Design and Analysis of Composite Structures

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, One Side Free 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