The first part of the paper introduces an orthogonal expansion method for earthquake ground motion. In the method, seismic acceleration process is represented as a linear combination of deterministic functions modulated by 10 uncorrelated random variables. In the second part of the paper, the recently developed probability density evolution method (PDEM) is employed to study nonlinear random response of structures which are subjected to the external excitations. In the PDEM, a completely uncoupled one-dimensional governing partial differential equation, the generalized density evolution equation, is derived first with regard to evolutionary probability density function of the stochastic response for nonlinear structures. The solution of this equation can put out the instantaneous probability density function. So it is natural to combine the PDEM and the orthogonal expansion of seismic ground motion to study the nonlinear random earthquake response.Furthermore, the aseismatic 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 nonlinear frame structure subjected to ground motions, is illustrated to validate the proposed method.
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