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中文核心期刊

非线性随机结构动力可靠度的密度演化方法

The probability density evolution method for dynamic reliability assessment of nonlinear stochastic structures

  • 摘要: 建议了一类新的非线性随机结构动力可靠度分析方法. 基于非线性随机结构反应分析的概率密度演化方法,根据首次超越破坏准则对概率密度演化方程施加相应的边界条件,求解带有初、边值条件的概率密度演化方程,可以给出非线性随机结构的动力可靠度. 研究了数值计算技术,建议了具有自适应功能的TVD差分格式. 以具有双线型恢复力性质的8层框架结构为例进行了地震作用下的动力可靠度分析,与随机模拟结果的比较表明,所建议的方法具有较高的精度和效率.

     

    Abstract: An original approach for dynamic reliability assessmentof nonlinear stochastic structures is proposed. In the past few years, a newmethod, named the probability density evolution method, has been developed,showing versatile capability in engineering stochastic mechanics such as thestochastic response analysis of either linear or nonlinear structures ineither static or dynamic occasions. In the method, the probability densityevolution equation, a first order quasi-linear partial differential equationin terms of the joint probability density, is deduced and uncoupled to aone-dimensional partial differential equation, which is easy to benumerically solved combining the deterministic dynamic response analysis ofstructures, such as the precise integration method or Newmark-Beta timeintegration method, and the finite difference method. Therefore, theinstantaneous probability density function, rather than the second orderstatistical characteristics such as the mean, the covariance function andthe power spectrum density and so on which are focused on by traditionalstochastic finite element methods, of the response quantities of interestcan be obtained. In the present paper, the probability density evolutionmethod is applied to assess the dynamic reliability of stochasticstructures. To achieve the purpose, an absorbing boundary conditioncorresponding to the failure criterion of the first passage problem isimposed on the probability density evolution equation. Solving theinitial-boundary-value partial differential equation problem with anumerical algorithm will give the ``remaining'' probability density functionof the response. The dynamic reliability can then be assessed throughintegrating the ``remaining'' probability density function over the safedomain. The numerical algorithm is studied in detail where an adaptive TVDdifference scheme is presented. In contrast to the widely usedlevel-crossing process based reliability assessment approach, in theproposed method the mean out-crossing rate, which is usually obtainedthrough the Rice formula, is not needed, nor the properties of thelevel-crossing process such as the Poisson and Markovian assumption.Therefore the proposed method is expected to have a high accuracy. An8-story frame structure with bilinear hysteretic restoring force, which issubjected to seismic excitation, is investigated. The results of dynamicreliability assessment are compared with those evaluated by the Monte Carlosimulation. The investigation shows that the proposed approach is of highaccuracy and efficiency.

     

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