Reliability Analysis Of Nonlinear Stochastic Structures Based On Probability Density Evolution

Static and dynamic reliability analysis and uncertainty propagation of nonlinear stochastic structure are important research topics for domestic and abroad scholars, which have wide application prospect in engineering practice, and provide a solid theoretical basis for reliability design of the large scale and complex structure. This paper extends the use of probability density evolution method (PDEM) into the reliability analysis of nonlinear stochastic structures with complex performance functions, and dynamic response and reliability analysis of nonlinear structure under non-stationary excitations. Meanwhile, the influence mechanism of stochastic uncertainty propagation is investigated. The detailed contents are listed as follows.In reliability analysis and optimal design of structures, there exist some complex limit state functions with failure domain separation, multiple design points and discontinuous response etc. For such kind of reliability analysis of structures with complex limit state functions, FORM and SORM which are widely used and highly efficient become fail. Despite the numerical simulation methods (such as Monte Carlo simulation, subset simulation and line sampling etc.) can solve this problem, but their computational efficiency is quite low. In addition, there is no accurate and efficient computing approach to address the random dynamic response and reliability analysis of nonlinear structures subject to non-stationary excitations. In recent years, Li Jie and Chen Jianbing proposed the probability density evolution method which provides a unified solution framework for random vibration and reliability analysis of nonlinear structures.In this paper, the PDEM is applied to solve the difficult and important research subject of reliability analysis of structures with complicated limit state functions and uncertainty propagation. Actually, PDEM can obtain the probability density function of random structures under static and dynamic load, and is independent of any form of explicit and implicit limit state functions. Numerical results of several typical examples indicate that, the PDF curves and failure probabilities of stochastic structures with disjoint failure domains, multiple design points and discontinuous response are calculated effectively and accurately. Moreover, the PDEM has much higher efficiency than the Monte Carlo simulation, and is a potential and general approach to attack the reliability analysis of complicated problems.Subsequently, the uncertainty propagation and dynamic reliability analysis of nonlinear random structure under non-stationary excitations are addressed. The first passage failure criterion and stochastic harmonic function of power spectrum density model of non-stationary random process for earthquake action are utilized. The dynamic reliability computing of structures is performed based on the Matlab platform with calling the ANSYS general program. Numerical examples illustrate that the PDEM can achieve efficiently and accurately the dynamic response, transient PDF and reliability of nonlinear structures. Finally, the effects of random parameters on structural reliability and uncertainty propagation are examined in detail, and some suggestions for reliability design of engineering structures are given.