Stochastic Analysis of Composite Materials
Author(s)
Whiteside, M. B.
Type
Thesis
Abstract
This thesis describes the development of stochastic analysis frameworks for
use in engineering design and optimisation. The research focuses on fibre-reinforced
composites, with the stochastic analyses of an existing analytical
failure model for unidirectional composites and of a unit cell numerical model
of a 2D 5-Harness satin weave.
Stochastic failure envelopes are generated through parallelised Monte Carlo
Simulation of deterministic, analytical, physically based failure criteria for
unidirectional carbon fibre/epoxy matrix composite plies. Monte Carlo integration
of global variance-based Sobol sensitivity indices is performed and
utilised to decompose observed variance within stochastic failure envelopes into
contributions from physical input parameters. It is observed how the interaction
effect can be used to identify domains of bi-modal failure, within which
the predicted failure probability is governed by multiple failure modes.
A reduced unit cell (rUC) model of a 5-Harness satin weave is constructed
and analysed deterministically in uniaxial and biaxial loading conditions. An
algorithm is developed and implemented to fully automate the rUC construction
such that stochastic variations of the crimp angle can be evaluated. Monte
Carlo Simulation is employed to propagate the effect of the crimp angle through
the deterministic model and the probabilistic response compared with data obtained
experimentally. It is observed how simulated variability compares well
in uni-axial compression, but under-predicts observed experimental variability
in uni-axial tension. The influence of vertical stacking sequence of plies
is also demonstrated through the study of in-phase and out-of-phase periodic
boundary conditions.
The research highlights various, potential advantages that stochastic methodologies
offer over the traditional deterministic approach, making a case for
their application in engineering design and providing a springboard for further
research come the day when greater computational power is available.
use in engineering design and optimisation. The research focuses on fibre-reinforced
composites, with the stochastic analyses of an existing analytical
failure model for unidirectional composites and of a unit cell numerical model
of a 2D 5-Harness satin weave.
Stochastic failure envelopes are generated through parallelised Monte Carlo
Simulation of deterministic, analytical, physically based failure criteria for
unidirectional carbon fibre/epoxy matrix composite plies. Monte Carlo integration
of global variance-based Sobol sensitivity indices is performed and
utilised to decompose observed variance within stochastic failure envelopes into
contributions from physical input parameters. It is observed how the interaction
effect can be used to identify domains of bi-modal failure, within which
the predicted failure probability is governed by multiple failure modes.
A reduced unit cell (rUC) model of a 5-Harness satin weave is constructed
and analysed deterministically in uniaxial and biaxial loading conditions. An
algorithm is developed and implemented to fully automate the rUC construction
such that stochastic variations of the crimp angle can be evaluated. Monte
Carlo Simulation is employed to propagate the effect of the crimp angle through
the deterministic model and the probabilistic response compared with data obtained
experimentally. It is observed how simulated variability compares well
in uni-axial compression, but under-predicts observed experimental variability
in uni-axial tension. The influence of vertical stacking sequence of plies
is also demonstrated through the study of in-phase and out-of-phase periodic
boundary conditions.
The research highlights various, potential advantages that stochastic methodologies
offer over the traditional deterministic approach, making a case for
their application in engineering design and providing a springboard for further
research come the day when greater computational power is available.
Date Issued
2012
Date Awarded
2012-08
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Silvestre, Pinho
Robinson, Paul
Sponsor
Engineering and Physical Sciences Research Council ; BAE SYSTEMS (Firm)
Grant Number
09000055
Publisher Department
Aeronautics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)