Theoretical and numerical investigation of stress mode shapes in multi-axial random fatigue

Abstract Random fatigue is inherently multi-axial due to the complex stress state in real vibrating structures. This paper investigates the role of Stress Modal Analysis (SMA) in multi-axial random fatigue. Predicting hotspots of multi-axial random fatigue by Stress Mode Shapes (SMSs) was theoretically demonstrated. An improved approach was proposed to exploit SMSs in random fatigue with a multi-axial criterion. First, SMA is conducted to locate the multi-axial fatigue hotspots in a vibrating structure. Second, the frequency-domain approach for random fatigue is performed at the identified hotspots. The capability of SMSs in locating multi-axial fatigue hotspots was verified by numerical investigation. The finite element (FE) model of an L-shaped thin-walled structure containing geometry changes was constructed for case study. Local regions were identified as hotspots by SMSs information. Then, random response and multi-axial fatigue damage of the whole structure were evaluated for verification. Damage map indicates that the critical positions predicted by SMSs have good accuracy. Results show the improved approach with SMA can ensure both accuracy and efficiency for multi-axial random fatigue.