About the Author xi
Series Preface xiii
Preface to First Edition xv
Preface to Second Edition xix
1 Applications of Advanced Composites in Aircraft Structures 1
References 7
2 Cost of Composites: a Qualitative Discussion 9
2.1 Recurring Cost 10
2.2 Nonrecurring Cost 18
2.3 Technology Selection 20
2.4 Summary and Conclusions 27
Exercises 30
References 31
3 Review of Classical Laminated Plate Theory 33
3.1 Composite Materials: Definitions, Symbols and Terminology 33
3.2 Constitutive Equations in Three Dimensions 35
3.2.1 Tensor Transformations 38
3.3 Constitutive Equations in Two Dimensions: Plane Stress 40
Exercises 52
References 53
4 Review of Laminate Strength and Failure Criteria 55
4.1 Maximum Stress Failure Theory 57
4.2 Maximum Strain Failure Theory 58
4.3 Tsai–Hill Failure Theory 58
4.4 Tsai–Wu Failure Theory 59
4.5 Puck Failure Theory 59
4.6 Other Failure Theories 61
References 62
5 Composite Structural Components and Mathematical Formulation 65
5.1 Overview of Composite Airframe 65
5.1.1 The Structural Design Process: The Analyst’s Perspective 66
5.1.2 Basic Design Concept and Process/Material Considerations for Aircraft Parts 71
5.1.3 Sources of Uncertainty: Applied Loads, Usage and Material Scatter 74
5.1.3.1 Knowledge of Applied Loads 75
5.1.3.2 Variability in Usage 75
5.1.3.3 Material Scatter 75
5.1.4 Environmental Effects 77
5.1.5 Effect of Damage 78
5.1.6 Design Values and Allowables 80
5.1.7 Additional Considerations of the Design Process 83
5.2 Governing Equations 84
5.2.1 Equilibrium Equations 84
5.2.2 Stress–Strain Equations 86
5.2.3 Strain–Displacement Equations 87
5.2.4 von Karman Anisotropic Plate Equations for Large Deflections 88
5.3 Reductions of Governing Equations: Applications to Specific Problems 94
5.3.1 Composite Plate under Localized In-Plane Load 94
5.3.2 Composite Plate under Out-of-Plane Point Load 105
5.4 Energy Methods 108
5.4.1 Energy Expressions for Composite Plates 109
5.4.1.1 Internal Strain Energy U 110
5.4.1.2 External Work W 113
Exercises 115
References 122
6 Buckling of Composite Plates 125
6.1 Buckling of Rectangular Composite Plate under Biaxial Loading 125
6.2 Buckling of Rectangular Composite Plate under Uniaxial Compression 129
6.2.1 Uniaxial Compression, Three Sides Simply Supported, OneSideFree 131
6.3 Buckling of Rectangular Composite Plate under Shear 133
6.4 Buckling of Long Rectangular Composite Plates under Shear 136
6.5 Buckling of Rectangular Composite Plates under Combined Loads 138
6.6 Design Equations for Different Boundary Conditions and Load Combinations 145
Exercises 145
References 152
7 Post-Buckling 153
7.1 Post-Buckling Analysis of Composite Panels under Compression 157
7.1.1 Application: Post-Buckled Panel under Compression 165
7.2 Post-Buckling Analysis of Composite Plates under Shear 168
7.2.1 Post-Buckling of Stiffened Composite Panels under Shear 172
7.2.1.1 Application: Post-Buckled Stiffened Fuselage Skin under Shear 177
7.2.2 Post-Buckling of Stiffened Composite Panels under Combined Uniaxial and Shear Loading 180
Exercises 181
References 187
8 Design and Analysis of Composite Beams 189
8.1 Cross-Section Definition Based on Design Guidelines 189
8.2 Cross-Sectional Properties 193
8.3 Column Buckling 199
8.4 Beam on an Elastic Foundation under Compression 200
8.5 Crippling 205
8.5.1 One-Edge-Free (OEF) Crippling 207
8.5.2 No-Edge-Free (NEF) Crippling 211
8.5.3 Crippling under Bending Loads 214
8.5.3.1 Application: Stiffener Design under Bending Loads 215
8.5.4 Crippling of Closed-Section Beams 219
8.6 Importance of Radius Regions at Flange Intersections 219
8.7 Inter-Rivet Buckling of Stiffener Flanges 222
8.8 Application: Analysis of Stiffeners in a Stiffened Panel under Compression 227
Exercises 230
References 235
9 Skin–Stiffened Structure 237
9.1 Smearing of Stiffness Properties (Equivalent Stiffness) 237
9.1.1 Equivalent Membrane Stiffnesses 237
9.1.2 Equivalent Bending Stiffnesses 239
9.2 Failure Modes of a Stiffened Panel 241
9.2.1 Local Buckling (between Stiffeners) versus Overall Panel Buckling (the Panel Breaker Condition) 242
9.2.1.1 Global Buckling = Local Buckling (Compression Loading) 243
9.2.1.2 Stiffener Buckling = PB × Buckling of Skin between Stiffeners (Compression Loading) 246
9.2.1.3 Example 249
9.2.2 Skin–Stiffener Separation 250
9.3 Additional Considerations for Stiffened Panels 265
9.3.1 ‘Pinching’ of Skin 265
9.3.2 Co-curing versus Bonding versus Fastening 266
Exercises 267
References 272
10 Sandwich Structure 275
10.1 Sandwich Bending Stiffnesses 276
10.2 Buckling of Sandwich Structure 278
10.2.1 Buckling of Sandwich under Compression 278
10.2.2 Buckling of Sandwich under Shear 280
10.2.3 Buckling of Sandwich under Combined Loading 281
10.3 Sandwich Wrinkling 281
10.3.1 Sandwich Wrinkling under Compression 282
10.3.2 Sandwich Wrinkling under Shear 293
10.3.3 Sandwich Wrinkling under Combined Loads 293
10.4 Sandwich Crimping 295
10.4.1 Sandwich Crimping under Compression 295
10.4.2 Sandwich Crimping under Shear 295
10.5 Sandwich Intracellular Buckling (Dimpling) under Compression 296
10.6 Attaching Sandwich Structures 296
10.6.1 Core Ramp-Down Regions 297
10.6.2 Alternatives to Core Ramp-Down 299
Exercises 301
References 306
11 Composite Fittings 309
11.1 Challenges in Creating Cost- and Weight-Efficient Composite Fittings 309
11.2 Basic Fittings 311
11.2.1 Clips 311
11.2.1.1 Tension Clips 311
11.2.1.2 Shear Clips 322
11.2.2 Lugs 328
11.2.2.1 Lug under Axial Loads 328
11.2.2.2 Lug under Transverse Loads 333
11.2.2.3 Lug under Oblique (Combined) Loads 337
11.3 Other Fittings 339
11.3.1 Bathtub Fittings 339
11.3.2 Root Fittings 340
Exercises 340
References 341
12 Good Design Practices and Design ‘Rules of Thumb’ 343
12.1 Layup/Stacking Sequence-related 343
12.2 Loading and Performance-related 344
12.3 Guidelines Related to Environmental Sensitivity and Manufacturing Constraints 345
12.4 Configuration and Layout-related 347
Exercises 348
References 349
13 Application – Design of a Composite Panel 351
13.1 Monolithic Laminate 351
13.2 Stiffened Panel Design 362
13.3 Sandwich Design 373
13.4 Cost Considerations 381
13.5 Comparison and Discussion 382
References 385
Index 387
