PSI - Issue 19

A. Halfpenny et al. / Procedia Structural Integrity 19 (2019) 150–167 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The discrete approach follows the same procedure as the continuous. When a random Uniform value is chosen on the y axis of the CDF, this will project to a discrete value on the x axis. In this way both continuous and discrete distributions share the same basic approach and are integrated into the stochastic simulation in the same way.

Fig. 6. Overview of the discrete random selection method

2.4. The ‘Reduced Order Model (ROM)’ Stochastic fatigue simulation often requires a large number of simulation runs. In the case of large FEA models this can lead to excessive run times and significant file storage. This is addressed through the use of a ‘Reduced Order Model (ROM)’ (or ‘Surrogate Model’). The ROM is a transfer function relating the input loads to the stress responses at the critical failure locations. In most cases the ROM can be post-processed and will not require the FEA analysis to be run continually within the deterministic wrapper illustrated in Fig. 2. Furthermore, fatigue damage is exponentially correlated with stress. This helpfully ensures that even large FEA models can be reduced to relatively few critical fatigue initiation sites. It is therefore desirable to restrict FEA output to only those critical sites identified.  Linear-static FEA For linear static FEA models, the ROM is simply a scaling factor that relates an input load case to the stress tensor at a particular failure site. The resulting stress tensors are then summed over all the load cases using linear static superposition as illustrated in Equation (1) and discussed in [HBM 19]: �� ( ∑ � � ( ��,� (1) Where �� ( is the stress tensor time history at a particular critical node, � ( is the load time history for load case , and ��,� is the stress tensor result for load case k obtained from FEA under a static unit input load.  Harmonic analysis