Design Aids for Stiffened Composite Shells with Cutouts

278 Pages·2017·11.18 MB·English

by  Sarmila Sahoo (auth.)

Springer Transactions in Civil
and Environmental Engineering
Sarmila Sahoo
Design Aids
for Stiffened
Composite
Shells with
Cutouts
Springer Transactions in Civil
and Environmental Engineering
Moreinformationabout thisseries athttp://www.springer.com/series/13593
Sarmila Sahoo
Design Aids for Stiffened
Composite Shells with
Cutouts
SarmilaSahoo
DepartmentofCivilEngineering
HeritageInstituteofTechnologyKolkata
Kolkata,WestBengal
India
ISSN2363-7633 ISSN2363-7641 (electronic)
SpringerTransactionsinCivilandEnvironmentalEngineering
ISBN978-981-10-2061-2 ISBN978-981-10-2062-9 (eBook)
DOI10.1007/978-981-10-2062-9
LibraryofCongressControlNumber:2016951724
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Preface
Laminated composites are increasingly being used nowadays in aerospace, civil,
marineandotherrelatedweight-sensitiveengineeringapplicationsthatrequirehigh
strength-to-weight and stiffness-to weight ratios. Some of the structural compo-
nentsofaircraftsandmissileandshipstructurescanbeidealizedascompositeshell
panels. Quite often, to save weight and also to provide a facility for inspection,
cutoutsareprovidedinthesepanels.Inpractice,themarginofthecutoutsmustbe
stiffened to take account of stress concentration effects. Also, there can be some
instrumentsdirectlyfixedonthesepanels,andthesafetyoftheseinstrumentscanbe
dependent on the vibration characteristics of the panels. Hence, free vibration
studies on laminated composite shell panels with cutouts are of interest to both
structuralengineersandmaterialsscientists.
Thisbookfocusesonthefreevibrationsofgraphite-epoxylaminatedcomposite
stiffened shells with cutouts both in terms of the natural frequencies and mode
shapes.Thedynamicanalysisofshellstructures,whichmayhavecomplexgeom-
etryandarbitraryloadingandboundaryconditions,issolvedefficientlybythefinite
element method, including cutouts in shells. The results may be readily used by
practising engineers dealing with stiffened composite shells with cutouts. Several
shellforms,viz.cylindricalshell,hyparshell,conoidalshell,sphericalshell,saddle
shell,hyperbolicparaboloidalshellandellipticparaboloidalshell,areconsideredin
thebook.Thedynamiccharacteristicsofstiffenedcompositeshellswithcutoutsare
describedintermsofthenaturalfrequencyandmodeshapes.Thesizeofthecutouts
and their positions with respect to the shell centre are varied for different edge
constraints of cross-ply and angle-ply laminated composite shells. The effects of
these parametric variations on the fundamental frequencies and mode shapes are
discussedindetail.Theinformationregardingthebehaviourofstiffenedshellswith
cutouts for a wide spectrum of eccentricity and boundary conditions for cross-ply
and angle-ply shells may be used as design aids for structural engineers. It is
believedthatthisbookwillhaveasignificantcontributiontotheexistingliterature
fromthepointofviewofbothindustrialimportanceandacademicinterest.
v

Contents
1 FundamentalConsideration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 LiteratureReview. .. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . 6
1.3 MathematicalFormulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3.1 FormulationforShell. . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3.2 FormulationforStiffener. . . . . . . . . . . . . . . . . . . . . . . . . 24
1.3.3 CutoutConsideration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.3.4 SolutionProcedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.4 ValidationStudy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.5 PresentScope. .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . 28
1.6 Closure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2 StiffenedCylindricalShellwithCutout. . . . . . . . . . . . . . . . . . . . . . 41
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2 Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3 ResultsandDiscussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.1 FreeVibrationBehaviourofShellswithConcentric
Cutouts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.2 EffectofEccentricityofCutoutPosition. . . . . . . . . . . . . . 49
2.4 Closure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3 StiffenedHyparShellwithCutout. . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2 Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3 ResultsandDiscussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3.1 FreeVibrationBehaviourofShellswithConcentric
Cutouts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3.2 EffectofEccentricityofCutoutPosition. . . . . . . . . . . . . . 77
vii
viii Contents
3.4 Closure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4 StiffenedConoidalShellwithCutout. . . . . . . . . . . . . . . . . . . . . . . . 107
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.2 Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3 ResultsandDiscussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.3.1 FreeVibrationBehaviourofShellswithConcentric
Cutouts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.3.2 EffectofEccentricityofCutoutPosition. . . . . . . . . . . . . . 113
4.4 Closure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5 StiffenedSphericalShellwithCutout. . . . . . . . . . . . . . . . . . . . . . . . 145
5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.2 Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.3 ResultsandDiscussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.3.1 FreeVibrationBehaviourofShellswithConcentric
Cutouts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.3.2 EffectofEccentricityofCutoutPosition. . . . . . . . . . . . . . 153
5.4 Closure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6 StiffenedSaddleShellwithCutout. . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.2 Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.3 ResultsandDiscussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.3.1 FreeVibrationBehaviourofShellswithConcentric
Cutouts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.3.2 EffectofEccentricityofCutoutPosition. . . . . . . . . . . . . . 179
6.4 Closure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
7 StiffenedHyperbolicParaboloidShellwithCutout. . . . . . . . . . . . . 197
7.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
7.2 Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
7.3 ResultsandDiscussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
7.3.1 FreeVibrationBehaviourofShellswithConcentric
Cutouts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
7.3.2 EffectofEccentricityofCutoutPosition. . . . . . . . . . . . . . 206
7.4 Closure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
8 StiffenedEllipticParaboloidShellwithCutout. . . . . . . . . . . . . . . . 231
8.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
8.2 Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
Contents ix
8.3 ResultsandDiscussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
8.3.1 FreeVibrationBehaviourofShellswithConcentric
Cutouts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
8.3.2 EffectofEccentricityofCutoutPosition. . . . . . . . . . . . . . 239
8.4 Closure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268