范文亮. 包含突变过程的结构时变可靠度的概率密度演化方法及其应用[J]. 工程力学, 2013, 30(12): 43-48,56. DOI: 10.6052/j.issn.1000-4750.2012.08.0627
引用本文: 范文亮. 包含突变过程的结构时变可靠度的概率密度演化方法及其应用[J]. 工程力学, 2013, 30(12): 43-48,56. DOI: 10.6052/j.issn.1000-4750.2012.08.0627
FAN Wen-liang. TIME-DEPENDENT RELIABILITY ANALYSIS OF STRUCTURE WITH PERFORMANCE MUTATIONS BASED ON PROBABILITY DENSITY EVOLUTION METHOD AND ITS APPLICATION[J]. Engineering Mechanics, 2013, 30(12): 43-48,56. DOI: 10.6052/j.issn.1000-4750.2012.08.0627
Citation: FAN Wen-liang. TIME-DEPENDENT RELIABILITY ANALYSIS OF STRUCTURE WITH PERFORMANCE MUTATIONS BASED ON PROBABILITY DENSITY EVOLUTION METHOD AND ITS APPLICATION[J]. Engineering Mechanics, 2013, 30(12): 43-48,56. DOI: 10.6052/j.issn.1000-4750.2012.08.0627

包含突变过程的结构时变可靠度的概率密度演化方法及其应用

TIME-DEPENDENT RELIABILITY ANALYSIS OF STRUCTURE WITH PERFORMANCE MUTATIONS BASED ON PROBABILITY DENSITY EVOLUTION METHOD AND ITS APPLICATION

  • 摘要: 结构的局部破坏或加固均会引起性能突变,导致结构功能函数严重不连续,从而增加可靠度分析的难度。为此,该文拟在概率密度演化理论的框架内建立突变结构的时变可靠度分析方法。首先,引入Heaviside函数建立了突变结构时变功能函数的统一表达式;其次,基于此表达式推导了突变结构承载力裕量的广义密度演化方程,本质上该方程为包含无穷系数的分段偏微分方程,数值求解困难;再次,针对该方程的形式解析解引入Dirac#x003b4;序列算法,为承载力裕量概率密度函数的获取提供了可行的方法;然后,给出了突变结构时变可靠度分析的一维积分公式,建立了包含突变过程的时变可靠度分析的概率密度演化方法;最后,将其应用于改造加固结构的时变可靠度分析,并以一个简单的悬臂梁破坏-加固算例验证了建议算法的可行性,且通过与MonteCarlo法的对比验证了建议方法的高效性和准确性。

     

    Abstract: Structural performance changes dramatically due to structure damaging or strengthening locally, and performance function becomes discontinuous, which causes much difficulty in time dependent reliability analysis. In this work, time-dependent reliability analysis method for structure with performance jump discontinuities is developed in the frame of probability density evolution theory. Firstly, Heaviside step function is introduced to rewrite a piecewise function into a general function. Secondly, a generalized density evolution equation (GDEE) for margin of ultimate limit capacity (ULC) is derived, where one of the coefficients is a Dirac #x003b4;function. In fact, this equation is a piecewise partial difference equation with infinite coefficient, which is very difficult to solve. Thirdly, approximation of Dirac #x003b4;function by Dirac #x003b4;sequences is introduced into the analytical solution of GDEE, and it becomes feasible to obtain the numerical solution for probability density function (PDF) for margin of ULC. And then, one dimensional integral formula for time dependent reliability analysis of structure with performance jump discontinuities is proposed, and the probability density evolution method (PDEM) is built up. Finally, the proposed method is used to analyze time-dependent reliability of strengthened structure, and its efficiency and precision are verified by comparing with Monte Carlo method (MCM), where a cantilever beam strengthened with carbon fiber sheet is taken as example.

     

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