非平稳随机激励下结构体系动力可靠度时域解法

将结构动力方程写成状态方程形式，采用精细积分法对其进行数值求解，导出了非平稳激励下结构随机响应的时域显式表达式，该过程的计算量仅相当于两次确定性时程分析的计算量. 基于该显式表达式，结合首次超越失效准则，提出了非平稳随机激励下结构体系动力可靠度的数值模拟算法. 与功率谱方法相比，该方法无需同时在时频域内进行大量数值积分，也无需引入关于响应过程跨越界限次数概率分布, 以及各失效模式相关性等方面的假定. 通过数值算例, 对比了该方法与泊松过程法、马尔可夫过程法、传统蒙特卡罗法的计算精度和计算效率，结果显示该方法具有理想的精度和相当高的效率. 

TIME-DOMAIN METHOD FOR DYNAMIC RELIABILITY OF STRUCTURAL SYSTEMS SUBJECTED TO NON-STATIONARY RANDOM EXCITATIONS

Structural dynamic equations are first transformed into the form of state equations, which are solved by the precise time integral method, and then explicit expressions of structural random responses under non-stationary excitations are deduced in the time domain. The computational effort for such explicit formulation is only equivalent to that for two deterministic time-history analyses of the structure. Based on the above explicit expressions and combined with the first-excursion failure criterion, a numerical simulation method is proposed for solving dynamic reliability of structural system under non-stationary random excitations. As compared with the power spectrum method, the proposed method does not require a large amount of numerical integrals in both frequency and time domains. Furthermore, the assumptions are no longer required in the present approach with respect to the probability distribution of the excursion number and the correlation between different failure modes. With numerical examples, the calculation accuracy and efficiency of the proposed method are compared with those of the conventional Monte Carlo simulation method, the Poisson process method and the Markov process method. Numerical results indicate that the proposed method has perfect accuracy and reasonably high efficiency.