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TABLEOFCONTENTS
1 ELASTICMODULIOFLAMINATES 1
1.1 Stressandstraintransformation 1
1.2 Transformationrelationsforstiffnesscomponents 4
1.3 Traceandotherinvariants 7
1.4 Transformedstiffnesscomponents 11
1.5 Transformationin3D 14
1.6 2Dand3Dtraces 19
1.7 Laminatedplates 24
1.8 Invariantsoflaminates 30
1.9 Quasi-Isotropiclaminates 34
1.10 Flexuralstiffnessofsymmetriclaminates 37
1.11 Generallaminates 40
1.12 Homogenization 45
1.13 In-planeandflexuralproblems 48
1.14 Conclusions 51
1.15 Sampleproblemsandtools 511.15.1 Stiffnessoflaminates 521.15.2 Accuracyoftrace-basedlaminatestiffness 57
2 LAMINATESTRENGTH 59
2.1 Basicplystrengthdata 60
2.2 Quadraticcriteriainstressspace 62
2.3 Quadraticcriteriainstrainspace 67
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2.4 Transformationoffailureenvelopes 69
2.5 Strength/stressratioandfailureindex 72
2.6 FirstPlyFailureenvelopesforlaminates 77
2.7 StrengthoflaminatesafterFirstPlyFailure–ultimatefailureenvelopes 82
2.8 Progressiveversussimultaneousdegradation 85
2.9 OmniStrainfailureenvelopesforlaminates 87
2.10 UnitCirclefailurecriterionforlaminates 93
2.11 Sampleproblemsandtools 99
3 LAMINATEDESIGN 113
3.1 Carpetplotoflegacyquad-axiallaminates 115
3.2 Bi-axiallaminates 123
3.3 Tri-axialsub-laminates 1273.3.1 Tri-axialregular 1293.3.2 Tri-axialhard 1313.3.3 Tri-axialsoft 1323.3.4 MatchingTri-axialwithLegacyQuad 133
3.4 Double-doublehelixsub-laminates 136
3.5 Double-doublehelixhybrids 145
3.6 Comparison between the legacy quad- and double-double helixsub-laminates 147
3.7 Replacementoflegacylaminatesbydouble-double 154
3.8 Hardandsoft[π/4] 157
3.9 Homogenizationasanenabler 161
3.10 Knock-downfactorfordouble-doublelaminates 164
3.11 Searchenginesforbestlaminate 168
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3.12 Summary 175
3.13 Toolsforbestlaminatesinsmoothandnotchedstrength 177
4 COMPOSITEGRID/SKINSTRUCTURES 185
4.1 Stiffnessofcompositesgrids 188
4.2 Threecommongrids 190
4.3 Compositegridswithskins 198
4.4 Efficiencyofgrid/skinconstructions 207
4.5 Failureenvelopes 213
4.6 Conclusions 216
4.7 Sampleproblemsandtools 218
5 TRACE-BASEDSCALINGANDBEAMOPTIMIZATIONUSINGPROFILERANK 223
5.1 Introduction 223
5.2 WeightoptimizationusingProfileRank 224
5.3 Trace-basedscaling 238
5.4 Scalingresultsandmastercurveofoptimalweight 242
5.5 Summaryanddiscussion 250
References 252
6 TRACE-BASEDDIRECTSIZINGMETHOD 253
6.1 Background 253
6.2 Laminatesizing 259
6.3 Materialselection 268
6.4 Casestudies 271
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6.4.1 Abi-axiallyloadedpanel 2716.4.2 Shearcasestudy 281
6.5 Finalremarksandperspectives 283
6.6 References 284
7 AUNIFIEDANDEFFICIENTDESIGN,TEST,ANDMANUFACTUREOFCOMPOSITELATTICESTRUCTURESANDPANELS 287
7.1 EllipsoidalPanelLatticeStructure 289
7.2 TubeLatticeStructure 293
7.3 BoxLatticeStructure 296
7.4 DoublePanel 297
7.5 BasicRecipe 300
7.6 ImportingIGESPanelGeometryintoTrueGrid® 301
7.7 COBELLSCommand 305
7.8 ElementProperties 309
7.9 AnalysisSteps 310
7.10 BoundarySplineCurve 311
7.11 LoadsandBoundaryConditions 312
7.12 VariableThickness 314
7.13 TapePaths 316
8 APPENDIXA-3D_BEAMMANUAL 319
8.1 Introduction 319
8.2 Generaldescription 3208.2.1 Coordinatesystems 3208.2.2 Element,nodeandelementgroup 3228.2.3 Directionsofsixdegreeoffreedomsandforces 322
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8.2.4 Brick,bricknodeandply 3238.2.5 Plyorientations 3238.2.6 Materialpropertyinput 324
8.3 Flowchart 325
8.4 Howtorun3D_Beam? 3268.4.1 Optionsetting 3278.4.2 Pre-processor 3288.4.3 Main-solver 3308.4.4 Post-processor 3338.4.5 Newrun 334
8.5 Examples 3358.5.1 Case1:CantileverRectangularboxbeam 3358.5.2 Case2:Cantileverbeamwithcircularcrosssection 3408.5.3 Case3:Compositebeamunderthree-pointbending 3448.5.4 Case4:ProfileRankforaluminumbeam 348
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Chapter 5 Sangwook Sihn University of Dayton Research Institute – USA [email protected]
Chapters 1 to 4 Stephen W. Tsai Department of Aeronautics & Astronautics Stanford University – USA [email protected]
Chapter 6 Albertino Jose Castanho Arteiro University of Porto – PORTUGAL
Chapter 7 Robert Rainsberger XYZ Scientific Applications, Inc. – USA [email protected]
Chapters 1 to 4 José Daniel D. Melo
Department of Materials Engineering Federal University of Rio Grande do Norte – BRAZIL
Visiting Scholar Department of Aeronautics & Astronautics
Stanford University – USA [email protected]
Dr. Arteiro wish to thank the support from FCT - Fundação para a Ciência e a Tecnologia through National Funds (project MITP-TB/PFM/0005/2013) for encouragement and support during the preparation of this work.
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