Christos Kassapoglou - Delft University of Technology, The Netherlands

"Nevertheless, this book is an important contribution to the field and will provide a useful aid to postgraduate aerostructural engineers." (The Aeronautical Journal, 1 June 2014)

• About the Author xiSeries Preface xiiiPreface to First Edition xvPreface to Second Edition xix1 Applications of Advanced Composites in Aircraft Structures 1References 72 Cost of Composites: a Qualitative Discussion 92.1 Recurring Cost 102.2 Nonrecurring Cost 182.3 Technology Selection 202.4 Summary and Conclusions 27Exercises 30References 313 Review of Classical Laminated Plate Theory 333.1 Composite Materials: Definitions, Symbols and Terminology 333.2 Constitutive Equations in Three Dimensions 353.2.1 Tensor Transformations 383.3 Constitutive Equations in Two Dimensions: Plane Stress 40Exercises 52References 534 Review of Laminate Strength and Failure Criteria 554.1 Maximum Stress Failure Theory 574.2 Maximum Strain Failure Theory 584.3 Tsai–Hill Failure Theory 584.4 Tsai–Wu Failure Theory 594.5 Puck Failure Theory 594.6 Other Failure Theories 61References 625 Composite Structural Components and Mathematical Formulation 655.1 Overview of Composite Airframe 655.1.1 The Structural Design Process: The Analyst’s Perspective 665.1.2 Basic Design Concept and Process/Material Considerations for Aircraft Parts 715.1.3 Sources of Uncertainty: Applied Loads, Usage and Material Scatter 745.1.3.1 Knowledge of Applied Loads 755.1.3.2 Variability in Usage 755.1.3.3 Material Scatter 755.1.4 Environmental Effects 775.1.5 Effect of Damage 785.1.6 Design Values and Allowables 805.1.7 Additional Considerations of the Design Process 835.2 Governing Equations 845.2.1 Equilibrium Equations 845.2.2 Stress–Strain Equations 865.2.3 Strain–Displacement Equations 875.2.4 von Karman Anisotropic Plate Equations for Large Deflections 885.3 Reductions of Governing Equations: Applications to Specific Problems 945.3.1 Composite Plate under Localized In-Plane Load 945.3.2 Composite Plate under Out-of-Plane Point Load 1055.4 Energy Methods 1085.4.1 Energy Expressions for Composite Plates 1095.4.1.1 Internal Strain Energy U 1105.4.1.2 External Work W 113Exercises 115References 1226 Buckling of Composite Plates 1256.1 Buckling of Rectangular Composite Plate under Biaxial Loading 1256.2 Buckling of Rectangular Composite Plate under Uniaxial Compression 1296.2.1 Uniaxial Compression, Three Sides Simply Supported, OneSideFree 1316.3 Buckling of Rectangular Composite Plate under Shear 1336.4 Buckling of Long Rectangular Composite Plates under Shear 1366.5 Buckling of Rectangular Composite Plates under Combined Loads 1386.6 Design Equations for Different Boundary Conditions and Load Combinations 145Exercises 145References 1527 Post-Buckling 1537.1 Post-Buckling Analysis of Composite Panels under Compression 1577.1.1 Application: Post-Buckled Panel under Compression 1657.2 Post-Buckling Analysis of Composite Plates under Shear 1687.2.1 Post-Buckling of Stiffened Composite Panels under Shear 1727.2.1.1 Application: Post-Buckled Stiffened Fuselage Skin under Shear 1777.2.2 Post-Buckling of Stiffened Composite Panels under Combined Uniaxial and Shear Loading 180Exercises 181References 1878 Design and Analysis of Composite Beams 1898.1 Cross-Section Definition Based on Design Guidelines 1898.2 Cross-Sectional Properties 1938.3 Column Buckling 1998.4 Beam on an Elastic Foundation under Compression 2008.5 Crippling 2058.5.1 One-Edge-Free (OEF) Crippling 2078.5.2 No-Edge-Free (NEF) Crippling 2118.5.3 Crippling under Bending Loads 2148.5.3.1 Application: Stiffener Design under Bending Loads 2158.5.4 Crippling of Closed-Section Beams 2198.6 Importance of Radius Regions at Flange Intersections 2198.7 Inter-Rivet Buckling of Stiffener Flanges 2228.8 Application: Analysis of Stiffeners in a Stiffened Panel under Compression 227Exercises 230References 2359 Skin–Stiffened Structure 2379.1 Smearing of Stiffness Properties (Equivalent Stiffness) 2379.1.1 Equivalent Membrane Stiffnesses 2379.1.2 Equivalent Bending Stiffnesses 2399.2 Failure Modes of a Stiffened Panel 2419.2.1 Local Buckling (between Stiffeners) versus Overall Panel Buckling (the Panel Breaker Condition) 2429.2.1.1 Global Buckling = Local Buckling (Compression Loading) 2439.2.1.2 Stiffener Buckling = PB × Buckling of Skin between Stiffeners (Compression Loading) 2469.2.1.3 Example 2499.2.2 Skin–Stiffener Separation 2509.3 Additional Considerations for Stiffened Panels 2659.3.1 ‘Pinching’ of Skin 2659.3.2 Co-curing versus Bonding versus Fastening 266Exercises 267References 27210 Sandwich Structure 27510.1 Sandwich Bending Stiffnesses 27610.2 Buckling of Sandwich Structure 27810.2.1 Buckling of Sandwich under Compression 27810.2.2 Buckling of Sandwich under Shear 28010.2.3 Buckling of Sandwich under Combined Loading 28110.3 Sandwich Wrinkling 28110.3.1 Sandwich Wrinkling under Compression 28210.3.2 Sandwich Wrinkling under Shear 29310.3.3 Sandwich Wrinkling under Combined Loads 29310.4 Sandwich Crimping 29510.4.1 Sandwich Crimping under Compression 29510.4.2 Sandwich Crimping under Shear 29510.5 Sandwich Intracellular Buckling (Dimpling) under Compression 29610.6 Attaching Sandwich Structures 29610.6.1 Core Ramp-Down Regions 29710.6.2 Alternatives to Core Ramp-Down 299Exercises 301References 30611 Composite Fittings 30911.1 Challenges in Creating Cost- and Weight-Efficient Composite Fittings 30911.2 Basic Fittings 31111.2.1 Clips 31111.2.1.1 Tension Clips 31111.2.1.2 Shear Clips 32211.2.2 Lugs 32811.2.2.1 Lug under Axial Loads 32811.2.2.2 Lug under Transverse Loads 33311.2.2.3 Lug under Oblique (Combined) Loads 33711.3 Other Fittings 33911.3.1 Bathtub Fittings 33911.3.2 Root Fittings 340Exercises 340References 34112 Good Design Practices and Design ‘Rules of Thumb’ 34312.1 Layup/Stacking Sequence-related 34312.2 Loading and Performance-related 34412.3 Guidelines Related to Environmental Sensitivity and Manufacturing Constraints 34512.4 Configuration and Layout-related 347Exercises 348References 34913 Application – Design of a Composite Panel 35113.1 Monolithic Laminate 35113.2 Stiffened Panel Design 36213.3 Sandwich Design 37313.4 Cost Considerations 38113.5 Comparison and Discussion 382References 385Index 387

Christos Kassapoglou - Delft University of Technology, The Netherlands

"Nevertheless, this book is an important contribution to the field and will provide a useful aid to postgraduate aerostructural engineers." (The Aeronautical Journal, 1 June 2014)

• About the Author xiSeries Preface xiiiPreface to First Edition xvPreface to Second Edition xix1 Applications of Advanced Composites in Aircraft Structures 1References 72 Cost of Composites: a Qualitative Discussion 92.1 Recurring Cost 102.2 Nonrecurring Cost 182.3 Technology Selection 202.4 Summary and Conclusions 27Exercises 30References 313 Review of Classical Laminated Plate Theory 333.1 Composite Materials: Definitions, Symbols and Terminology 333.2 Constitutive Equations in Three Dimensions 353.2.1 Tensor Transformations 383.3 Constitutive Equations in Two Dimensions: Plane Stress 40Exercises 52References 534 Review of Laminate Strength and Failure Criteria 554.1 Maximum Stress Failure Theory 574.2 Maximum Strain Failure Theory 584.3 Tsai–Hill Failure Theory 584.4 Tsai–Wu Failure Theory 594.5 Puck Failure Theory 594.6 Other Failure Theories 61References 625 Composite Structural Components and Mathematical Formulation 655.1 Overview of Composite Airframe 655.1.1 The Structural Design Process: The Analyst’s Perspective 665.1.2 Basic Design Concept and Process/Material Considerations for Aircraft Parts 715.1.3 Sources of Uncertainty: Applied Loads, Usage and Material Scatter 745.1.3.1 Knowledge of Applied Loads 755.1.3.2 Variability in Usage 755.1.3.3 Material Scatter 755.1.4 Environmental Effects 775.1.5 Effect of Damage 785.1.6 Design Values and Allowables 805.1.7 Additional Considerations of the Design Process 835.2 Governing Equations 845.2.1 Equilibrium Equations 845.2.2 Stress–Strain Equations 865.2.3 Strain–Displacement Equations 875.2.4 von Karman Anisotropic Plate Equations for Large Deflections 885.3 Reductions of Governing Equations: Applications to Specific Problems 945.3.1 Composite Plate under Localized In-Plane Load 945.3.2 Composite Plate under Out-of-Plane Point Load 1055.4 Energy Methods 1085.4.1 Energy Expressions for Composite Plates 1095.4.1.1 Internal Strain Energy U 1105.4.1.2 External Work W 113Exercises 115References 1226 Buckling of Composite Plates 1256.1 Buckling of Rectangular Composite Plate under Biaxial Loading 1256.2 Buckling of Rectangular Composite Plate under Uniaxial Compression 1296.2.1 Uniaxial Compression, Three Sides Simply Supported, OneSideFree 1316.3 Buckling of Rectangular Composite Plate under Shear 1336.4 Buckling of Long Rectangular Composite Plates under Shear 1366.5 Buckling of Rectangular Composite Plates under Combined Loads 1386.6 Design Equations for Different Boundary Conditions and Load Combinations 145Exercises 145References 1527 Post-Buckling 1537.1 Post-Buckling Analysis of Composite Panels under Compression 1577.1.1 Application: Post-Buckled Panel under Compression 1657.2 Post-Buckling Analysis of Composite Plates under Shear 1687.2.1 Post-Buckling of Stiffened Composite Panels under Shear 1727.2.1.1 Application: Post-Buckled Stiffened Fuselage Skin under Shear 1777.2.2 Post-Buckling of Stiffened Composite Panels under Combined Uniaxial and Shear Loading 180Exercises 181References 1878 Design and Analysis of Composite Beams 1898.1 Cross-Section Definition Based on Design Guidelines 1898.2 Cross-Sectional Properties 1938.3 Column Buckling 1998.4 Beam on an Elastic Foundation under Compression 2008.5 Crippling 2058.5.1 One-Edge-Free (OEF) Crippling 2078.5.2 No-Edge-Free (NEF) Crippling 2118.5.3 Crippling under Bending Loads 2148.5.3.1 Application: Stiffener Design under Bending Loads 2158.5.4 Crippling of Closed-Section Beams 2198.6 Importance of Radius Regions at Flange Intersections 2198.7 Inter-Rivet Buckling of Stiffener Flanges 2228.8 Application: Analysis of Stiffeners in a Stiffened Panel under Compression 227Exercises 230References 2359 Skin–Stiffened Structure 2379.1 Smearing of Stiffness Properties (Equivalent Stiffness) 2379.1.1 Equivalent Membrane Stiffnesses 2379.1.2 Equivalent Bending Stiffnesses 2399.2 Failure Modes of a Stiffened Panel 2419.2.1 Local Buckling (between Stiffeners) versus Overall Panel Buckling (the Panel Breaker Condition) 2429.2.1.1 Global Buckling = Local Buckling (Compression Loading) 2439.2.1.2 Stiffener Buckling = PB × Buckling of Skin between Stiffeners (Compression Loading) 2469.2.1.3 Example 2499.2.2 Skin–Stiffener Separation 2509.3 Additional Considerations for Stiffened Panels 2659.3.1 ‘Pinching’ of Skin 2659.3.2 Co-curing versus Bonding versus Fastening 266Exercises 267References 27210 Sandwich Structure 27510.1 Sandwich Bending Stiffnesses 27610.2 Buckling of Sandwich Structure 27810.2.1 Buckling of Sandwich under Compression 27810.2.2 Buckling of Sandwich under Shear 28010.2.3 Buckling of Sandwich under Combined Loading 28110.3 Sandwich Wrinkling 28110.3.1 Sandwich Wrinkling under Compression 28210.3.2 Sandwich Wrinkling under Shear 29310.3.3 Sandwich Wrinkling under Combined Loads 29310.4 Sandwich Crimping 29510.4.1 Sandwich Crimping under Compression 29510.4.2 Sandwich Crimping under Shear 29510.5 Sandwich Intracellular Buckling (Dimpling) under Compression 29610.6 Attaching Sandwich Structures 29610.6.1 Core Ramp-Down Regions 29710.6.2 Alternatives to Core Ramp-Down 299Exercises 301References 30611 Composite Fittings 30911.1 Challenges in Creating Cost- and Weight-Efficient Composite Fittings 30911.2 Basic Fittings 31111.2.1 Clips 31111.2.1.1 Tension Clips 31111.2.1.2 Shear Clips 32211.2.2 Lugs 32811.2.2.1 Lug under Axial Loads 32811.2.2.2 Lug under Transverse Loads 33311.2.2.3 Lug under Oblique (Combined) Loads 33711.3 Other Fittings 33911.3.1 Bathtub Fittings 33911.3.2 Root Fittings 340Exercises 340References 34112 Good Design Practices and Design ‘Rules of Thumb’ 34312.1 Layup/Stacking Sequence-related 34312.2 Loading and Performance-related 34412.3 Guidelines Related to Environmental Sensitivity and Manufacturing Constraints 34512.4 Configuration and Layout-related 347Exercises 348References 34913 Application – Design of a Composite Panel 35113.1 Monolithic Laminate 35113.2 Stiffened Panel Design 36213.3 Sandwich Design 37313.4 Cost Considerations 38113.5 Comparison and Discussion 382References 385Index 387

Christos Kassapoglou - Delft University of Technology, The Netherlands

"Nevertheless, this book is an important contribution to the field and will provide a useful aid to postgraduate aerostructural engineers." (The Aeronautical Journal, 1 June 2014)

• About the Author xiSeries Preface xiiiPreface to First Edition xvPreface to Second Edition xix1 Applications of Advanced Composites in Aircraft Structures 1References 72 Cost of Composites: a Qualitative Discussion 92.1 Recurring Cost 102.2 Nonrecurring Cost 182.3 Technology Selection 202.4 Summary and Conclusions 27Exercises 30References 313 Review of Classical Laminated Plate Theory 333.1 Composite Materials: Definitions, Symbols and Terminology 333.2 Constitutive Equations in Three Dimensions 353.2.1 Tensor Transformations 383.3 Constitutive Equations in Two Dimensions: Plane Stress 40Exercises 52References 534 Review of Laminate Strength and Failure Criteria 554.1 Maximum Stress Failure Theory 574.2 Maximum Strain Failure Theory 584.3 Tsai–Hill Failure Theory 584.4 Tsai–Wu Failure Theory 594.5 Puck Failure Theory 594.6 Other Failure Theories 61References 625 Composite Structural Components and Mathematical Formulation 655.1 Overview of Composite Airframe 655.1.1 The Structural Design Process: The Analyst’s Perspective 665.1.2 Basic Design Concept and Process/Material Considerations for Aircraft Parts 715.1.3 Sources of Uncertainty: Applied Loads, Usage and Material Scatter 745.1.3.1 Knowledge of Applied Loads 755.1.3.2 Variability in Usage 755.1.3.3 Material Scatter 755.1.4 Environmental Effects 775.1.5 Effect of Damage 785.1.6 Design Values and Allowables 805.1.7 Additional Considerations of the Design Process 835.2 Governing Equations 845.2.1 Equilibrium Equations 845.2.2 Stress–Strain Equations 865.2.3 Strain–Displacement Equations 875.2.4 von Karman Anisotropic Plate Equations for Large Deflections 885.3 Reductions of Governing Equations: Applications to Specific Problems 945.3.1 Composite Plate under Localized In-Plane Load 945.3.2 Composite Plate under Out-of-Plane Point Load 1055.4 Energy Methods 1085.4.1 Energy Expressions for Composite Plates 1095.4.1.1 Internal Strain Energy U 1105.4.1.2 External Work W 113Exercises 115References 1226 Buckling of Composite Plates 1256.1 Buckling of Rectangular Composite Plate under Biaxial Loading 1256.2 Buckling of Rectangular Composite Plate under Uniaxial Compression 1296.2.1 Uniaxial Compression, Three Sides Simply Supported, OneSideFree 1316.3 Buckling of Rectangular Composite Plate under Shear 1336.4 Buckling of Long Rectangular Composite Plates under Shear 1366.5 Buckling of Rectangular Composite Plates under Combined Loads 1386.6 Design Equations for Different Boundary Conditions and Load Combinations 145Exercises 145References 1527 Post-Buckling 1537.1 Post-Buckling Analysis of Composite Panels under Compression 1577.1.1 Application: Post-Buckled Panel under Compression 1657.2 Post-Buckling Analysis of Composite Plates under Shear 1687.2.1 Post-Buckling of Stiffened Composite Panels under Shear 1727.2.1.1 Application: Post-Buckled Stiffened Fuselage Skin under Shear 1777.2.2 Post-Buckling of Stiffened Composite Panels under Combined Uniaxial and Shear Loading 180Exercises 181References 1878 Design and Analysis of Composite Beams 1898.1 Cross-Section Definition Based on Design Guidelines 1898.2 Cross-Sectional Properties 1938.3 Column Buckling 1998.4 Beam on an Elastic Foundation under Compression 2008.5 Crippling 2058.5.1 One-Edge-Free (OEF) Crippling 2078.5.2 No-Edge-Free (NEF) Crippling 2118.5.3 Crippling under Bending Loads 2148.5.3.1 Application: Stiffener Design under Bending Loads 2158.5.4 Crippling of Closed-Section Beams 2198.6 Importance of Radius Regions at Flange Intersections 2198.7 Inter-Rivet Buckling of Stiffener Flanges 2228.8 Application: Analysis of Stiffeners in a Stiffened Panel under Compression 227Exercises 230References 2359 Skin–Stiffened Structure 2379.1 Smearing of Stiffness Properties (Equivalent Stiffness) 2379.1.1 Equivalent Membrane Stiffnesses 2379.1.2 Equivalent Bending Stiffnesses 2399.2 Failure Modes of a Stiffened Panel 2419.2.1 Local Buckling (between Stiffeners) versus Overall Panel Buckling (the Panel Breaker Condition) 2429.2.1.1 Global Buckling = Local Buckling (Compression Loading) 2439.2.1.2 Stiffener Buckling = PB × Buckling of Skin between Stiffeners (Compression Loading) 2469.2.1.3 Example 2499.2.2 Skin–Stiffener Separation 2509.3 Additional Considerations for Stiffened Panels 2659.3.1 ‘Pinching’ of Skin 2659.3.2 Co-curing versus Bonding versus Fastening 266Exercises 267References 27210 Sandwich Structure 27510.1 Sandwich Bending Stiffnesses 27610.2 Buckling of Sandwich Structure 27810.2.1 Buckling of Sandwich under Compression 27810.2.2 Buckling of Sandwich under Shear 28010.2.3 Buckling of Sandwich under Combined Loading 28110.3 Sandwich Wrinkling 28110.3.1 Sandwich Wrinkling under Compression 28210.3.2 Sandwich Wrinkling under Shear 29310.3.3 Sandwich Wrinkling under Combined Loads 29310.4 Sandwich Crimping 29510.4.1 Sandwich Crimping under Compression 29510.4.2 Sandwich Crimping under Shear 29510.5 Sandwich Intracellular Buckling (Dimpling) under Compression 29610.6 Attaching Sandwich Structures 29610.6.1 Core Ramp-Down Regions 29710.6.2 Alternatives to Core Ramp-Down 299Exercises 301References 30611 Composite Fittings 30911.1 Challenges in Creating Cost- and Weight-Efficient Composite Fittings 30911.2 Basic Fittings 31111.2.1 Clips 31111.2.1.1 Tension Clips 31111.2.1.2 Shear Clips 32211.2.2 Lugs 32811.2.2.1 Lug under Axial Loads 32811.2.2.2 Lug under Transverse Loads 33311.2.2.3 Lug under Oblique (Combined) Loads 33711.3 Other Fittings 33911.3.1 Bathtub Fittings 33911.3.2 Root Fittings 340Exercises 340References 34112 Good Design Practices and Design ‘Rules of Thumb’ 34312.1 Layup/Stacking Sequence-related 34312.2 Loading and Performance-related 34412.3 Guidelines Related to Environmental Sensitivity and Manufacturing Constraints 34512.4 Configuration and Layout-related 347Exercises 348References 34913 Application – Design of a Composite Panel 35113.1 Monolithic Laminate 35113.2 Stiffened Panel Design 36213.3 Sandwich Design 37313.4 Cost Considerations 38113.5 Comparison and Discussion 382References 385Index 387