A gradient-free method for determining the design point in nonlinear stochastic dynamic analysis

A gradient-free method is developed for finding the design point in nonlinear stochastic dynamic analysis, where the input excitation is discretized into a large number of random variables. This point defines the realization of the excitation that is most likely to give rise to a specific response threshold at a given time. The design point is the essential information in the recently developed tail-equivalent linearization method. The proposed approach employs a variant of the model correction factor method developed by O. Ditlevsen, which is further improved by the use of a novel response surface technique. Example applications to single- and multi-degree-of-freedom hysteretic systems demonstrate the efficiency and accuracy of the method.

► First-order reliability method, FORM, solves nonlinear stochastic dynamic problems.
► Novel response surface method avoids the need to compute response gradients.
► Example applications demonstrate the accuracy and efficiency of the method.