Preface xiii be introduced more easily as special cases of plate buckling and post-buckling.Buckling under compression is discussed first,followed by buckling under shear.Combined load cases are treated next and a table including different boundary conditions and load cases is provided. Post-buckling under compression and shear is treated in Chapter 7.For applied compression, an approximate solution to the governing(von Karman)equations for large deflections of plates is presented.For applied shear,an approach that is a modification of the standard approach for metals undergoing diagonal tension is presented.A brief section follows suggesting how post- buckling under combined compression and shear could be treated. Design and analysis of composite beams(stiffeners,stringers,panel breakers,etc.)are treated in Chapter 8.Calculation of equivalent membrane and bending stiffnesses for cross- sections consisting of members with different layups are presented first.These can be used with standard beam design equations and some examples are given.Buckling of beams and beams on elastic foundations is discussed next.This does not differentiate between metals and composites.The standard equations for metals can be used with appropriate(re)definition of terms such as membrane and bending stiffness.The effect of different end-conditions is also discussed.Crippling,or collapse after very-short-wavelength buckling,is discussed in detail deriving design equations from plate buckling presented earlier and from semi-empirical approaches.Finally,conditions for inter-rivet buckling are presented. The two constituents,plates and beams are brought together in Chapter 9 where stiffened panels are discussed.The concept of smeared stiffness is introduced and its applicability discussed briefly.Then,special design conditions such as the panel breaker condition and failure modes such as skin-stiffener separation are analyzed in detail,concluding with design guidelines for stiffened panels derived from the previous analyses. Sandwich structure is treated in Chapter 10.Aspects of sandwich modeling,in particular the effect of transverse shear on buckling,are treated first.Various failure modes such as wrinkling. crimping,and intracellular buckling are then discussed with particular emphasis on wrinkling with and without waviness.Interaction equations are introduced for analyzing sandwich structure under combined loading.A brief discussion on attachments including ramp-downs and associated design guidelines close this chapter. The final chapter,Chapter 11,summarizes design guidelines and rules presented throughout the previous chapters.It also includes some additional rules,presented for the first time in this book,that have been found to be useful in designing composite structures. To facilitate material coverage and in order to avoid having to read some chapters that may be considered of lesser interest or not directly related to the reader's needs,certain concepts and equations are presented in more than one place.This is minimized to avoid repetition and is done in such a way that reader does not have to interrupt reading a certain chapter and go back to find the original concept or equation on which the current derivation is based. Specific problems are worked out in detail as examples of applications throughout the book Representative exercises are given at the end of each chapter.These require the determination of geometry and/or stacking sequence for a specific structure not to fail under certain applied loads.Many of them are created in such a way that more than one answer is acceptable reflecting real-life situations.Depending on the assumptions made and design rules enforced, different but still acceptable designs can be created.Even though low weight is the primary objective of most of the exercises,situations where other issues are important and end up
be introduced more easily as special cases of plate buckling and post-buckling. Buckling under compression is discussed first, followed by buckling under shear. Combined load cases are treated next and a table including different boundary conditions and load cases is provided. Post-buckling under compression and shear is treated in Chapter 7. For applied compression, an approximate solution to the governing (von Karman) equations for large deflections of plates is presented. For applied shear, an approach that is a modification of the standard approach for metals undergoing diagonal tension is presented. A brief section follows suggesting how postbuckling under combined compression and shear could be treated. Design and analysis of composite beams (stiffeners, stringers, panel breakers, etc.) are treated in Chapter 8. Calculation of equivalent membrane and bending stiffnesses for crosssections consisting of members with different layups are presented first. These can be used with standard beam design equations and some examples are given. Buckling of beams and beams on elastic foundations is discussed next. This does not differentiate between metals and composites. The standard equations for metals can be used with appropriate (re)definition of terms such as membrane and bending stiffness. The effect of different end-conditions is also discussed. Crippling, or collapse after very-short-wavelength buckling, is discussed in detail deriving design equations from plate buckling presented earlier and from semi-empirical approaches. Finally, conditions for inter-rivet buckling are presented. The two constituents, plates and beams are brought together in Chapter 9 where stiffened panels are discussed. The concept of smeared stiffness is introduced and its applicability discussed briefly. Then, special design conditions such as the panel breaker condition and failure modes such as skin–stiffener separation are analyzed in detail, concluding with design guidelines for stiffened panels derived from the previous analyses. Sandwich structure is treated in Chapter 10. Aspects of sandwich modeling, in particular the effect of transverse shear on buckling, are treated first. Various failure modes such as wrinkling, crimping, and intracellular buckling are then discussed with particular emphasis on wrinkling with and without waviness. Interaction equations are introduced for analyzing sandwich structure under combined loading. A brief discussion on attachments including ramp-downs and associated design guidelines close this chapter. The final chapter, Chapter 11, summarizes design guidelines and rules presented throughout the previous chapters. It also includes some additional rules, presented for the first time in this book, that have been found to be useful in designing composite structures. To facilitate material coverage and in order to avoid having to read some chapters that may be considered of lesser interest or not directly related to the reader’s needs, certain concepts and equations are presented in more than one place. This is minimized to avoid repetition and is done in such a way that reader does not have to interrupt reading a certain chapter and go back to find the original concept or equation on which the current derivation is based. Specific problems are worked out in detail as examples of applications throughout the book Representative exercises are given at the end of each chapter. These require the determination of geometry and/or stacking sequence for a specific structure not to fail under certain applied loads. Many of them are created in such a way that more than one answer is acceptable reflecting real-life situations. Depending on the assumptions made and design rules enforced, different but still acceptable designs can be created. Even though low weight is the primary objective of most of the exercises, situations where other issues are important and end up Preface xiii
Xiv Preface driving the design are also given.For academic applications,experience has shown that students benefit the most if they work out some of these exercises in teams so design ideas and concepts can be discussed and an approach to a solution formulated. It is recognized that analysis of composite structures is very much in a state of flux and new and better methods are being developed (for example failure theories with and without damage).The present edition includes what are felt to be the most useful approaches at this point in time.As better approaches mature in the future,it will be modified accordingly
driving the design are also given. For academic applications, experience has shown that students benefit the most if they work out some of these exercises in teams so design ideas and concepts can be discussed and an approach to a solution formulated. It is recognized that analysis of composite structures is very much in a state of flux and new and better methods are being developed (for example failure theories with and without damage). The present edition includes what are felt to be the most useful approaches at this point in time. As better approaches mature in the future, it will be modified accordingly. xiv Preface
1 Applications of Advanced Composites in Aircraft Structures Some of the milestones in the implementation of advanced composites on aircraft and rotorcraft are discussed in this chapter.Specific applications have been selected that highlight various phases that the composites industry went through while trying to extend the application of composites. The application of composites in civilian or military aircraft followed the typical stages that every new technology goes through during its implementation.At the beginning,limited application on secondary structure minimized risk and improved understanding by collecting data from tests and fleet experience.This limited usage was followed by wider applications, first in smaller aircraft,capitalizing on the experience gained earlier.More recently,with the increased demand on efficiency and low operation costs,composites have being applied widely on larger aircraft. Perhaps the first significant application of advanced composites was on the Akaflieg Phonix FS-24(Figure 1.1)in the late 1950s.What started as a balsa wood and paper sailplane designed by professors at the University of Stuttgart and built by the students was later transformed into a fiberglass/balsa wood sandwich design.Eight planes were eventually built. The helicopter industry was among the first to recognize the potential of the composite materials and use them on primary structure.The main and tail rotor blades with their beam-like behavior were one of the major structural parts designed and built with composites towards the end of the 1960s.One such example is the Aerospatiale Gazelle (Figure 1.2).Even though,to first order,helicopter blades can be modeled as beams,the loading complexity and the multiple static and dynamic performance requirements(strength,buckling,stiffness distribution,fre- quency placement,etc.)make for a very challenging design and manufacturing problem. In the 1970s,with the composites usage on sailplanes and helicopters increasing,the first all- composite planes appeared.These were small recreational or aerobatic planes.Most notable among them were the Burt Rutan designs such as the Long EZ and Vari-Eze(Figure 1.3).These were largely co-cured and bonded constructions with very limited numbers of fasteners. Efficient aerodynamic designs with mostly laminar flow and light weight led to a combination of speed and agility Design and Analysis of Composite Structures:With Applications to Aerospace Structures Christos Kassapoglou 2010 John Wiley Sons,Ltd
1 Applications of Advanced Composites in Aircraft Structures Some of the milestones in the implementation of advanced composites on aircraft and rotorcraft are discussed in this chapter. Specific applications have been selected that highlight various phases that the composites industry went through while trying to extend the application of composites. The application of composites in civilian or military aircraft followed the typical stages that every new technology goes through during its implementation. At the beginning, limited application on secondary structure minimized risk and improved understanding by collecting data from tests and fleet experience. This limited usage was followed by wider applications, first in smaller aircraft, capitalizing on the experience gained earlier. More recently, with the increased demand on efficiency and low operation costs, composites have being applied widely on larger aircraft. Perhaps the first significant application of advanced composites was on the Akaflieg Ph€onix FS-24 (Figure 1.1) in the late 1950s. What started as a balsa wood and paper sailplane designed by professors at the University of Stuttgart and built by the students was later transformed into a fiberglass/balsa wood sandwich design. Eight planes were eventually built. The helicopter industry was among the first to recognize the potential of the composite materials and use them on primary structure. The main and tail rotor blades with their beam-like behavior were one of the major structural parts designed and built with composites towards the end of the 1960s. One such example is the Aerospatiale Gazelle (Figure 1.2). Even though, to first order, helicopter blades can be modeled as beams, the loading complexity and the multiple static and dynamic performance requirements (strength, buckling, stiffness distribution, frequency placement, etc.) make for a very challenging design and manufacturing problem. In the 1970s, with the composites usage on sailplanes and helicopters increasing, the first allcomposite planes appeared. These were small recreational or aerobatic planes. Most notable among them were the Burt Rutan designs such as the Long EZ and Vari-Eze (Figure 1.3). These were largely co-cured and bonded constructions with very limited numbers of fasteners. Efficient aerodynamic designs with mostly laminar flow and light weight led to a combination of speed and agility. Design and Analysis of Composite Structures: With Applications to Aerospace Structures Christos Kassapoglou 2010 John Wiley & Sons, Ltd
2 Design and Analysis of Composite Structures Figure 1.1 Akaflieg Phonix FS-24(Courtesy Deutsches Segelflugzeugmuseum;see Plate 1 for the colour figure) Figure 1.2 Aerospatiale SA341G Gazelle(Copyright Jenny Coffey printed with permission;see Plate 2 for the colour figure) Figure 1.3 Long EZ and Vari-Eze.(Vari-Eze photo:courtesy Stephen Kearney;Long EZ photo: courtesy Ray McCrea;see Plate 3 for the colour figure) Up to that point,usage of composites was limited and/or was applied to small aircraft with relatively easy structural requirements.In addition,the performance of composites was not completely understood.For example,their sensitivity to impact damage and its implications for design only came to the forefront in the late 1970s and early1980s.At that time,efforts to build the first all-composite airplane of larger size began with the LearFan 2100(Figure 1.4).This was the first civil aviation all-composite airplane to seek FAA certification(see Section 2.2)
Up to that point, usage of composites was limited and/or was applied to small aircraft with relatively easy structural requirements. In addition, the performance of composites was not completely understood. For example, their sensitivity to impact damage and its implications for design only came to the forefront in the late 1970s and early1980s. At that time, efforts to build the first all-composite airplane of larger size began with the LearFan 2100 (Figure 1.4). This was the first civil aviation all-composite airplane to seek FAA certification (see Section 2.2). Figure 1.1 Akaflieg Ph€onix FS-24 (Courtesy Deutsches Segelflugzeugmuseum; see Plate 1 for the colour figure) Figure 1.2 Aerospatiale SA 341G Gazelle (Copyright Jenny Coffey printed with permission; see Plate 2 for the colour figure) Figure 1.3 Long EZ and Vari-Eze. (Vari-Eze photo: courtesy Stephen Kearney; Long EZ photo: courtesy Ray McCrea; see Plate 3 for the colour figure) 2 Design and Analysis of Composite Structures
Applications of Advanced Composites in Aircraft Structures 3 N2B\ Figure 1.4 Lear Avia LearFan 2100(Copyright:Thierry Deutsch;see Plate 4 for the colour figure) It used a pusher propeller and combined high speed and low weight with excellent range and fuel consumption.Unfortunately,while it met all the structural certification requirements, delays in certifying the drive system,and the death of Bill Lear the visionary designer and inventor behind the project,kept the LearFan from making it into production and the company, LearAvia,went bankrupt. The Beech Starship I(Figure 1.5),which followed on the heels of the LearFan in the early 1980s was the first all-composite airplane to obtain FAA certification.It was designed to the new composite structure requirements specially created for it by the FAA.These requirements were the precursor of the structural requirements for composite aircraft as they are today. Unlike the LearFan which was a more conventional skin-stiffened structure with frames and stringers,the Starship fuselage was made of sandwich (graphite/epoxy facesheets with Nomex core)and had a very limited number of frames,increasing cabin head room for a given cabin diameter,and minimizing fabrication cost.It was co-cured in large pieces that were bonded together and,in critical connections such as the wing-box or the main fuselage joints, were also fastened.Designed also by Burt Rutan the Starship was meant to have mostly laminar flow and increased range through the use efficient canard design and blended main wing.Two engines with pusher propellers located at the aft fuselage were to provide enough power for high cruising speed.In the end,the aerodynamic performance was not met and the fuel Figure 1.5 Beech (Raytheon Aircraft)Starship I(Photo courtesy Brian Bartlett;see Plate 5 for the colour figure)
It used a pusher propeller and combined high speed and low weight with excellent range and fuel consumption. Unfortunately, while it met all the structural certification requirements, delays in certifying the drive system, and the death of Bill Lear the visionary designer and inventor behind the project, kept the LearFan from making it into production and the company, LearAvia, went bankrupt. The Beech Starship I (Figure 1.5), which followed on the heels of the LearFan in the early 1980s was the first all-composite airplane to obtain FAA certification. It was designed to the new composite structure requirements specially created for it by the FAA. These requirements were the precursor of the structural requirements for composite aircraft as they are today. Unlike the LearFan which was a more conventional skin-stiffened structure with frames and stringers, the Starship fuselage was made of sandwich (graphite/epoxy facesheets with Nomex core) and had a very limited number of frames, increasing cabin head room for a given cabin diameter, and minimizing fabrication cost. It was co-cured in large pieces that were bonded together and, in critical connections such as the wing-box or the main fuselage joints, were also fastened. Designed also by Burt Rutan the Starship was meant to have mostly laminar flow and increased range through the use efficient canard design and blended main wing. Two engines with pusher propellers located at the aft fuselage were to provide enough power for high cruising speed. In the end, the aerodynamic performance was not met and the fuel Figure 1.4 Lear Avia LearFan 2100 (Copyright: Thierry Deutsch; see Plate 4 for the colour figure) Figure 1.5 Beech (Raytheon Aircraft) Starship I (Photo courtesy Brian Bartlett; see Plate 5 for the colour figure) Applications of Advanced Composites in Aircraft Structures 3