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
viii Contents 11 Good Design Practices and Design Rules of Thumb' 289 11.1 Lay up/Stacking Sequence-related 289 11.2 Loading and Performance-related 290 11.3 Guidelines Related to Environmental Sensitivity and Manufacturing Constraints 292 11.4 Configuration and Layout-related 292 Exercises 294 References 295 Index 297
11 Good Design Practices and Design ‘Rules of Thumb’ 289 11.1 Lay up/Stacking Sequence-related 289 11.2 Loading and Performance-related 290 11.3 Guidelines Related to Environmental Sensitivity and Manufacturing Constraints 292 11.4 Configuration and Layout-related 292 Exercises 294 References 295 Index 297 viii Contents
About the author Christos Kassapoglou received his BS degree in Aeronautics and Astronautics and two MS degrees(Aeronautics and Astronautics and Mechanical Engineering)all from Massachusetts Institute of Technology.Since 1984 he has worked in industry,first at Beech Aircraft on the all-composite Starship I and then at Sikorsky Aircraft in the Structures Research Group specializing on analysis of composite structures of the all-composite Comanche and other helicopters,and leading internally funded research and programs funded by NASA and the US Army.Since 2001 he has been consulting with various companies in the US on applications of composite structures on airplanes and helicopters.He joined the faculty of the Aerospace Engineering Department of the Delft University of Technology (Aerospace Structures)in 2007 as an Associate Professor.His interests include fatigue and damage tolerance of composites,analysis of sandwich structures,design and optimization for cost and weight,and technology optimization.He has over 40 journal papers and 3 issued or pending patents on related subjects.He is a member of AIAA,AHS,and SAMPE
About the Author Christos Kassapoglou received his BS degree in Aeronautics and Astronautics and two MS degrees (Aeronautics and Astronautics and Mechanical Engineering) all from Massachusetts Institute of Technology. Since 1984 he has worked in industry, first at Beech Aircraft on the all-composite Starship I and then at Sikorsky Aircraft in the Structures Research Group specializing on analysis of composite structures of the all-composite Comanche and other helicopters, and leading internally funded research and programs funded by NASA and the US Army. Since 2001 he has been consulting with various companies in the US on applications of composite structures on airplanes and helicopters. He joined the faculty of the Aerospace Engineering Department of the Delft University of Technology (Aerospace Structures) in 2007 as an Associate Professor. His interests include fatigue and damage tolerance of composites, analysis of sandwich structures, design and optimization for cost and weight, and technology optimization. He has over 40 journal papers and 3 issued or pending patents on related subjects. He is a member of AIAA, AHS, and SAMPE
Series Preface The field of aerospace is wide ranging and covers a variety of products,disciplines and domains,not merely in engineering but in many related supporting activities.These combine to enable the aerospace industry to produce exciting and technologically challenging products.A wealth of knowledge is contained by practitioners and professionals in the aerospace fields that is of benefit to other practitioners in the industry,and to those entering the industry from University. The Aerospace Series aims to be a practical and topical series of books aimed at engineering professionals,operators,users and allied professions such as commercial and legal executives in the aerospace industry.The range of topics is intended to be wide ranging,covering design and development,manufacture,operation and support of aircraft as well as topics such as infrastructure operations,and developments in research and technology.The intention is to provide a source of relevant information that will be of interest and benefit to all those people working in aerospace. The use of composite materials for aerospace structures has increased dramatically in the last three decades.The attractive strength-to-weight ratios,improved fatigue and corrosion resistance,and ability to tailor the geometry and fibre orientations,combined with recent advances in fabrication,have made composites a very attractive option for aerospace applications from both a technical and financial viewpoint.This has been tempered by problems associated with damage tolerance and detection,damage repair,environmental degradation and assembly joints.The anisotropic nature of composites also dramatically increases the number of variables that need to be considered in the design of any aerospace structure. This book,Design and Analysis of Composite Structures:With Application to Aerospace Structures,provides a methodology of various analysis approaches that can be used for the preliminary design of aerospace structures without having to resort to finite elements. Representative types of composite structure are described,along with techniques to define the geometry and lay-up stacking sequence required to withstand the applied loads.The value of such a set of tools is to enable rapid initial trade-off preliminary design studies to be made, before using a detailed Finite Element analysis on the finalized design configurations. Allan Seabridge,Roy Langton, Jonathan Cooper and Peter Belobaba
Series Preface The field of aerospace is wide ranging and covers a variety of products, disciplines and domains, not merely in engineering but in many related supporting activities. These combine to enable the aerospace industry to produce exciting and technologically challenging products. A wealth of knowledge is contained by practitioners and professionals in the aerospace fields that is of benefit to other practitioners in the industry, and to those entering the industry from University. The Aerospace Series aims to be a practical and topical series of books aimed at engineering professionals, operators, users and allied professions such as commercial and legal executives in the aerospace industry. The range of topics is intended to be wide ranging, covering design and development, manufacture, operation and support of aircraft as well as topics such as infrastructure operations, and developments in research and technology. The intention is to provide a source of relevant information that will be of interest and benefit to all those people working in aerospace. The use of composite materials for aerospace structures has increased dramatically in the last three decades. The attractive strength-to-weight ratios, improved fatigue and corrosion resistance, and ability to tailor the geometry and fibre orientations, combined with recent advances in fabrication, have made composites a very attractive option for aerospace applications from both a technical and financial viewpoint. This has been tempered by problems associated with damage tolerance and detection, damage repair, environmental degradation and assembly joints. The anisotropic nature of composites also dramatically increases the number of variables that need to be considered in the design of any aerospace structure. This book, Design and Analysis of Composite Structures: With Application to Aerospace Structures, provides a methodology of various analysis approaches that can be used for the preliminary design of aerospace structures without having to resort to finite elements. Representative types of composite structure are described, along with techniques to define the geometry and lay-up stacking sequence required to withstand the applied loads. The value of such a set of tools is to enable rapid initial trade-off preliminary design studies to be made, before using a detailed Finite Element analysis on the finalized design configurations. Allan Seabridge, Roy Langton, Jonathan Cooper and Peter Belobaba
Preface This book is a compilation of analysis and design methods for structural components made of advanced composites.The term 'advanced composites'is used here somewhat loosely and refers to materials consisting of a high-performance fiber (graphite,glass,Kevlar,etc) embedded in a polymeric matrix (epoxy,bismaleimide,PEEKetc).The material in this book is the product of lecture notes used in graduate-level classes in Advanced Composites Design and Optimization courses taught at the Delft University of Technology. The book is aimed at fourth year undergraduate or graduate level students and starting engineering professionals in the composites industry.The reader is expected to be familiar with classical laminated-plate theory (CLPT)and first ply failure criteria.Also,some awareness of energy methods,and Rayleigh-Ritz approaches will make following some of the solution methods easier.In addition,basic applied mathematics knowledge such as Fourier series, simple solutions of partial differential equations,and calculus of variations are subjects that the reader should have some familiarity with. A series of attractive properties of composites such as high stiffness and strength-to-weight ratios,reduced sensitivity to cyclic loads,improved corrosion resistance,and,above all,the ability to tailor the configuration (geometry and stacking sequence)to specific loading conditions for optimum performance has made them a prime candidate material for use in aerospace applications.In addition,the advent of automated fabrication methods such as advanced fiber/tow placement,automated tape laying,filament winding,etc.has made it possible to produce complex components at costs competitive with if not lower than metallic counterparts.This increase in the use of composites has brought to the forefront the need for reliable analysis and design methods that can assist engineers in implementing composites in aerospace structures.This book is a small contribution towards fulfilling that need. The objective is to provide methodology and analysis approaches that can be used in preliminary design.The emphasis is on methods that do not use finite elements or other computationally expensive approaches in order to allow the rapid generation of alternative designs that can be traded against each other.This will provide insight in how different design variables and parameters of a problem affect the result. The approach to preliminary design and analysis may differ according to the application and the persons involved.It combines a series of attributes such as experience,intuition,inspiration and thorough knowledge of the basics.Of these,intuition and inspiration cannot be captured in the pages of a book or itemized in a series of steps.For the first attribute,experience,an attempt can be made to collect previous best practices which can serve as guidelines for future work
Preface This book is a compilation of analysis and design methods for structural components made of advanced composites. The term ‘advanced composites’ is used here somewhat loosely and refers to materials consisting of a high-performance fiber (graphite, glass, Kevlar, etc) embedded in a polymeric matrix (epoxy, bismaleimide, PEEK etc). The material in this book is the product of lecture notes used in graduate-level classes in Advanced Composites Design and Optimization courses taught at the Delft University of Technology. The book is aimed at fourth year undergraduate or graduate level students and starting engineering professionals in the composites industry. The reader is expected to be familiar with classical laminated-plate theory (CLPT) and first ply failure criteria. Also, some awareness of energy methods, and Rayleigh–Ritz approaches will make following some of the solution methods easier. In addition, basic applied mathematics knowledge such as Fourier series, simple solutions of partial differential equations, and calculus of variations are subjects that the reader should have some familiarity with. A series of attractive properties of composites such as high stiffness and strength-to-weight ratios, reduced sensitivity to cyclic loads, improved corrosion resistance, and, above all, the ability to tailor the configuration (geometry and stacking sequence) to specific loading conditions for optimum performance has made them a prime candidate material for use in aerospace applications. In addition, the advent of automated fabrication methods such as advanced fiber/tow placement, automated tape laying, filament winding, etc. has made it possible to produce complex components at costs competitive with if not lower than metallic counterparts. This increase in the use of composites has brought to the forefront the need for reliable analysis and design methods that can assist engineers in implementing composites in aerospace structures. This book is a small contribution towards fulfilling that need. The objective is to provide methodology and analysis approaches that can be used in preliminary design. The emphasis is on methods that do not use finite elements or other computationally expensive approaches in order to allow the rapid generation of alternative designs that can be traded against each other. This will provide insight in how different design variables and parameters of a problem affect the result. The approach to preliminary design and analysis may differ according to the application and the persons involved. It combines a series of attributes such as experience, intuition, inspiration and thorough knowledge of the basics. Of these, intuition and inspiration cannot be captured in the pages of a book or itemized in a series of steps. For the first attribute, experience, an attempt can be made to collect previous best practices which can serve as guidelines for future work
xii Preface Only the last attribute,knowledge of the basics,can be formulated in such a way that the reader can learn and understand them and then apply them to his/her own applications.And doing that is neither easy nor guaranteed to be exhaustive.The wide variety of applications and the peculiarities that each may require in the approach,preclude any complete and in-depth presentation of the material.It is only hoped that the material presented here will serve as a starting point for most types of design and analysis problems. Given these difficulties,the material covered in this book is an attempt to show representative types of composite structure and some of the approaches that may be used in determining the geometry and stacking sequences that meet applied loads without failure.It should be emphasized that not all methods presented here are equally accurate nor do they have the same range of applicability.Every effort has been made to present,along with each approach, its limitations.There are many more methods than the ones presented here and they vary in accuracy and range of applicability.Additional references are given where some of these methods can be found. These methods cannot replace thorough finite element analyses which,when properly set up,will be more accurate than most of the methods presented here.Unfortunately,the complexity of some of the problems and the current (and foreseeable)computational efficiency in implementing finite element solutions precludes their extensive use during preliminary design or,even,early phases of the detailed design.There is not enough time to trade hundreds or thousands of designs in an optimization effort to determine the 'best' design if the analysis method is based on detailed finite elements.On the other hand,once the design configuration has been finalized or a couple of configurations have been down- selected using simpler,more efficient approaches,detailed finite elements can and should be used to provide accurate predictions for the performance,point to areas where revisions of the design are necessary,and,eventually,provide supporting analysis for the certification effort of a product. Some highlights of composite applications from the 1950s to today are given in Chapter 1 with emphasis on nonmilitary applications.Recurring and nonrecurring cost issues that may affect design decisions are presented in Chapter 2 for specific fabrication processes.Chapter 3 provides a review of CLPT and Chapter 4 summarizes strength failure criteria for composite plates;these two chapters are meant as a quick refresher of some of the basic concepts and equations that will be used in subsequent chapters. Chapter 5 presents the governing equations for anisotropic plates.It includes the von Karman large-deflection equations that are used later to generate simple solutions for post- buckled composite plates under compression.These are followed by a presentation of the types of composite parts found in aerospace structures and the design philosophy typically used to come up with a geometric shape.Design requirements and desired attributes are also discussed.This sets the stage for quantitative requirements that address uncertainties during the design and during service of a fielded structure.Uncertainties in applied loads,and variations in usage from one user to another are briefly discussed.A more detailed discussion about uncertainties in material performance (material scatter)leads to the introduction of statistically meaningful (A-and B-basis)design values or allowables.Finally,sensitivity to damage and environmental conditions is discussed and the use of knockdown factors for preliminary design is introduced. Chapter 6 contains a discussion of buckling of composite plates.Plates are introduced first and beams follow (Chapter 8)because failure modes of beams such as crippling can
Only the last attribute, knowledge of the basics, can be formulated in such a way that the reader can learn and understand them and then apply them to his/her own applications. And doing that is neither easy nor guaranteed to be exhaustive. The wide variety of applications and the peculiarities that each may require in the approach, preclude any complete and in-depth presentation of the material. It is only hoped that the material presented here will serve as a starting point for most types of design and analysis problems. Given these difficulties, the material covered in this book is an attempt to show representative types of composite structure and some of the approaches that may be used in determining the geometry and stacking sequences that meet applied loads without failure. It should be emphasized that not all methods presented here are equally accurate nor do they have the same range of applicability. Every effort has been made to present, along with each approach, its limitations. There are many more methods than the ones presented here and they vary in accuracy and range of applicability. Additional references are given where some of these methods can be found. These methods cannot replace thorough finite element analyses which, when properly set up, will be more accurate than most of the methods presented here. Unfortunately, the complexity of some of the problems and the current (and foreseeable) computational efficiency in implementing finite element solutions precludes their extensive use during preliminary design or, even, early phases of the detailed design. There is not enough time to trade hundreds or thousands of designs in an optimization effort to determine the ‘best’ design if the analysis method is based on detailed finite elements. On the other hand, once the design configuration has been finalized or a couple of configurations have been downselected using simpler, more efficient approaches, detailed finite elements can and should be used to provide accurate predictions for the performance, point to areas where revisions of the design are necessary, and, eventually, provide supporting analysis for the certification effort of a product. Some highlights of composite applications from the 1950s to today are given in Chapter 1 with emphasis on nonmilitary applications. Recurring and nonrecurring cost issues that may affect design decisions are presented in Chapter 2 for specific fabrication processes. Chapter 3 provides a review of CLPT and Chapter 4 summarizes strength failure criteria for composite plates; these two chapters are meant as a quick refresher of some of the basic concepts and equations that will be used in subsequent chapters. Chapter 5 presents the governing equations for anisotropic plates. It includes the von Karman large-deflection equations that are used later to generate simple solutions for postbuckled composite plates under compression. These are followed by a presentation of the types of composite parts found in aerospace structures and the design philosophy typically used to come up with a geometric shape. Design requirements and desired attributes are also discussed. This sets the stage for quantitative requirements that address uncertainties during the design and during service of a fielded structure. Uncertainties in applied loads, and variations in usage from one user to another are briefly discussed. A more detailed discussion about uncertainties in material performance (material scatter) leads to the introduction of statistically meaningful (A- and B-basis) design values or allowables. Finally, sensitivity to damage and environmental conditions is discussed and the use of knockdown factors for preliminary design is introduced. Chapter 6 contains a discussion of buckling of composite plates. Plates are introduced first and beams follow (Chapter 8) because failure modes of beams such as crippling can xii Preface
