【作者】 律梦泽； 陈建兵；

【Author】 Meng-Ze Lyu;Jian-Bing Chen;College of Civil Engineering,Tongji University;

【机构】 同济大学土木工程学院；

【摘要】 高维非线性系统在随机动力作用下的可靠性分析对实际工程结构的抗灾设计和优化具有重要意义,但长久以来是力学和工程领域的重要挑战性难题。实际工程结构遭受的灾害性动力作用(如强风、地震等)往往具有显著的随机性、非平稳性和非白噪声特性,考虑这些复杂随机激励因素下的动力可靠度精细化分析尤为关键。本文基于广义概率密度全局演化方程,给出了一类高维非线性系统在非平稳非白噪声激励下动力可靠度计算的数值方法。具体地,对于非平稳非白噪声激励下的高维非线性系统,若仅关心某一感兴趣响应量在给定安全域下的首次超越可靠度,则可以构造该感兴趣量和某一辅助过程在安全域内的吸收边界过程,并建立吸收边界过程的广义密度全局演化方程。一般地,广义密度全局演化方程是一个二维偏微分方程,其中的本征漂移系数是驱动概率密度演化的全局性物理驱动力,可以通过原系统有限次代表性确定性动力分析的数据进行数值构造。通过数值求解广义密度全局演化方程,可以获得吸收边界过程的瞬时概率密度函数,进而将其在安全域内积分即为系统的动力可靠度。本文通过非平稳随机地震动作用下十层滞回非线性框架结构的可靠度分析,验证了该方法的数值精度的有效性,并讨论了需要进一步研究的问题。更多还原

【Abstract】 The reliability analysis of high-dimensional nonlinear systems under stochastic dynamic actions has long been an important challenge in mechanics and engineering.The disastrous dynamic actions,such as strong wind and earthquake,usually have complex non-stationary and non-white property.Based on the globally-evolving-based generalized density evolution equation(GE-GDEE),a numerical method for solving the dynamic reliability of high-dimensional nonlinear systems excited by non-stationary non-white noise is developed in this paper.Specifically,for the studied systems,if the first-passage reliability of one quantity of interest in a specified safe domain is of concern,the absorbing boundary processes(ABPs) of the quantity of interest and an auxiliary process can be constructed,and the GE-GDEE of the ABPs can be established.In general,the GE-GDEE is a two-dimensional partial differential equation,in which the intrinsic drift coefficient is the global physical driving force for evolution of the probability density function(PDF).It can be identified via the data of some representative deterministic dynamic analyses.The transient PDF of the ABP can be obtained by solving the GE-GDEE,and then the dynamic reliability is given.In this paper,an example is given for the reliability analysis of a ten-story hysteretic nonlinear frame structure under non-stationary stochastic ground motion,and the efficiency and accuracy of the proposed method is verified.Finally,the problems that need to be further studied are discussed.更多还原