Engineering Analysis with ANSYS Software

473 Pages·2007·25.71 MB·English

by  Tadeusz Stolarski

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Engineering Analysis
With ANSYS Software
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Engineering Analysis
With ANSYS Software
Y. Nakasone and S. Yoshimoto
Department of Mechanical Engineering
Tokyo University of Science,Tokyo,Japan
T. A. Stolarski
Department of Mechanical Engineering
School of Engineering and Design
Brunel University,Middlesex,UK
AMSTERDAM (cid:127) BOSTON (cid:127) HEIDELBERG (cid:127) LONDON (cid:127) NEW YORK (cid:127) OXFORD
PARIS (cid:127) SAN DIEGO (cid:127) SAN FRANCISCO (cid:127) SINGAPORE (cid:127) SYDNEY (cid:127) TOKYO
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C o n t e n t s
Preface
xiii
The aims and scope of the book
xv
Ch1apter
Basics of finite-element method
1
Methodofweightedresiduals
1.1 2
1.1.1 Sub-domainmethod(Finitevolumemethod) 2
1.1.2 Galerkinmethod 4
Rayleigh–Ritzmethod
1.2 5
Finite-elementmethod
1.3 7
1.3.1 One-elementcase 10
1.3.2 Three-elementcase 11
FEMintwo-dimensionalelastostaticproblems
1.4 14
1.4.1 Elements of finite-element procedures in the analysis of
planeelastostaticproblems 15
1.4.2 Fundamentalformulaeinplaneelastostaticproblems 16
1.4.2.1 Equationsofequilibrium 16
1.4.2.2 Strain–displacementrelations 16
1.4.2.3 Stress–strainrelations(constitutiveequations) 17
1.4.2.4 Boundaryconditions 19
1.4.3 Variationalformulaeinelastostaticproblems:theprinciple
ofvirtualwork 21
1.4.4 Formulation of the fundamental finite-element equations
inplaneelastostaticproblems 21
1.4.4.1 Strain–displacementmatrixor[B]matrix 21
1.4.4.2 Stress–strainmatrixor[D]matrix 25
1.4.4.3 Elementstiffnessequations 25
1.4.4.4 Globalstiffnessequations 27
1.4.4.5 Example:Finite-elementcalculationsforasquare
platesubjectedtouniaxialuniformtension 30
Bibliography
34
v
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vi Contents
Ch2apter
Overview of ANSYS structure and visual
capabilities
37
Introduction
2.1 37
Startingtheprogram
2.2 38
2.2.1 Preliminaries 38
2.2.2 Savingandrestoringjobs 40
2.2.3 Organizationoffiles 41
2.2.4 Printingandplotting 42
2.2.5 Exitingtheprogram 43
Preprocessingstage
2.3 43
2.3.1 Buildingamodel 43
2.3.1.1 Definingelementtypesandrealconstants 44
2.3.1.2 Definingmaterialproperties 46
2.3.2 Constructionofthemodel 47
2.3.2.1 Creatingthemodelgeometry 47
2.3.2.2 Applyingloads 48
Solutionstage
2.4 49
Postprocessingstage
2.5 50
Ch3apter
Application of ANSYS to stress analysis
51
Cantileverbeam
3.1 51
3.1.1 Exampleproblem:Acantileverbeam 52
3.1.2 Problemdescription 53
3.1.2.1 Reviewofthesolutionsobtainedbythe
elementarybeamtheory 53
3.1.3 Analyticalprocedures 53
3.1.3.1 Creationofananalyticalmodel 53
3.1.3.2 Inputoftheelasticpropertiesofthebeam
material 56
3.1.3.3 Finite-elementdiscretizationofthebeamarea 57
3.1.3.4 Inputofboundaryconditions 62
3.1.3.5 Solutionprocedures 71
3.1.3.6 Graphicalrepresentationoftheresults 73
3.1.4 ComparisonofFEMresultswithexperimentalones 76
3.1.5 Problemstosolve 76
Appendix:Proceduresforcreatingsteppedbeams
80
A3.1 Creationofasteppedbeam 80
A3.1.1 Howtocanceltheselectionofareas 81
A3.2 Creationofasteppedbeamwitharoundedfillet 81
A3.2.1 Howtodisplayareanumbers 84
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Contents vii
TheprincipleofSt.Venant
3.2 84
3.2.1 Exampleproblem:Anelasticstripsubjectedtodistributed
uniaxialtensilestressornegativepressureatoneend
andclampedattheotherend 84
3.2.2 Problemdescription 85
3.2.3 Analyticalprocedures 85
3.2.3.1 Creationofananalyticalmodel 85
3.2.3.2 Inputoftheelasticpropertiesofthestripmaterial 86
3.2.3.3 Finite-elementdiscretizationofthestriparea 86
3.2.3.4 Inputofboundaryconditions 88
3.2.3.5 Solutionprocedures 89
3.2.3.6 Contourplotofstress 92
3.2.4 Discussion 92
Stressconcentrationduetoellipticholes
3.3 93
3.3.1 Exampleproblem: Anelasticplatewithanellipticholein
itscentersubjectedtouniformlongitudinaltensilestressσ
o
atoneendanddampedattheotherend 93
3.3.2 Problemdescription 94
3.3.3 Analyticalprocedures 94
3.3.3.1 Creationofananalyticalmodel 94
3.3.3.2 Inputoftheelasticpropertiesoftheplate
material 97
3.3.3.3 Finite-elementdiscretizationofthequarter
platearea 98
3.3.3.4 Inputofboundaryconditions 99
3.3.3.5 Solutionprocedures 100
3.3.3.6 Contourplotofstress 101
3.3.3.7 Observationof thevariationof thelongitudinal
stressdistributionintheligamentregion 101
3.3.4 Discussion 102
3.3.5 Problemstosolve 105
Stresssingularityproblem
3.4 106
3.4.1 Exampleproblem:Anelasticplatewithacrackoflength2a
initscentersubjectedtouniformlongitudinaltensilestress
σ atoneendandclampedattheotherend 106
0
3.4.2 Problemdescription 106
3.4.3 Analyticalprocedures 107
3.4.3.1 Creationofananalyticalmodel 107
3.4.3.2 Inputoftheelasticpropertiesoftheplate
material 110
3.4.3.3 Finite-elementdiscretizationofthecenter-
crackedtensionplatearea 110
3.4.3.4 Inputofboundaryconditions 113
3.4.3.5 Solutionprocedures 114
3.4.3.6 Contourplotofstress 115
3.4.4 Discussion 116
3.4.5 Problemstosolve 118
Two-dimensionalcontactstress
3.5 120
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viii Contents
3.5.1 Exampleproblem:Anelasticcylinderwitharadiusoflength
(a)pressedagainstaflatsurfaceofalinearlyelasticmedium
(cid:1)
byaforce 120
3.5.2 Problemdescription 120
3.5.3 Analyticalprocedures 121
3.5.3.1 Creationofananalyticalmodel 121
3.5.3.2 Inputoftheelasticpropertiesofthematerialfor
thecylinderandtheflatplate 123
3.5.3.3 Finite-elementdiscretizationofthecylinderand
theflatplateareas 123
3.5.3.4 Inputofboundaryconditions 133
3.5.3.5 Solutionprocedures 135
3.5.3.6 Contourplotofstress 136
3.5.4 Discussion 136
3.5.5 Problemstosolve 138
References
141
Ch4apter
Mode analysis
143
Introduction
4.1 143
Modeanalysisofastraightbar
4.2 144
4.2.1 Problemdescription 144
4.2.2 Analyticalsolution 144
4.2.3 Modelforfinite-elementanalysis 145
4.2.3.1 Elementtypeselection 145
4.2.3.2 Realconstantsforbeamelement 147
4.2.3.3 Materialproperties 147
4.2.3.4 Createkeypoints 149
4.2.3.5 Createalineforbeamelement 151
4.2.3.6 Createmeshinaline 152
4.2.3.7 Boundaryconditions 154
4.2.4 Executionoftheanalysis 157
4.2.4.1 Definitionofthetypeofanalysis 157
4.2.4.2 Executecalculation 159
4.2.5 Postprocessing 161
4.2.5.1 Read the calculated results of the first mode of
vibration 161
4.2.5.2 Plotthecalculatedresults 161
4.2.5.3 Readthecalculatedresultsofthesecondandthird
modesofvibration 161
Modeanalysisofasuspensionforhard-discdrive
4.3 163
4.3.1 Problemdescription 163
4.3.2 Createamodelforanalysis 163
4.3.2.1 Elementtypeselection 163
4.3.2.2 Realconstantsforbeamelement 165
4.3.2.3 Materialproperties 168
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Contents ix
4.3.2.4 Createkeypoints 168
4.3.2.5 Createareasforsuspension 171
4.3.2.6 Booleanoperation 175
4.3.2.7 Createmeshinareas 177
4.3.2.8 Boundaryconditions 179
4.3.3 Analysis 182
4.3.3.1 Definethetypeofanalysis 182
4.3.3.2 Executecalculation 182
4.3.4 Postprocessing 183
4.3.4.1 Read the calculated results of the first mode of
vibration 183
4.3.4.2 Plotthecalculatedresults 183
4.3.4.3 Read the calculated results of higher modes of
vibration 184
Mode analysis of a one-axis precision moving table
4.4
usingelastichinges
188
4.4.1 Problemdescription 188
4.4.2 Createamodelforanalysis 189
4.4.2.1 Selectelementtype 189
4.4.2.2 Materialproperties 189
4.4.2.3 Createkeypoints 192
4.4.2.4 Createareasforthetable 193
4.4.2.5 Createmeshinareas 197
4.4.2.6 Boundaryconditions 201
4.4.3 Analysis 205
4.4.3.1 Definethetypeofanalysis 205
4.4.3.2 Executecalculation 208
4.4.4 Postprocessing 209
4.4.4.1 Read the calculated results of the first mode of
vibration 209
4.4.4.2 Plotthecalculatedresults 209
4.4.4.3 Readthecalculatedresultsofthesecondandthird
modesofvibration 210
4.4.4.4 Animatethevibrationmodeshape 211
Ch5apter
Analysis for fluid dynamics
215
Introduction
5.1 215
Analysisofflowstructureinadiffuser
5.2 216
5.2.1 Problemdescription 216
5.2.2 Createamodelforanalysis 216
5.2.2.1 Selectkindofanalysis 216
5.2.2.2 Elementtypeselection 217
5.2.2.3 Createkeypoints 219
5.2.2.4 Createareasfordiffuser 221