Spectral Method for Fatigue Damage Assessment of Structures with Uncertain Parameters

This study presents a spectral method for fatigue damage evaluation of linear structures with uncertain-but-bounded parameters subjected to the stationary multi-correlated Gaussian random excitation. The first step of the proposed method is to model uncertain parameters by introducing interval theory. Within the framework of interval analysis, the approximate expressions of the bounds of spectral moments of generic response are obtained by the improved interval analysis via the Extra Unitary Interval and Interval Rational Series Expansion. Based on the cumulative damage theory and the Tovo-Benasciutti method, the lower and upper bounds of expected fatigue damage rate are accurately evaluated by properly combining the bounds of the spectral parameters of the power density spectral function of stress of critical points. Finally, a numerical example concerning a truss under random excitation is used to illustrate the accuracy and efficiency of the proposed method by comparing with the vertex method.