Physical synthesis method for global reliability analysis of engineering structures

Abstract

Global reliability analysis is quite essential for safety design and serviceability maintenance of modern engineering structures. Various reliability analysis methods have been proposed though, the issues of combination explosion as well as probabilistic correlation of system failure paths remain challenging. Practical applications of these methods are thus hindered, especially when complex, implicit, and nonlinear performance functions are involved. There isn’t an efficient way out of this dilemma until the emergence of the probability density evolution method (PDEM) combined with the equivalent extreme value event principle in recent years. The governing partial differential equations regarding the probability density evolution of a stochastic dynamical system are decoupled to a one-dimensional generalized probability density evolution equation (GPDEE) by employing the random event description. In conjunction with the PDEM, this paper explores a physical synthesis approach towards the global reliability analysis of actual engineering structures. Evaluation of multiple failure potential is incorporated into the mathematical resolving of the GPDEE for structural response at a representative point. An accurate and efficient solving procedure for the global reliability of probabilistic dissipative systems is presented where no need of seeking the failure paths and their associated probabilities. Numerical applications are examined to illustrate the use of the physical synthesis method as a practical analysis tool.