PSI - Issue 57

Andrew Halfpenny et al. / Procedia Structural Integrity 57 (2024) 718–730 Andrew Halfpenny / Structural Integrity Procedia 00 (2023) 000–000

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Fig. 3. Simulation of Uncertainty and Variability in Design

Even though aleatoric uncertainties are irreducible, it is important that accurate measurements are taken in order to characterise them. In the case of fatigue tests, for example, accurate loadcells and strain values are required to minimise the epistemic uncertainties such that the aleatoric uncertainties are accurately quantified.

3.1. Monte Carlo simulation and Reduced Order Models (ROM)

Stochastic simulation is performed using a Monte Carlo approach as illustrated in Fig. 3. The deterministic fa tigue analysis is run repeatedly with input parameters varied statistically with each run according to their individual probability distributions. This creates a sample of simulated fatigue life results which are processed using statistical reliability analysis. Stochastic fatigue simulation often requires a large number of simulation runs. In the case of large FE models this can lead to excessive run times and significant file storage. This is addressed through the use of a ‘Reduced Order Model’ (ROM), (also known as a ’Surrogate Model’). The ROM is e ff ectively a linear transfer function. It transforms input loads into resulting stress responses at the critical failure locations. It is based on the principal of linear superposition. In most cases the ROM is processed directly by the Monte Carlo loop and it is unnecessary to perform expensive FE analysis within the Monte Carlo process. An additional benefit with fatigue analysis is that fatigue is exponentially proportional to stress. This tends to minimise the number of critical failure modes and reduces the complexity of the ROM. 3.1.1. Linear-static FE analysis For linear static FE analysis, 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 eq. 1. σ ( t ) = k P k ( t ) · s k (1)