A Random Function Model of Ground Motion and PDEM-Based Seismic Reliability Analysis of Nonlinear Structures

Using the idea of random function, the standard orthogonal random variables in the spectral representation method are expressed as the orthogonal function form of basic random variables. Through the construction of two different forms of stochastic orthogonal trigonometric functions, non-Gaussian orthogonal random variables and Gaussian independent random variables can be represented by the orthogonal trigonometric functions of the basic random variables. Combining the power spectral density function of ground motion acceleration process, a numerical example is given to illustrate the effectiveness of the hybrid random function and spectral representation approach. It is natural to combine the recently developed probability density evolution method (PDEM) and the random function model of ground motion to study the non-linear random earthquake response. Moreover, the seismic reliability of structures is assessed using the idea of equivalent extreme-value, which can be used accurately to evaluate structural systems under compound failure criterion. Finally, an example which deals with a non-linear frame structure subjected to ground motions is illustrated to validate the above approach.