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Random loadings (RL) are prevalent in mechanical systems, yet their inherent stochasticity poses significant challenges to structural fatigue reliability assessment. In this study, a three-dimensional fatigue reliability model is developed under RL through amplitude modulating and Fourier transformation. The non-Gaussian RL characteristics are accurately characterized by employing power spectral density and loading kurtosis. The equivalent initial crack size distributions are evaluated through three-dimensional fatigue growth theory by joint use of the standard fatigue stress-life (S-N) data and the fatigue crack growth data of the materials. Fatigue life distributions in specimens made of different materials with different geometries and thicknesses are analyzed under RL. It is shown that fatigue life exhibits negative correlations with power spectral density, kurtosis, and initial crack size. Especially, it is found that fatigue life and kurtosis approximately follow a power–law relationship, with both mean and variance decreasing as kurtosis increases. Validations against the experimental data available in the literature show that the present model can provide an efficient prediction of the fatigue life of mechanical systems under RL with limited experiment data.

https://doi.org/10.1002/msd2.70042