Table Of ContentHaimAbramovich
AdvancedAerospaceMaterials
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Haim Abramovich
Advanced
Aerospace
Materials
Aluminum-Based and Composite Structures
Author
Prof.Dr.HaimAbramovich
Technion-IsraelInst.ofTechnology
AerospaceStructuralLaboratory
TechnionCity
32000Haifa
Israel
ISBN978-3-11-053756-7
e-ISBN(PDF)978-3-11-053757-4
e-ISBN(EPUB)978-3-11-053763-5
LibraryofCongressControlNumber:2019941309
BibliographicinformationpublishedbytheDeutscheNationalbibliothek
TheDeutscheNationalbibliothekliststhispublicationintheDeutscheNationalbibliografie;
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Preface
Advanced Aerospace Materials aims at dissemination of advanced engineering
topics using isotropic and composite materials. The present book was written to
providestudentsandscholarsagoodunderstandingofnewemergingtechnologies
usingcompositematerials,mainlyintheaerospacesector.Itcanserveasanintro-
ductory book for graduate students wishing to study about composite made struc-
tures, enabling them to acquire the necessary physical and mathematical tools to
understand the various aspects of composite based structures as compared to iso-
tropicones.
Thebookisbasedonthevariousresearchesandinvestigationsperformeddur-
ingtheyearsbytheauthoronmetalandcompositestructures.
The present book aims at providing a textbook to a graduate or graduate–un-
dergraduate course on thin walled structures. It also can serve as a reference for
engineersandscientistsworkinginindustryoracademia.
Thebookstartswithanextendedintroductoryonthinwalledstructures,char-
acterizingaerospaceandaeronauticalstructures.Itstressesthetransitionfromalu-
minum-based structures to laminated composite ones, to save weight. An
introductorytoelasticitytopicsandequationsofmotionisalsopresentedtoenable
the understanding of structural analysis of aerospace-aeronautical structures.
Chapter 2 is devoted to laminated composite materials, and presents the classical
lamination theory and the first order shear deformation theory. This chapter aims
atprovidingmathematicalandphysicalinsightofcompositematerials.Tocomple-
mentthistopic,higherordertheoriesarealsodisplayed.Thefirsttwochaptersare
thereforesuitableforanintroductiononaluminumand/orcompositematerialsfor
aerospace/aeronauticalstructurestothegraduateorundergraduatestudents.
The third chapter is devoted to some design formulas to be used by engineers
onsolvingvariousproblemsofthinwalledstructures.Fatigueissuesarepresented
in chapter four of the book. This chapter presents introductory topics in this well
documented subject of engineering Crack propagation subject is described and re-
viewedinthefifthchapterofthebook,thuscomplementingthetopicspresentedin
Chapter four, enabling the reader to understand and use the various equations to
predictthelifeofasinglestructuralcomponent.
The sixth chapter displays various issues for the buckling for columns and
plates,usingisotropicandlaminatedcompositematerials.Acomplementarychap-
ter, chapter seven, presents the vibrational aspects for the structures presented in
thepreviouschapter.
Another important topic in the analysis of thin walled structure, the dynamic
bucklingofstructuralcomponentsduetopulseloading,isdescribedandpresented
indetailinchaptereight,highlightingbothanalyticalandexperimentalaspectsof
thesubject.
https://doi.org/10.1515/9783110537574-201
VI Preface
The two last chapters of the book, optimization of thin-walled structures in
chapternine,andstructuralhealthmonitoringinchapterten,aimatpresentingthe
readers with two emerging engineering topics, by providing the basic definitions
andthepresentstateoftheart.
Iwishthatthisbook,togetherwithotherbooksandthehugenumbersofrefer-
ences existing in the literature, would enable readers to become familiar with the
treatment of thin walled structures, and how to investigate and calculate their
structuralbehavior.
I would like to thank all my former graduate students for their dedicated re-
searchinthefieldofcompositebasedstructures,Mr.JoshuaHarrisforhisinvolve-
mentinChapter9andMr.OsherShapiraforhiscontributiontoChapter10.
Iwanttothank,mywife,Doritandmychildren,Chen,Oz,ShirandOrfortheir
support, understanding, love and devotion. Their continuous support throughout
thewritingperiodenabledthepublishingofthepresentbook.
Haifa,June2019
HaimAbramovich
Contents
Preface V
1 Introduction 1
1.1 Introduction 1
1.2 Aerospacestructures 1
1.3 Aerospacestructures–transitiontocompositematerials 5
1.4 Basictopicsinelasticity 9
1.4.1 Stresses,strainsandrigidbodyrotations 9
1.4.2 Equilibriumandcompatibilityequationsinelasticity 15
1.4.3 Planestressandplanestrain(2Drepresentations) 21
1.4.4 TheAiryfunctionϕðx,yÞ 25
1.4.5 Thermalfield 27
References 28
2 Compositematerials 30
2.1 Introduction 30
2.1.1 Generalintroduction 30
2.2 Unidirectionalcomposites 31
2.3 Propertiesofasingleply 35
2.4 Transformationofstressesandstrains 36
2.5 Theclassicallaminationtheory 39
2.6 First-ordersheardeformationtheory 46
2.7 Higherordertheories 51
References 66
3 Designformulas 69
3.1 Introduction 69
3.2 Airyfunctions 69
3.3 Distributionoftheshearforces,moments,deflectionsand
slopesforbeams 69
3.4 Naturalfrequenciesforcommonbasicstructures 70
3.5 Torsionofbars 81
References 86
4 Introductiontofatigue 87
4.1 Introduction 87
4.2 Definitionoffatigue 87
4.2.1 Basicfatigueconcepts 87
4.2.2 Thefourstepsoffatiguefailure 90
4.3 TheS–Ncurve 91
VIII Contents
4.3.1 Theprobabilitydistributionsforfatiguelife 93
4.3.2 Fatiguelifeforvariouscombinationsofalternatingandmean
stresses 95
4.4 Minerrule–thecumulativedamage 97
4.5 Fatigueofcompositematerials 97
References 101
AppendixA:ApplicationofFig.4.6anditsassociated
equations 103
5 Introductiontocrackpropagationanalysis 105
5.1 Introduction 105
5.2 Foundationsoffracturemechanics 105
5.2.1 Introductoryconcepts 105
5.2.2 Basicfailuremodes 107
5.2.3 Thestressintensityfactor,K 108
5.2.4 Theenergyreleaserate,G 109
5.2.5 TheJ-integral 111
5.2.6 Thecrackopeningdisplacement 112
5.2.7 Someclosurenotes 112
5.3 Fatiguecrackpropagation 112
5.3.1 Introductoryconcepts 112
5.3.2 TheParislaw 113
5.3.3 Experimentalfracturemechanics 115
References 119
6 Bucklingofthin-walledstructures 121
6.1 Introduction 121
6.2 Bucklingofcolumns 121
6.2.1 Eulerbuckling 121
6.2.2 Rankin–Gordonformula 124
6.2.3 Compositecolumns–CLTapproach 125
6.3 Bucklingofcolumns–FSDTapproach 133
6.4 Bucklingofplates 138
6.4.1 Bucklingofisotropicplates 138
6.4.2 Bucklingoforthotropicplates 143
References 148
AppendixA:Nonsymmetriclaminatedcompositebeam–CLT
approach 150
7 Vibrationsofthin-walledstructures 153
7.1 Introduction 153
7.1.1 CLPTapproach 153
Contents IX
7.1.2 FSDPTapproach 155
7.2 Vibrationsofcolumns–CLTapproach 157
7.2.1 Symmetriclaminate(B =0,I =0) 157
11 1
7.2.2 Nonsymmetriclaminate(B ≠0,I ≠0) 162
11 1
7.3 Vibrationsofcolumns–FSDTapproach 163
7.3.1 Symmetriclaminate(B =0,I =0) 164
11 1
7.3.2 Nonsymmetriclaminate(B ≠0,I ≠0) 166
11 1
7.4 Vibrationsofplates–CLPTapproach 170
7.4.1 Simplysupportedspecialorthotropicplates 170
7.4.2 Simplysupportedontwooppositeedgesofspecialorthotropic
plates 171
References 172
AppendixA:Generalsolutionforanonsymmetricalbeamresting
onanyboundaryconditions 173
AppendixB:Matrixnotationfortheequilibriumequationsusing
CLTapproach 175
AppendixC:Thetermsofthematrixnotationfortheequilibrium
equationsusingFSDPTapproach 176
8 Dynamicbucklingofthin-walledstructures 177
8.1 Introduction 177
8.2 Dynamicbucklingofcolumns 181
8.2.1 DynamicbucklingofcolumnsusingCLT 181
8.2.2 DynamicbucklingofcolumnsusingFSDT 184
8.3 Dynamicbucklingofplates 186
8.4 Dynamicbucklingofthin-walledstructures–numericaland
experimentalresults 191
References 201
AppendixA:Calculationofthecriticalbucklingloadofauniaxial
loadedplatefromtestresults 203
9 Optimizationofthin-walledstructures 205
9.1 Introduction 205
9.2 Theoptimizationprocess 206
9.2.1 Vocabularyandconcepts 206
9.3 Structuraloptimization 209
9.4 Multidisciplinaryandmultiobjectivedesignoptimization 209
9.5 Methodsofoptimization 211
9.6 Classicaloptimizationtechniques 211
9.7 Numericalmethodsofoptimization 212
9.7.1 Linearprogramming 213
9.7.2 Integerprogramming 214
X Contents
9.7.3 Nonlinearprogramming 214
9.7.4 Quadraticprogramming 215
9.7.5 Stochasticprogramming 215
9.7.6 Dynamicprogramming 215
9.8 Advancedoptimizationtechniques 216
9.8.1 Hillclimbing 216
9.8.2 Simulatedannealing 217
9.8.3 Geneticalgorithms 217
9.8.4 Antcolonyoptimization 218
9.8.5 Neuralnetworkoptimization 218
9.9 Gradient-basedmethods 219
9.9.1 Unconstrainedmethods 219
9.9.2 Constrainedmethods 220
9.10 Heuristicmethods 222
9.10.1 Tabusearch 222
9.11 Optimizationoftopologyofaerospacestructures 223
9.12 Historyoftopologyoptimization 224
9.13 Density-basedmethods 225
9.14 Hard-killmethods 229
9.14.1 Evolutionarystructuraloptimizationmethods 229
9.15 Boundaryvariationmethods 231
9.15.1 Level-setmethods 232
9.15.2 Phasefieldmethod 233
9.16 Recentlydevelopedmethods 235
9.16.1 Bio-inspiredcellulardivision-basedmethod 235
9.17 Applicationsintheaerospacefield 237
9.17.1 Generaltopologyoptimizationapplications 237
9.17.2 Applicationsofdensity-basedmethods 237
9.17.3 Applicationsofhard-killmethods 238
9.17.4 Applicationsofboundaryvariationmethods 238
9.17.5 Applicationsofbio-inspiredcellulardivision-basedmethod 239
9.18 Conclusions 239
References 240
AppendixA:Responsesurfacemethodology 243
10 Structuralhealthmonitoring(SHM) 272
10.1 Introduction 272
10.1.1 Diagnosis 273
10.1.2 Damageprognosis 274
10.1.3 Predictivemaintenance 277
10.2 Applications 278
10.2.1 Aerospaceapplications 278
