DESIGN AND ANALYSIS OF COMPOSITE STRUCTURES WITH APPLICATIONS TO AEROSPACE STRUCTURES Christos Kassapoglou Delft University of Technology,The Netherlands WILEY AJohn Wiley and Sons,Ltd,Publication
DESIGN AND ANALYSIS OF COMPOSITE STRUCTURES WITH APPLICATIONS TO AEROSPACE STRUCTURES Christos Kassapoglou Delft University of Technology, The Netherlands
Aerospace Series List Cooperative Path Planning of Unmanned Tsourdos et al November 2010 Aerial Vehicles Principles of Flight for Pilots Swatton October 2010 Air Travel and Health:A Systems Seabridge et al September 2010 Perspective Design and Analysis of Composite Kassapoglou September 2010 Structures:With Applications to Aerospace Structures Unmanned Aircraft Systems:UAVS Austin April 2010 Design,Development and Deployment Introduction to Antenna Placement Installations Macnamara April 2010 Principles of Flight Simulation Allerton October 2009 Aircraft Fuel Systems Langton et al May 2009 The Global Airline Industry Belobaba April 2009 Computational Modelling and Simulation of Diston April 2009 Aircraft and the Environment:Volume 1- Platform Kinematics and Synthetic Environment Handbook of Space Technology Ley,Wittmann April 2009 Hallmann Aircraft Performance Theory and Swatton August 2008 Practice for Pilots Surrogate Modelling in Engineering Forrester,Sobester, August 2008 Design:A Practical Guide Keane Aircraft Systems,3rd Edition Moir Seabridge March 2008 Introduction to Aircraft Aeroelasticity And Loads Wright Cooper December 2007 Stability and Control of Aircraft Systems Langton September 2006 Military Avionics Systems Moir Seabridge February 2006 Design and Development of Aircraft Systems Moir Seabridge June 2004 Aircraft Loading and Structural Layout Howe May 2004 Aircraft Display Systems Jukes December 2003 Civil Avionics Systems Moir Seabridge December 2002
Aerospace Series List Cooperative Path Planning of Unmanned Tsourdos et al November 2010 Aerial Vehicles Principles of Flight for Pilots Swatton October 2010 Air Travel and Health: A Systems Seabridge et al September 2010 Perspective Design and Analysis of Composite Kassapoglou September 2010 Structures: With Applications to Aerospace Structures Unmanned Aircraft Systems: UAVS Design, Development and Deployment Austin April 2010 Introduction to Antenna Placement & Installations Macnamara April 2010 Principles of Flight Simulation Allerton October 2009 Aircraft Fuel Systems Langton et al May 2009 The Global Airline Industry Belobaba April 2009 Computational Modelling and Simulation of Diston April 2009 Aircraft and the Environment: Volume 1 - Platform Kinematics and Synthetic Environment Handbook of Space Technology Ley, Wittmann April 2009 Hallmann Aircraft Performance Theory and Swatton August 2008 Practice for Pilots Surrogate Modelling in Engineering Forrester, Sobester, August 2008 Design: A Practical Guide Keane Aircraft Systems, 3rd Edition Moir & Seabridge March 2008 Introduction to Aircraft Aeroelasticity And Loads Wright & Cooper December 2007 Stability and Control of Aircraft Systems Langton September 2006 Military Avionics Systems Moir & Seabridge February 2006 Design and Development of Aircraft Systems Moir & Seabridge June 2004 Aircraft Loading and Structural Layout Howe May 2004 Aircraft Display Systems Jukes December 2003 Civil Avionics Systems Moir & Seabridge December 2002
Contents About the Author ix Series Preface X Preface xi 1 Applications of Advanced Composites in Aircraft Structures 1 References 7 2 Cost of Composites:a Qualitative Discussion 2.1 Recurring Cost 10 2.2 Nonrecurring Cost 18 2.3 Technology Selection 0 2.4 Summary and Conclusions Exercises 30 References 3 3 Review of Classical Laminated Plate Theory 3.1 Composite Materials:Definitions,Symbols and Terminology 3.2 Constitutive Equations in Three Dimensions 3.2.1 Tensor Transformations 3.3 Constitutive Equations in Two Dimensions:Plane Stress Exercises 13335370923 References 4 Review of Laminate Strength and Failure Criteria 4.1 Maximum Stress Failure Theory 4.2 Maximum Strain Failure Theory 4.3 Tsai-Hill Failure Theory 575858 4.4 Tsai-Wu Failure Theory 4.5 Other Failure Theories 5 References 0 Composite Structural Components and Mathematical Formulation 63 5.1 Overview of Composite Airframe 63 5.1.1 The Structural Design Process:The Analyst's Perspective 4
Contents About the Author ix Series Preface x Preface xi 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 30 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 37 3.3 Constitutive Equations in Two Dimensions: Plane Stress 39 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 Other Failure Theories 59 References 60 5 Composite Structural Components and Mathematical Formulation 63 5.1 Overview of Composite Airframe 63 5.1.1 The Structural Design Process: The Analyst’s Perspective 64
Contents 5.1.2 Basic Design Concept and Process/Material Considerations for Aircraft Parts 69 5.1.3 Sources of Uncertainty:Applied Loads,Usage and Material Scatter 72 5.1.4 Environmental Effects 75 5.1.5 Effect of Damage 76 5.1.6 Design Values and Allowables 78 5.1.7 Additional Considerations of the Design Process 81 5.2 Governing Equations 82 5.2.1 Equilibrium Equations 82 5.2.2 Stress-Strain Equations 84 5.2.3 Strain-Displacement Equations 85 5.2.4 von Karman Anisotropic Plate Equations for Large Deflections 86 5.3 Reductions of Governing Equations:Applications to Specific Problems 91 5.3.1 Composite Plate Under Localized in-Plane Load 92 5.3.2 Composite Plate Under Out-of-Plane Point Load 103 5.4 Energy Methods 106 5.4.1 Energy Expressions for Composite Plates 107 Exercises 113 References 116 6 Buckling of Composite Plates 119 6.1 Buckling of Rectangular Composite Plate under Biaxial Loading 119 6.2 Buckling of Rectangular Composite Plate under Uniaxial Compression 122 6.2.1 Uniaxial Compression,Three Sides Simply Supported,One Side Free 124 6.3 Buckling of Rectangular Composite Plate under Shear 127 6.4 Buckling of Long Rectangular Composite Plates under Shear 129 6.5 Buckling of Rectangular Composite Plates under Combined Loads 132 6.6 Design Equations for Different Boundary Conditions and Load Combinations 138 Exercises 141 References 143 Post-Buckling 145 7.1 Post-Buckling Analysis of Composite Panels under Compression 149 7.1.1 Application:Post-Buckled Panel Under Compression 157 7.2 Post-Buckling Analysis of Composite Plates under Shear 159 7.2.1 Post-buckling of Stiffened Composite Panels under Shear 163 72.2 Post-buckling of Stiffened Composite Panels under Combined Uniaxial and Shear Loading 171 Exercises 174 References 177 f Design and Analysis of Composite Beams 179 8.1 Cross-section Definition Based on Design Guidelines 179 8.2 Cross-sectional Properties 182 8.3 Column Buckling 188
5.1.2 Basic Design Concept and Process/Material Considerations for Aircraft Parts 69 5.1.3 Sources of Uncertainty: Applied Loads, Usage and Material Scatter 72 5.1.4 Environmental Effects 75 5.1.5 Effect of Damage 76 5.1.6 Design Values and Allowables 78 5.1.7 Additional Considerations of the Design Process 81 5.2 Governing Equations 82 5.2.1 Equilibrium Equations 82 5.2.2 Stress–Strain Equations 84 5.2.3 Strain-Displacement Equations 85 5.2.4 von Karman Anisotropic Plate Equations for Large Deflections 86 5.3 Reductions of Governing Equations: Applications to Specific Problems 91 5.3.1 Composite Plate Under Localized in-Plane Load 92 5.3.2 Composite Plate Under Out-of-Plane Point Load 103 5.4 Energy Methods 106 5.4.1 Energy Expressions for Composite Plates 107 Exercises 113 References 116 6 Buckling of Composite Plates 119 6.1 Buckling of Rectangular Composite Plate under Biaxial Loading 119 6.2 Buckling of Rectangular Composite Plate under Uniaxial Compression 122 6.2.1 Uniaxial Compression, Three Sides Simply Supported, One Side Free 124 6.3 Buckling of Rectangular Composite Plate under Shear 127 6.4 Buckling of Long Rectangular Composite Plates under Shear 129 6.5 Buckling of Rectangular Composite Plates under Combined Loads 132 6.6 Design Equations for Different Boundary Conditions and Load Combinations 138 Exercises 141 References 143 7 Post-Buckling 145 7.1 Post-Buckling Analysis of Composite Panels under Compression 149 7.1.1 Application: Post-Buckled Panel Under Compression 157 7.2 Post-Buckling Analysis of Composite Plates under Shear 159 7.2.1 Post-buckling of Stiffened Composite Panels under Shear 163 7.2.2 Post-buckling of Stiffened Composite Panels under Combined Uniaxial and Shear Loading 171 Exercises 174 References 177 8 Design and Analysis of Composite Beams 179 8.1 Cross-section Definition Based on Design Guidelines 179 8.2 Cross-sectional Properties 182 8.3 Column Buckling 188 vi Contents
Contents viⅷ 8.4 Beam on an Elastic Foundation under Compression 189 8.5 Crippling 194 8.5.1 One-Edge-Free (OEF)Crippling 196 8.5.2 No-Edge-Free (NEF)Crippling 200 8.5.3 Crippling under Bending Loads 202 8.5.4 Crippling of Closed-Section Beams 207 8.6 Importance of Radius Regions at Flange Intersections 207 8.7 Inter-rivet Buckling of Stiffener Flanges 210 8.8 Application:Analysis of Stiffeners in a Stiffened Panel under Compression 215 Exercises 218 References 222 9 Skin-Stiffened Structure 223 9.1 Smearing of Stiffness Properties(Equivalent Stiffness) 223 9.1.1 Equivalent Membrane Stiffnesses 223 9.1.2 Equivalent Bending Stiffnesses 225 9.2 Failure Modes of a Stiffened Panel 227 9.2.1 Local Buckling (Between Stiffeners)Versus Overall Panel Buckling (the Panel Breaker Condition) 228 9.22 Skin-Stiffener Separation 236 9.3 Additional Considerations for Stiffened Panels 251 9.3.1 'Pinching'of Skin 251 9.3.2 Co-Curing Versus Bonding Versus Fastening 251 Exercises 253 References 258 10 Sandwich Structure 259 10.1 Sandwich Bending Stiffnesses 260 10.2 Buckling of Sandwich Structure 262 10.2.1 Buckling of Sandwich Under Compression 262 10.2.2 Buckling of Sandwich Under Shear 264 10.2.3 Buckling of Sandwich Under Combined Loading 265 10.3 Sandwich Wrinkling 265 10.3.1 Sandwich Wrinkling Under Compression 265 10.3.2 Sandwich Wrinkling Under Shear 276 10.3.3 Sandwich Wrinkling Under Combined Loads 276 10.4 Sandwich Crimping 278 10.4.1 Sandwich Crimping Under Compression 278 10.4.2 Sandwich Crimping Under Shear 278 10.5 Sandwich Intracellular Buckling (Dimpling)under Compression 278 10.6 Attaching Sandwich Structures 279 10.6.1 Core Ramp-Down Regions 280 10.6.2 Alternatives to Core Ramp-Down 282 Exercises 284 References 288
8.4 Beam on an Elastic Foundation under Compression 189 8.5 Crippling 194 8.5.1 One-Edge-Free (OEF) Crippling 196 8.5.2 No-Edge-Free (NEF) Crippling 200 8.5.3 Crippling under Bending Loads 202 8.5.4 Crippling of Closed-Section Beams 207 8.6 Importance of Radius Regions at Flange Intersections 207 8.7 Inter-rivet Buckling of Stiffener Flanges 210 8.8 Application: Analysis of Stiffeners in a Stiffened Panel under Compression 215 Exercises 218 References 222 9 Skin-Stiffened Structure 223 9.1 Smearing of Stiffness Properties (Equivalent Stiffness) 223 9.1.1 Equivalent Membrane Stiffnesses 223 9.1.2 Equivalent Bending Stiffnesses 225 9.2 Failure Modes of a Stiffened Panel 227 9.2.1 Local Buckling (Between Stiffeners) Versus Overall Panel Buckling (the Panel Breaker Condition) 228 9.2.2 Skin–Stiffener Separation 236 9.3 Additional Considerations for Stiffened Panels 251 9.3.1 ‘Pinching’ of Skin 251 9.3.2 Co-Curing Versus Bonding Versus Fastening 251 Exercises 253 References 258 10 Sandwich Structure 259 10.1 Sandwich Bending Stiffnesses 260 10.2 Buckling of Sandwich Structure 262 10.2.1 Buckling of Sandwich Under Compression 262 10.2.2 Buckling of Sandwich Under Shear 264 10.2.3 Buckling of Sandwich Under Combined Loading 265 10.3 Sandwich Wrinkling 265 10.3.1 Sandwich Wrinkling Under Compression 265 10.3.2 Sandwich Wrinkling Under Shear 276 10.3.3 Sandwich Wrinkling Under Combined Loads 276 10.4 Sandwich Crimping 278 10.4.1 Sandwich Crimping Under Compression 278 10.4.2 Sandwich Crimping Under Shear 278 10.5 Sandwich Intracellular Buckling (Dimpling) under Compression 278 10.6 Attaching Sandwich Structures 279 10.6.1 Core Ramp-Down Regions 280 10.6.2 Alternatives to Core Ramp-Down 282 Exercises 284 References 288 Contents vii