Multilevel Monte Carlo simulations of composite structures with uncertain manufacturing defects

By adopting a Multilevel Monte Carlo (MLMC) framework, this paper shows 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 many thousands typically needed in classical Monte Carlo analyses. The paper introduces the MLMC method and provides an extension called MLMC with selective refinement to efficiently calculated structural failure probabilities. Simple-to-implement, self-adaptive algorithms are given, and the results demonstrate huge computational gains for two novel, real world example problems in composites performance analysis: (i) the effects of fibre waviness on the compressive strength of a composite material and (ii) the uncertain buckling performance of a composite panel with random ply orientations. For the most challenging test case of estimating a 1/150 probability of buckling failure of a composite panel the results demonstrate a speed-up factor of > 1000 over classical Monte Carlo. In absolute terms, the computational time was reduced from 218 CPU days to just 4.4 CPU hours, making stochastic simulations that would otherwise be unthinkable now possible.