Techniques for Optimisation and Analysis of Composite Structures for Damage Tolerance and Buckling Stiffness

Neil Baker

Research output: ThesisDoctoral Thesis

Abstract

This thesis explores methods by which carbon fibre reinforced polymers may be
fficiently designed with the inclusion of damage tolerance criteria. An efficient method of modelling the compression after impact (CAI) strength of composite materials is selected, and this forms the basis of analysis performed.
The CAI model is initially used as the objective in an optimisation routine using
a simple genetic algorithm. This indicates features of a damage tolerant composite laminate, namely that plies near the surface are less axially sti® in the loading direction than those nearer the laminate midplane, with a lower Poisson's ratio than the full laminate. This delays sublaminate buckling under laminate uniaxial compression, thus restricting delamination propagation. The designs produced by the optimisation are verified experimentally.
In order to improve the computational efficiency of the CAI model a simple surrogate modelling technique for sublaminate buckling is presented. This allows a complete database of results to be produced for a given set of ply angles, in this case standard 0/90/§45± plies. This is used in the full analysis of a collection of layups produced elsewhere to be fully uncoupled, but without the stipulation of midplane symmetry.
The surrogate method is shown to reduce computation time by over 99%, and produce results with an average error of less than 0.1% compared to exhaustive analysis. The analysis of the damage tolerance of fully uncoupled laminates shows that the relaxation of midplane symmetry as a design rule gives the designer far more flexibility in layup, and may allow for more damage tolerant laminates to be selected.
Finally, the CAI model is incorporated into a stiffened panel design optimisation
problem as a constraint. Firstly the panel is optimised using the in¯nite strip analysis tool VICONOPT, with three stiffener geometries. The objective function is minimum mass for a panel subject to compressive and out-of-plane loading, with buckling and strain allowable constraints applied. Damage tolerance constraints are then applied in place of a strain allowable, using a bi-level optimisation approach. This method is shown to allow efficient inclusion of damage tolerance as a constraint in stiffened panel design, although it does not account for interactions in global buckling and local sublaminate buckling which may reduce the strength of the panel. Results indicate that the inclusion of damage tolerance analysis in stiffened panel design shows little benefit for low load panels, but can give significant reductions in mass (up to 30%) for higher load panels.
LanguageEnglish
QualificationPh.D.
Awarding Institution
  • University of Bath
Supervisors/Advisors
  • Butler, Richard, Supervisor
Award date30 Jun 2012
StatusUnpublished - Jun 2012

Fingerprint

Damage tolerance
Composite structures
Laminates
Buckling
Stiffness
Compaction
Composite materials
Poisson ratio
Impact strength
Computational efficiency
Delamination
Carbon fibers
Crack propagation
Genetic algorithms
Geometry
Polymers

Keywords

  • composites
  • structures
  • damage tolerance

Cite this

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title = "Techniques for Optimisation and Analysis of Composite Structures for Damage Tolerance and Buckling Stiffness",
abstract = "This thesis explores methods by which carbon fibre reinforced polymers may befficiently designed with the inclusion of damage tolerance criteria. An efficient method of modelling the compression after impact (CAI) strength of composite materials is selected, and this forms the basis of analysis performed.The CAI model is initially used as the objective in an optimisation routine usinga simple genetic algorithm. This indicates features of a damage tolerant composite laminate, namely that plies near the surface are less axially sti{\circledR} in the loading direction than those nearer the laminate midplane, with a lower Poisson's ratio than the full laminate. This delays sublaminate buckling under laminate uniaxial compression, thus restricting delamination propagation. The designs produced by the optimisation are verified experimentally.In order to improve the computational efficiency of the CAI model a simple surrogate modelling technique for sublaminate buckling is presented. This allows a complete database of results to be produced for a given set of ply angles, in this case standard 0/90/§45± plies. This is used in the full analysis of a collection of layups produced elsewhere to be fully uncoupled, but without the stipulation of midplane symmetry.The surrogate method is shown to reduce computation time by over 99{\%}, and produce results with an average error of less than 0.1{\%} compared to exhaustive analysis. The analysis of the damage tolerance of fully uncoupled laminates shows that the relaxation of midplane symmetry as a design rule gives the designer far more flexibility in layup, and may allow for more damage tolerant laminates to be selected.Finally, the CAI model is incorporated into a stiffened panel design optimisationproblem as a constraint. Firstly the panel is optimised using the in¯nite strip analysis tool VICONOPT, with three stiffener geometries. The objective function is minimum mass for a panel subject to compressive and out-of-plane loading, with buckling and strain allowable constraints applied. Damage tolerance constraints are then applied in place of a strain allowable, using a bi-level optimisation approach. This method is shown to allow efficient inclusion of damage tolerance as a constraint in stiffened panel design, although it does not account for interactions in global buckling and local sublaminate buckling which may reduce the strength of the panel. Results indicate that the inclusion of damage tolerance analysis in stiffened panel design shows little benefit for low load panels, but can give significant reductions in mass (up to 30{\%}) for higher load panels.",
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author = "Neil Baker",
year = "2012",
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school = "University of Bath",

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N2 - This thesis explores methods by which carbon fibre reinforced polymers may befficiently designed with the inclusion of damage tolerance criteria. An efficient method of modelling the compression after impact (CAI) strength of composite materials is selected, and this forms the basis of analysis performed.The CAI model is initially used as the objective in an optimisation routine usinga simple genetic algorithm. This indicates features of a damage tolerant composite laminate, namely that plies near the surface are less axially sti® in the loading direction than those nearer the laminate midplane, with a lower Poisson's ratio than the full laminate. This delays sublaminate buckling under laminate uniaxial compression, thus restricting delamination propagation. The designs produced by the optimisation are verified experimentally.In order to improve the computational efficiency of the CAI model a simple surrogate modelling technique for sublaminate buckling is presented. This allows a complete database of results to be produced for a given set of ply angles, in this case standard 0/90/§45± plies. This is used in the full analysis of a collection of layups produced elsewhere to be fully uncoupled, but without the stipulation of midplane symmetry.The surrogate method is shown to reduce computation time by over 99%, and produce results with an average error of less than 0.1% compared to exhaustive analysis. The analysis of the damage tolerance of fully uncoupled laminates shows that the relaxation of midplane symmetry as a design rule gives the designer far more flexibility in layup, and may allow for more damage tolerant laminates to be selected.Finally, the CAI model is incorporated into a stiffened panel design optimisationproblem as a constraint. Firstly the panel is optimised using the in¯nite strip analysis tool VICONOPT, with three stiffener geometries. The objective function is minimum mass for a panel subject to compressive and out-of-plane loading, with buckling and strain allowable constraints applied. Damage tolerance constraints are then applied in place of a strain allowable, using a bi-level optimisation approach. This method is shown to allow efficient inclusion of damage tolerance as a constraint in stiffened panel design, although it does not account for interactions in global buckling and local sublaminate buckling which may reduce the strength of the panel. Results indicate that the inclusion of damage tolerance analysis in stiffened panel design shows little benefit for low load panels, but can give significant reductions in mass (up to 30%) for higher load panels.

AB - This thesis explores methods by which carbon fibre reinforced polymers may befficiently designed with the inclusion of damage tolerance criteria. An efficient method of modelling the compression after impact (CAI) strength of composite materials is selected, and this forms the basis of analysis performed.The CAI model is initially used as the objective in an optimisation routine usinga simple genetic algorithm. This indicates features of a damage tolerant composite laminate, namely that plies near the surface are less axially sti® in the loading direction than those nearer the laminate midplane, with a lower Poisson's ratio than the full laminate. This delays sublaminate buckling under laminate uniaxial compression, thus restricting delamination propagation. The designs produced by the optimisation are verified experimentally.In order to improve the computational efficiency of the CAI model a simple surrogate modelling technique for sublaminate buckling is presented. This allows a complete database of results to be produced for a given set of ply angles, in this case standard 0/90/§45± plies. This is used in the full analysis of a collection of layups produced elsewhere to be fully uncoupled, but without the stipulation of midplane symmetry.The surrogate method is shown to reduce computation time by over 99%, and produce results with an average error of less than 0.1% compared to exhaustive analysis. The analysis of the damage tolerance of fully uncoupled laminates shows that the relaxation of midplane symmetry as a design rule gives the designer far more flexibility in layup, and may allow for more damage tolerant laminates to be selected.Finally, the CAI model is incorporated into a stiffened panel design optimisationproblem as a constraint. Firstly the panel is optimised using the in¯nite strip analysis tool VICONOPT, with three stiffener geometries. The objective function is minimum mass for a panel subject to compressive and out-of-plane loading, with buckling and strain allowable constraints applied. Damage tolerance constraints are then applied in place of a strain allowable, using a bi-level optimisation approach. This method is shown to allow efficient inclusion of damage tolerance as a constraint in stiffened panel design, although it does not account for interactions in global buckling and local sublaminate buckling which may reduce the strength of the panel. Results indicate that the inclusion of damage tolerance analysis in stiffened panel design shows little benefit for low load panels, but can give significant reductions in mass (up to 30%) for higher load panels.

KW - composites

KW - structures

KW - damage tolerance

M3 - Doctoral Thesis

ER -