Substructuring for spectral fatigue analysis

Fatigue analysis under dynamic loading is a fundamental aspect of structural reliability. In many operating systems, such as wind turbines and marine vessels which the excitation is inherently random, spectral methods offer an efficient means of assessing vibration-induced fatigue, particularly in the high-cycle regime. A critical step in spectral fatigue assessment involves deriving the structural response spectrum, which can be computationally demanding. However, since fatigue damage is typically localized within critical substructures, this paper introduces a substructuring formulation for spectral fatigue analysis. A closed-form input–output relationship is derived to relate the power spectral density (PSD) of multiaxial zero-mean stationary Gaussian random excitations to the PSD of the stress tensor at the fatigue process zone through the frequency response function (FRF) of individual substructures. The equivalent von Mises stress criterion is employed to transform the multiaxial stress tensor response into an equivalent uniaxial stress for fatigue evaluation. Fatigue damage is estimated using Dirlik’s empirical formula for peak amplitude distribution, the Palmgren–Miner rule for linear damage accumulation, and the Basquin’s law for S–N curve characterization. Case studies demonstrate the efficiency and modularity of the proposed stochastic substructuring approach in the fatigue design process, in contrast to full-system spectral analysis, particularly for systems with a large number of degrees of freedom.