Multilevel Monte Carlo Simulations of Composite Structures with Uncertain Manufacturing Defects

07/24/2019
by   T. J. Dodwell, et al.
0

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.?

READ FULL TEXT

page 5

page 10

research
10/29/2019

Accelerating System Adequacy Assessment using the Multilevel Monte Carlo Approach

Accurately and efficiently estimating system performance under uncertain...
research
10/10/2019

A full multigrid multilevel Monte Carlo method for the single phase subsurface flow with random coefficients

The subsurface flow is usually subject to uncertain porous media structu...
research
12/08/2022

A probabilistic peridynamic framework with an application to the study of the statistical size effect

Mathematical models are essential for understanding and making predictio...
research
08/10/2022

Adaptive multilevel subset simulation with selective refinement

In this work we propose an adaptive multilevel version of subset simulat...
research
10/06/2020

Efficient Graph-based Tensile Strength Simulations of Random Fiber Structures

In this paper, we propose a model-simulation framework for virtual tensi...
research
09/20/2019

SPSC: a new execution policy for exploring discrete-time stochastic simulations

In this paper, we introduce a new method called SPSC (Simulation, Partit...
research
08/21/2018

Efficient Propagation of Uncertainties in Manufacturing Supply Chains: Time Buckets, L-leap and Multilevel Monte Carlo

Uncertainty propagation of large scale discrete supply chains can be pro...

Please sign up or login with your details

Forgot password? Click here to reset