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Nonlinear stochastic dynamic analysis by evolutionary tail-equivalent linearization method
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DOI：10.1016/j.strusafe.2020.102044.png)
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This study introduces the evolutionary tail-equivalent linearization method (ETELM) for nonlinear stochastic dynamic analysis. The method builds on the recently developed tail-equivalent linearization method (TELM) and it is designed for the class of evolutionary processes. The original TELM employs a tail-equivalent linear system (TELS) by equating the tail probability of a linear system response for a specified threshold to the first-order approximation of the tail probability of the nonlinear system response. For stationary problems, the TELS is time-independent and only one linear system needs to be defined for the specified threshold. However, for a transient input, the TELS is time dependent and an evolutionary tail-equivalent linear system (ETELS) must be defined to study the entire transient response. Algorithms are developed to determine a discrete-time ETELS based on a sequence of linearization points, and a continuous-time approximation based on Priestley's evolutionary theory. The linearized evolutionary system is used to compute the response statistics of interest, including the first-passage probability, in first-order approximation. Numerical examples demonstrate the accuracy and limitations of the proposed method.
Keyword:
Dynamics
Equivalent linearization
Evolutionary process
First-order methods
Nonlinear
Stochastic process
Non-stationary process
Metamodeling
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