Fatigue analysis of structures with interval axial stiffness subjected to stationary stochastic excitations

The fatigue analysis of linear discretized structures with uncertain axial stiffnesses modeled as interval variables subjected to stationary multi-correlated Gaussian stochastic excitation is addressed. Due to uncertainty, all response quantities, including the expected fatigue life, are described by intervals. The key idea is to extend an empirical spectral approach proposed by Benasciutti and Tovo (Probab Eng Mech 21(4):287–299, 2006. https://​doi.​org/​10.​1016/​j.​probengmech.​2005.​10.​003), called \( \alpha_{0.75}^{{}} \)-method, to the interval framework. According to this approach, the expected fatigue life depends on four interval spectral moments of the critical stress process. Within the interval framework, the range of the interval expected fatigue life may be significantly overestimated by the classical interval analysis due to the dependency phenomenon which is particularly insidious for stress-related quantities. To limit the overestimation, a novel sensitivity-based procedure relying on a combination of the Interval Rational Series Expansion (Muscolino and Sofi in Mech Syst Signal Process 37(1–2):163–181, 2013. https://​doi.​org/​10.​1016/​j.​ymssp.​2012.​06.​016) and the Improved Interval Analysis via Extra Unitary Interval (Muscolino and Sofi in Probab Eng Mech 28:152–163, 2012. https://​doi.​org/​10.​1016/​j.​probengmech.​2011.​08.​011) is proposed. This procedure allows one to detect the combinations of the bounds of the interval axial stiffnesses which yield the lower bound and upper bound of the interval expected fatigue life. Sensitivity analysis is also exploited to identify the most influential uncertain parameters on the expected fatigue life. For validation purposes, a truss structure with uncertain axial stiffness under wind excitation is analyzed.