Coupled critical plane-pseudo excitation method for multiaxial fatigue analysis of structures under random vibration

This study proposes a coupled critical plane–pseudo excitation method for assessing multiaxial fatigue damage in mechanical structures subjected to random loads. Within the modal coordinate framework, we derive an expression for the spectral moment of the structural stress response using the pseudo excitation method, which facilitates the decoupling of spatial characteristics from frequency domain properties. For the input power spectral density, represented as an integer power function, we employ eigenvalue decomposition and the residue theorem to derive an analytical expression for the spectral moment of the modal displacement response. By constructing equivalent stress modes based on the maximum shear stress and normal stress criteria, we obtain an expression for the equivalent stress variance. Intelligent optimization algorithms are utilized to determine the critical plane position and the corresponding equivalent stress spectral moments, followed by the application of the Dirlik method for fatigue assessment. A numerical example involving random vibration multiaxial fatigue analysis of an L-shaped thin-walled plate demonstrates the effectiveness of the proposed coupled critical plane–pseudo excitation method in comparison to the traditional critical plane method that relies on the stress covariance matrix for calculating equivalent variance. The results confirm the accuracy and efficiency of our approach, and we further explore the impact of different forms of the excitation power spectral density and the damping ratios on the computational outcomes.