Non-Stationary Stochastic Dynamic Analysis by Tail-Equivalent Linearization

The Tail-Equivalent Linearization Method (TELM) is a recently developed computational method to solve nonlinear stochastic dynamic problems by the First-Order Reliability Method (FORM). TELM employs a Tail-Equivalent Linear System (TELS) by equating the tail probability of a linear system to the first-order approximation of the tail probability of the nonlinear system. For stationary problems, the TELS is time-independent and only one linear system needs to be defined to study the statistics of the response. However, for a transient input, the TELS is time-dependent. Thus, TELSs for different time points must be defined to study the non-stationary response. Since each TELS is obtained from the solution of an optimization problem, the computational cost required to solve the non-stationary problem can be prohibitive. This paper tackles the class of non-stationary problems described via evolutionary power spectral density by defining an evolutionary TELS (ETELS) in place of a series of point-in-time TELSs. An example shows the accuracy and effectiveness of the method. © 2013 Taylor & Francis Group, London.