论文部分内容阅读
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?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Monte Carlo法的对比验证了建议方法的高效性和准确性。
Local structural failure or reinforcement will lead to sudden changes in performance, resulting in serious structural discontinuity function, thus increasing the difficulty of reliability analysis. To this end, this paper intends to establish a time-varying reliability analysis method of the mutation structure within the framework of probability density evolution theory. First, the Heaviside function is introduced to establish the unified expression of the time-varying functional function of the abrupt structure. Secondly, the generalized density evolution equation of the bearing capacity of the abrupt structure is deduced based on this expression. In essence, The differential equation and the numerical solution are difficult to be solved. Thirdly, the Dirac? Sequence algorithm is introduced for the formal analytical solution of this equation, which provides a feasible method for obtaining the probability density function of bearing capacity margin. Then, , The probability density evolution method including time-dependent reliability analysis of catastrophe process is established. Finally, this method is applied to the time-dependent reliability analysis of the rebuilt and reinforced structure. A simple cantilever failure- The example proves the feasibility of the proposed algorithm and verifies the efficiency and accuracy of the proposed method by comparing with Monte Carlo method.