Time-dependent reliability analysis for structures under multilevel loads based on fatigue damage theory

This paper proposes an efficient method to evaluate the time-dependent fatigue reliability of structures under complex multilevel loads using a finite set of fatigue test data obtained under single-level loading conditions. The method preserves the simplicity of linear damage accumulation theory while considering the interactions among multiple load levels and the influence of load sequence on reliability. Leveraging the linear damage rule, a cumulative damage probability model was established under single-level constant amplitude loading. This model incorporates a fatigue life degradation function to characterize the cumulative damage effect of load cycles and corrects the fatigue reliability curve under single-level constant amplitude loading. By employing the principle of fatigue damage equivalence, the method determines the damage equivalence at the load switching point using the damage curve method, enabling the conversion of equivalent reliability under multilevel loads. The proposed method was validated by combining the test data obtained under three working conditions, including two-level loads loading, load blocks loading, and changing loads loading. The results demonstrate that the proposed method can accurately and efficiently evaluate the time-dependent fatigue reliability under different types of multilevel loads, using only a limited set of fatigue life data under single constant amplitude loads.