Multilevel Monte Carlo Simulations of Composite Structures with Uncertain Manufacturing Defects

T. J. Dodwell, S. Kynaston, R. Butler, R. T. Haftka, Nam H. Kim, R. Scheichl

Research output: Contribution to journalArticlepeer-review

17 Citations (SciVal)


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.

Original languageEnglish
Article number103116
JournalProbabilistic Engineering Mechanics
Early online date17 Dec 2020
Publication statusPublished - 31 Jan 2021

Bibliographical note

Funding Information:
This work was supported by the EPSRC, United Kingdom ‘Multiscale Modelling of Aerospace Composites’ project ( EP/K031368/1 ), Dodwell is supported by a Turing AI, United Kingdom fellowship ( EP/N510129/1 ) and Butler held a Royal Academy of Engineering-GKN Aerospace Research Chair in Composites, United Kingdom .

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Civil and Structural Engineering
  • Nuclear Energy and Engineering
  • Aerospace Engineering
  • Condensed Matter Physics
  • Ocean Engineering
  • Mechanical Engineering


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