and step load on the fuzzy randomness of the dynamic response are demonstrated via an engineering example, and Monte-Carlo method is used to simulate this example, verifying the feasibility and validity of the modeling and method given in this paper.     

A novel intelligent fuzzy estimator for uniform load determination on a beam with varying boundary conditions

A novel intelligent fuzzy input estimation method that estimates the uniform input load on a beam structural system is presented in this article. The uniform input load acting on a beam structural system is estimated from the measured dynamic responses using the inverse method. The algorithm includes the fuzzy Kalman filter and the fuzzy-weighted recursive least square method. This study presents an efficient estimator accelerated and weighted using fuzzy-accelerating and -weighting factors proposed based on the fuzzy logic inference system. The capability of the proposed algorithm is demonstrated through several beam structural system examples with different types of boundary conditions. The simulation results are compared by alternating between the constant, adaptive, and fuzzy weighting factors. The results demonstrate that the presented method applied to beams with various structural system boundary conditions is successful.     

The analyses of dynamic response and reliability of fuzzy-random truss under stationary stochastic excitation

A new two-factor method based on the probability and the fuzzy sets theory is used for the analyses of the dynamic response and reliability of fuzzy-random truss systems under the stationary stochastic excitation. Considering the fuzzy-randomness of the structural physical parameters and geometric dimensions simultaneously, the fuzzy-random correlation function matrix of structural displacement response in time domain and the fuzzy-random mean square values of structural dynamic response in frequency domain are developed by using the two-factor method, and the fuzzy numerical characteristics of dynamic responses are then derived. Based on numerical characteristics of structural fuzzy-random dynamic responses, the structural fuzzy-random dynamic reliability and its fuzzy numerical characteristic are obtained from the Poisson equation. The effects of the uncertainty of the structural parameters on structural dynamic response and reliability are illustrated via two engineering examples and some important conclusions are obtained.     

模糊参数平面连续体结构的拓扑优化设计

研究了具有模糊参数的连续体结构在模糊载荷作用下的拓扑优化设计问题。利用信息熵将模糊变量转换为随机变量,构建了随机载荷作用下的随机参数的连续体结构的拓扑优化设计数学模型,以结构的形状拓扑信息为设计变量,结构总质量均值极小化为目标函数,满足单元应力可靠性为约束条件,利用分布函数法对应力可靠性约束进行了等价显式化处理。基于随机因子法,利用代数综合法导出了应力响应的数字特征的计算表达式。采用双方向渐进结构优化(BESO)方法求解。通过两个算例验证了该文模型及求解方法的合理性和有效性。     

Dynamic response of structures with uncertain parameters: A comparative study of probabilistic and fuzzy sets models

This paper presents the results of a study on the response of structures with uncertain properties such as mass, stiffness and damping. The effect of the uncertain parameters on the response and the effect of the modelling of the uncertainties on the response are investigated. In particular, two types of uncertainties are distinguished: random and fuzzy uncertainties. Two kinds of models are studied: probabilistic and fuzzy set models. The two approaches to uncertainty modelling are compared with regard to their impacts on the analysis and on the uncertain structural response obtained. The study considers free vibration, forced vibration with deterministic excitation, and forced vibration with Gaussian white noise excitation. It is concluded that, in general, fuzzy models are much easier to implement and the associated analysis easier to perform than their probabilistic counterparts. When the available data on the structural parameters are crude and do not support a rigorous probabilistic model, the fuzzy set approach should be considered in view of its simplicity.     

Structural parameters identification of uncertain multi-storey shear buildings using fuzzy neural network modelling

Present paper proposes a fuzzy neural network (FNN)-based modelling for the identification of structural parameters of uncertain multi-storey shear buildings. Here, the method is developed to identify uncertain structural mass, stiffness and damping matrices from the dynamic responses of the structure without any optimization processes that are generally used to solve inverse vibration problems. Uncertainty has been taken in term of fuzzy numbers. The governing equations of motion are first solved by the classical method to get responses of the consecutive stories. Further the governing equations of motion are modified based on relative responses of consecutive stories in such a way that the new set of equations can be implemented in a cluster of FNNs. As such the model starts solving the nth floor by FNN modelling to estimate the structural parameters. Subsequently, series of FNN models are used to estimate the parameters for (n ? 1)th storey to the first storey. One may note that single layer FNNs have been used for training for each cluster of the FNN such that the converged weights give the uncertain structural parameters. The initial weights in the FNN architecture are taken as the design parameters in uncertain (fuzzy) form. In order to validate the present model, various example problems of different multi-storey shear structures have been considered. Related results are incorporated in term of tables and graphs. Comparisons between theoretical and identified results are carried out and are found to be in good agreement.     

Interval spectral stochastic finite element analysis of structures with aggregation of random field and bounded parameters

This paper presents the study on non‐deterministic problems of structures with a mixture of random field and interval material properties under uncertain‐but‐bounded forces. Probabilistic framework is extended to handle the mixed uncertainties from structural parameters and loads by incorporating interval algorithms into spectral stochastic finite element method. Random interval formulations are developed based on K–L expansion and polynomial chaos accommodating the random field Young's modulus, interval Poisson's ratios and bounded applied forces. Numerical characteristics including mean value and standard deviation of the interval random structural responses are consequently obtained as intervals rather than deterministic values. The randomised low‐discrepancy sequences initialized particles and high‐order nonlinear inertia weight with multi‐dimensional parameters are employed to determine the change ranges of statistical moments of the random interval structural responses. The bounded probability density and cumulative distribution of the interval random response are then visualised. The feasibility, efficiency and usefulness of the proposed interval spectral stochastic finite element method are illustrated by three numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

模糊结构有限元分析的一种新方法

本文利用信息熵的概念,将模糊变量转变为随机变量,将模糊结构视为随机结构进行处理,从而提出了模糊结构有限元分析的一种新方法。当模糊结构转换的随机变量处于小扰动情况下,利用摄动法得到有限元递归方程组,解之可以得到响应量的均值和方差。     

基于模糊因子法的模糊桁架结构动力特性分析

研究了模糊桁架结构动力特性的分析方法,在结构的物理和几何参数同时为模糊变量的情况下,利用模糊因子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,利用区间运算法则推导出结构模糊特征值的表达式。通过算例考察了结构各参数的模糊性对其动力特性模糊性的影响,并获得了一些有意义的结论。该法对模糊结构进行一次动力分析便可求得动力特性,且可充分地反映任一模糊参数对结构模糊动力特性的影响。