Multilevel Monte Carlo Simulations of Composite Structures with Uncertain Manufacturing Defects

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 ($\sim 1/150$) 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.?