Computational Methods for Debonding in Composites

Contents xiii
10.5 VerificationsandExamples .................................210
10.5.1 TestCases........................................210
10.5.2 DiscussionontheEvaluationProcess.................215
10.5.3 4-phaseCompositeMaterial.........................216
10.6 ClosingRemarks..........................................219
Appendix–Thefourpartialderivatives.............................219
References.....................................................220
11 Prediction of Mechanical Properties of Composite Materials
by Asymptotic Expansion Homogenisation ...................... 223
J.A. Oliveira, J. Pinho-da-Cruz, and F. Teixeira-Dias
11.1 Introduction . . ............................................224
11.2 AsymptoticExpansionHomogenisation ......................224
11.2.1 AEHinLinearElasticity ...........................224
11.2.2 Localisation Methodology . . ........................228
11.3 FiniteElementMethodinAEH..............................229
11.3.1 Corrector χ ......................................229
11.3.2 Periodicity Boundary Conditions . ...................229
11.3.3 Homogenised Elasticity Matrix D h ...................230
11.4 NumericalProcedures .....................................230
11.4.1 TheMainProgram ................................230
11.4.2 RepresentativeUnit-CellGeneration..................231
11.4.3 AutomaticAssociationofDegreesofFreedom.........231
11.5 NumericalApplications....................................233
11.6 FinalRemarks............................................240
References.....................................................241
12 On Buckling Optimization of a Wind Turbine Blade .............. 243
Erik Lund and Leon S. Johansen
12.1 Introduction . . ............................................243
12.2 DiscreteMaterialOptimization(DMO)Approach..............245
12.2.1 Parametrization for Single Layered Laminate Structures . 246
12.2.2 Parametrization for Multi Layered Laminate Structures . . 247
12.2.3 PatchDesignVariables.............................247
12.2.4 DMOConvergence................................247
12.3 AnalysisandDesignSensitivityAnalysis .....................248
12.4 TheOptimizationProblem..................................249
12.5 BucklingOptimizationofWindTurbineBladeTestSection......250
12.6 Conclusion...............................................258
References.....................................................258
13 Computation of Effective Stiffness Properties for Textile-Reinforced
Composites Using X-FEM .................................... 261
M. Kästner, G. Haasemann, J. Brummund, and V. Ulbricht
13.1 Homogenization ..........................................261
13.1.1 Boundary Conditions and Deformation Modes .........264