Multilevel Monte Carlo Simulations of Composite Structures with Uncertain Manufacturing Defects
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By adopting a Multilevel Monte Carlo (MLMC) framework, we show that only a handful of costly fine scale computations are needed to accurately estimate statistics of the failure of a composite structure, as opposed to the thousands typically needed in classical Monte Carlo analyses. We introduce the MLMC method, compare its theoretical complexity with classical Monte Carlo, and give a simple-to-implement algorithm which includes a simple extension called MLMC with selective refinement to efficiently calculated structural failure probabilities. To demonstrate the huge computational gains we present two benchmark problems in composites: (1) the effects of fibre waviness on the compressive strength of a composite material, (2) uncertain buckling performance of a composite panel with uncertain ply orientations. For our most challenging test case, estimating a rare (∼ 1/150) probability of buckling failure of a composite panel, we see a speed-up factor > 1000. Our approach distributed over 1024 processors reduces the computation time from 218 days to just 4.5 hours. This level of speed up makes stochastic simulations that would otherwise be unthinkable now possible.?
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