An introduction to the finite element method:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
McGraw-Hill
2009
|
| Edition: | 3. ed., Internat. ed., [Nachdr.] |
| Series: | McGraw-Hill series in mechanical engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XVI, 766 S. graph. Darst. 24 cm |
| ISBN: | 9780071267618 |
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| 245 | 1 | 0 | |a An introduction to the finite element method |c J. N. Reddy |
| 250 | |a 3. ed., Internat. ed., [Nachdr.] | ||
| 264 | 1 | |a Boston [u.a.] |b McGraw-Hill |c 2009 | |
| 300 | |a XVI, 766 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a McGraw-Hill series in mechanical engineering | |
| 500 | |a Literaturangaben | ||
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Record in the Search Index
| _version_ | 1804143786938335232 |
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| adam_text | IMAGE 1
ANINTRODUCTIONTOTHE FINITEELEMENTMETHOD
THIRDEDITION
J. N.REDDY DEPARTMENT01MECHANICALENGINEERING TEXAS
A&M UNIVERSITY
COLLEGESTATION,TEXAS,USA77843
11
BOSTONBURRRIDGE, IL DUBUQUE, IA MADISON, WI NEW YORK SAN FRANCISCO SI.
LOUIS
BANGKOK
BOGOTE. CARACASKUALALUMPURLISBONLONDONMADRIDMEXICOCITY
MILANMONTREALNEWDELHISANTIAGOSEOULSINGAPORESYDNEYTAIPEITORONTO
IMAGE 2
PREFACE
1INTRODUCTION
1.1 GENERALCOMMENTS 1.2MATHEMATICALMODELS 1.3NUMERICALSIMULATIONS
1.4THEFINITEELEMENTMETHOD
1.4.1THEBASICIDEA 1.4.2THEBASICFEATURES 1.4.3
SOME REMARKS
1.4.4A
BRIEF REVIEW OF HISTORYANDRECENTDEVELOPMENTS
1
.5 THE PRESENTSTUDY
1.6SUMMARY PROBLEMS REFERENCESFORADDITIONALREADING
CONTENTS
XIV
1 I
2 9
13 13
13
21 23 24 24 25 26
2MATHEMATICALPRELIMINARIES,INTEGRALFORMULATIONS, ANDVARIATIONALMETHODS
2.1GENERALINTRODUCTION 2.1.1VARIATIONALPRINCIPLESANDMETHODS
2.1.2VARIATIONALFORMULATIONS 2.1.3NEEDFORWEIGHTED-INTEGRALSTATEMENTS 2.2
SOME MATHEMATICALCONCEPTSANDFORMULAE
2.2.1COORDINATESYSTEMSANDTHEDEIOPERATOR
2.2.2BOUNDARYVALUE,INITIALVALUE,ANDEIGENVALUEPROBLEMS
2.2.3INTEGRALIDENTITIES 2.2.4LINEARANDBILINEARFUNCTIONALS 2.3ELEMENTS
OF CALCULUS OF VARIATIONS
2.3.1INTRODUCTION 2.3.2VARIATIONALOPERATORANDFIRSTVARIATION
2.3.3FUNDAMENTAL
LEMMA OF VARIATIONALCALCULUS
2.3.4THEEULEREQUATIONS 2.3.5NATURALANDESSENTIALBOUNDARYCONDITIONS
2.3.6HAMILTON SPRINCIPLE
27 27 27
28 28
31 31
33 36 39
41
41
41
44 44
47 54
VII
IMAGE 3
VIII CONTENTS
2.4INTEGRALFORMULATIONS 2.4.1INTRODUCTION
2.4.2WEIGHTED-INTEGRALANDWEAKFORMULATIONS
2.4.3LINEARANDBILINEARFORMSANDQUADRATICFUNCTIONALS 2.4.4EXAMPLES
2.5VARIATIONALMETHODS
2.5.1INTRODUCTION 2.5.2THERITZMETHOD 2.5.3APPROXIMATIONFUNCTIONS
2.5.4EXAMPLES 2.5.5THEMETHOD
OF WEIGHTEDRESIDUALS
2.6SUMMARY PROBLEMS REFERENCESFORADDITIONALREADING
3SECOND-ORDERDIFFERENTIALEQUATIONSINONEDIMENSION: FINITEELEMENTMODELS
3.1 BACKGROUND 3.2BASICSTEPS
OF FINITEELEMENTANALYSIS
3.2.1MODELBOUNDARYVALUEPROBLEM 3.2.2DISCRETIZATION
OF THEDOMAIN
3.2.3DERIVATION
OF ELEMENTEQUATIONS
3.2.4CONNECTIVITY
OF ELEMENTS
3.2.5IMPOSITION
OF BOUNDARYCONDITIONS
3.2.6SOLUTION
OF EQUATIONS
3.2.7POSTCOMPUTATION
OF THESOLUTION
3.3SOMEREMARKS 3.4AXISYMMETRICPROBLEMS 3.4.1MODELEQUATION 3.4.2WEAKFORM
3.4.3FINITEELEMENTMODEL 3.5SUMMARY PROBLEMS
REFERENCESFORADDITIONALREADING
4SECOND-ORDERDIFFERENTIALEQUATIONSINONEDIMENSION: APPLICATIONS
4.1 PRELIMINARYCOMMENTS 4.2DISCRETESYSTEMS 4.2.1LINEARELASTICSPRING
4.2.2TORSION
OF CIRCULARSHAFTS
4.2.3ELECTRICALRESISTORCIRCUITS 4.2.4FLUIDFLOWTHROUGHPIPES
4.3HEATTRANSFER 4.3.1GOVERNINGEQUATIONS
4.3.2FINITEELEMENTMODELS 4.3.3NUMERICALEXAMPLES
58 58
58 64 66 74 74 74 76 77
91 97
98 102
103 103
105 105
106 108
125 132
132 134
141 146 146
147 148
150 151
154
155 155
156 156
158 159
161 162
162 166 166
IMAGE 4
CONTENTS IX
4.4FLUIDMECHANICS 181 4.4.1GOVERNINGEQUATIONS[81
4.4.2FINITEELEMENTMODEL
181
4.5SOLIDANDSTRUCTURAL MECHANICS 183 4.5.1PRELIMINARYCOMMENTS 183
4.5.2FINITEELEMENTMODEL OF BARSANDCABLES184
4.5.3NUMERICALEXAMPLES
185
4.6PLANETROSSES194
4.6.1INTRODUCTION194
4.6.2BASICTROSSELEMENT194
4.6.3GENERALTROSSELEMENT
195
4.6.4CONSTRAINTEQUATIONS: PENALTYAPPROACH202
4.6.5CONSTRAINTEQUATIONS:ADIRECTAPPROACH
211
4.7SUMMARY214
PROBLEMS
21S
REFERENCESFARADDITIONALREADING 231
5 BEAMSANDFRAMES233
5.1 INTRODUCTION233
5.2EULER-BERNOULLIBEAMELEMENT233
5.2.1GOVERNINGEQUATION233
5.2.2DISCRETIZATION
OF THEDOMAIN234
5.2.3DERIVATION
OF ELEMENTEQUATIONS234
5.2.4ASSEMBLY
OF ELEMENTEQUATIONS243
5.2.5IMPOSITION
OF BOUNDARYCONDITIONS245
5.2.6POSTPROCESSING
OF THESOLUTION247
5.2.7NUMERICALEXAMPLES248
5.3TIMOSHENKOBEAMELEMENTS
261
5.3.1GOVERNINGEQUATIONS 261 5.3.2 WEAKFORM 262
5.3.3GENERALFINITEELEMENTMODEL264
5.3.4CONSISTENTINTERPOLATIONELEMENTS266
5.3.5REDUCEDINTEGRATIONELEMENT270
5.3.6NUMERICALEXAMPLES
271
S.4PLANEFRAMEELEMENTS274
5.4.1INTRODUCTORYCOMMENTS274
5.4.2FRAMEELEMENT274
5.5SUMMARY
281
PROBLEMS282
REFERENCESFORADDITIONALREADING290
6 EIGENVALUEANDTIME-DEPENDENTPROBLEMS291
6.1 EIGENVALUEPROBLEMS 291 6.1.1INTRODUCTION 291
6.1.2FARMULATION OF EIGENVALUEPROBLEMS292
6.1.3FINITEELEMENTFARMULATION295
6.2TIME-DEPENDENTPROBLEMS314
6.2.1INTRODUCTION314
6.2.2SEMIDISCRETEFINITEELEMENTMODELS316
IMAGE 5
XCONTENTS
6.2.3PARABOLICEQUATIONS 6.2.4HYPERBOLICEQUATIONS 6.2.5MASSLUMPING
6.2.6APPLICATIONS 6.3SUMMARY PROBLEMS REFERENCESFORADDITIONALREADING
7 COMPUTERIMPLEMENTATION 7.1 NUMERICALINTEGRATION 7.1.1BACKGROUND
7.1.2NATURALCOORDINATES 7.1.3APPROXIMATION
OF GEOMETRY
7.1.4ISOPARAMETRICFORMULATIONS 7.1.5NUMERICALINTEGRATION
7.2COMPUTERIMPLEMENTATION 7.2.1INTRODUCTORYCOMMENTS
7.2.2GENERALOUTLINE 7.2.3PREPROCESSOR 7.2.4CALCULATION
OF ELEMENTMATRICES(PROCESSOR)
7.2.5ASSEMBLY
OF ELEMENTEQUATIONS(PROCESSOR)
7.2.6IMPOSITION
OF BOUNDARYCONDITIONS(PROCESSOR)
7.2.7SOLVINGEQUATIONSANDPOSTPROCESSING 7.3APPLICATIONS
OF PROGRAM FEMID
7.3.1GENERALCOMMENTS 7.3.2ILLUSTRATIVEEXAMPLES 7.4SUMMARY PROBLEMS
REFERENCESFORADDITIONALREADING
8 SINGLE-VARIABLEPROBLEMSINTWODIMENSIONS
318 324 326 328
337 337 342
343 343 343 345 346 347
348 356 356 357 359 360 363 365 367 370 370 370
401 401
406
409
8.1 INTRODUCTION409
8.2BOUNDARYVALUEPROBLEMS410
8.2.1THEMODELEQUATION410
8.2.2FINITEELEMENTDISCRETIZATION
411
8.2.3WEAKFORM412
8.2.4FINITEELEMENTMODEL415
8.2.5DERIVATION
OF INTERPOLATION FUNCTIONS417
8.2.6EVALUATION
OF ELEMENTMATRICESANDYECTORS425
8.2.7ASSEMBLY
OF ELEMENTEQUATIONS436
8.2.8POSTCOMPUTATIONS440
8.2.9AXISYMMETRICPROBLEMS
441
8.3ANUMERICALEXAMPLE442
8.4SOMECOMMENTSONMESHGENERATIONANDIMPOSITION
OF BOUNDARYCONDITIONS453
8.4.1DISCRETIZATION
OF ADOMAIN453
8.4.2GENERATION
OF FINITEELEMENTDATA455
8.4.3IMPOSITION
OF BOUNDARYCONDITIONS456
IMAGE 6
CONTENTS XI
8.5APPLICATIONS458
8.5.1CONDUCTIONANDCONVECTIONHEATTRANSFER458
8.5.2FLUIDMECHANICS472
8.5.3SOLIDMECHANICS485
8.6EIGENVALUEANDTIME-DEPENDENTPROBLEMS490
8.6.1INTRODUCTION490
8.6.2PARABOLICEQUATIONS491
8.6.3HYPERBOLICEQUATIONS499
8.7
SUMMARY. 504PROBLEMS504REFERENCES
FAR ADDITIONALREADING522
9INTERPOLATIONFUNCTIONS,NUMERICALLNTEGRATION, ANDMODELINGCONSIDERATIONS
9.1INTRODUCTION
9.2ELEMENTLIBRARY 9.2.1TRIANGULARELEMENTS 9.2.2RECTANGULARELEMENTS
9.2.3THESERENDIPITYELEMENTS 9.2.4HERMITECUBICINTERPOLATIONFUNCTIONS
9.3NUMERICALINTEGRATION 9.3.1PRELIMINARYCOMMENTS
9.3.2COARDINATETRANSFORMATIONS
9.3.3INTEGRATIONOVERAMASTERRECTANGULARELEMENT
9.3.4INTEGRATIONOVERAMASTERTRIANGULARELEMENT 9.4MODELINGCONSIDERATIONS
9.4.1PRELIMINARYCOMMENTS 9.4.2ELEMENTGEOMETRIES 9.4.3MESHGENERATION
9.4.4LOADREPRESENTATION
9.5SUMMARY
PROBLEMS
REFERENCES
FAR ADDITIONALREADING
10 FLOWS OF VISCOUSINCOMPRESSIBLEFLUIDS 10.1PRELIMINARYCOMMENTS
10.2GOVERNINGEQUATIONS 10.3YE1OCITY-PRESSUREFARMULATION
10.3.1WEAKFARMULATION 10.3.2FINITE
ELEMENT MODEL
10.4PENALTYFUNCTIONFARMULATION 10.4.1PRELIMINARYCOMMENTS
]0.4.2FARMULATION
OF THEFLOWPROBLEM AS ACONSTRAINEDPROBLEM
10.4.3LAGRANGEMULTIPLIERMODEL 10.4.4PENALTYMODEL 10.4.5TIMEAPPROXIMATION
525 525 525 525
532 537 539
540 540
543 549 557
561
561 562 563 567
569
570
575
577 577 577 579 579 581
583 583 583
584 585 588
IMAGE 7
XII CONTENTS
10.5COMPUTATIONALASPECTS588
10.5.1PROPERTIES
OF THEMATRIXEQUATIONS588
10.5.2CHOICE
OF ELEMENTS589
10.5.3EVALUATION
OF ELEMENTMATRICESINTHEPENALTYMODEL590
10.5.4POSTCOMPUTATION
OF STRESSES 591
10.6NUMERICALEXAMPLES 591 10.7SUMMARY602
PROBLEMS603
REFERENCESFORADDITIONALREADING605
11 PLANEELASTICITY607
11.1 INTRODUCTION607
11.2GOVERNINGEQUATIONS607
11.2.1PLANESTRAIN607
11.2.2PLANESTRESS608
11.2.3SUMMARY
OF EQUATIONS610
11.3WEAKFORMULATIONS612
11.3.1PRELIMINARY COMMENTS612
11.3.2PRINCIPLE
OF VIRTUA1 DISPLACEMENTS IN VECTORFORM612
11.3.3WEAKFORM
OF THEGOVERNINGDIFFERENTIALEQUATIONS613
11.4FINITEELEMENTMODEL614
1
1.4.1 GENERALMODEL614
11.4.2EIGENVA1UEANDTRANSIENTPROBLEMS617
1
1.5 EVALUATION OF INTEGRALS617
11.6ASSEMBLY
OF FINITEELEMENTEQUATIONS620
11.7EXAMP1ES622
11.8SUMMARY629
PROBLEMS629
REFERENCESFORADDITIONALREADING633
12BENDING OF ELASTICPLATES635
12.1 INTRODUCTION635
12.2CLASSICALPIATETHEORY637
12.2.1DISPLACEMENTFIELD637
12.2.2VIRTUALWORKSTATEMENT638
12.2.3FINITEELEMENTMODEL642
12.2.4PLATEBENDINGELEMENTS643
12.3SHEARDEFORMATIONPLATETHEORY646
12.3.1DISPLACEMENT
FIE1D 646
12.3.2VIRTUA1WORKSTATEMENT648
12.3.3FINITEELEMENTMODEL650
12.3.4SHEARLOCKINGANDREDUCEDINTEGRATION652
J 2.4EIGENVALUEANDTIME-DEPENDENTPROBLEMS653
12.5EXAMPLES655
12.6SUMMARY663
PROBLEMS663
REFERENCESFORADDITIONALREADING665
IMAGE 8
13 COMPUTERIMPLEMENTATION OF TWO-DIMENSIONALPROBLEMS 13.1 INTRODUCTION
13.2PREPROCESSOR 13.3ELEMENTCOMPUTATIONS(PROCESSOR) 13.4APPLICATIONS
OF THECOMPUTERPROGRAMFEM2D
13.4.1INTRODUCTION 13.4.2DESCRIPTION
OF MESHGENERATORS
13.4.3APPLICATIONS(ILLUSTRATIVEEXAMPLES) 13.5SUMMARY PROBLEMS
REFERENCESFORADDITIONALREADING
14 PRELUDETOADVANCEDTOPICS 14.1 INTRODUCTION
14.2ALTERNATIVEFINITEELEMENTMODELS 14.2.1INTRODUCTORYCOMMENTS
14.2.2WEIGHTEDRESIDUALFINITEELEMENTMODELS 14.2.3MIXEDFORMULATIONS
14.3THREE-DIMENSIONALPROBLEMS 14.3.1HEATTRANSFER
14.3.2FLOWS
OF VISCOUSINCOMPRESSIBLEFLUIDS
14.3.3ELASTICITY 14.3.4THREE-DIMENSIONALFINITE ELEMENTS
14.3.5ANUMERICALEXAMPLE 14.4NONLINEARPROBLEMS 14.4.1GENERALCOMMENTS
14.4.2BENDING
OF EULER-BERNOULLIBEAMS
14.4.3THENAVIER-STOKESEQUATIONSINTWODIMENSIONS
14.4.4SOLUTIONMETHODSFORNONLINEARALGEBRAICEQUATIONS
14.4.5NUMERICALEXAMPLES 14.5ERRORSINFINITEELEMENTANALYSIS
14.5.1TYPES
OF ERRORS
14.5.2MEASURES
OF ERRORS
14.5.3CONVERGENCEANDACCURACY
OF SOLUTIONS
14.6SUMMARY PROBLEMS REFERENCESFORADDITIONALREADING
INDEX
CONTENTS XIII
667 667 669 669
675 675
681 686 703
705 709
711 711
711 711
712 722 725 726 727 728
731 735 736 736 736
738 739 740 743
743 744 745 750
751 753
757
|
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| author | Reddy, Junuthula Narasimha 1945- |
| author_GND | (DE-588)108393232 |
| author_facet | Reddy, Junuthula Narasimha 1945- |
| author_role | aut |
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| bvnumber | BV037199159 |
| classification_rvk | SK 910 |
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| discipline | Mathematik |
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| id | DE-604.BV037199159 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:53:12Z |
| institution | BVB |
| isbn | 9780071267618 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021113437 |
| oclc_num | 699879319 |
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| owner | DE-29T |
| owner_facet | DE-29T |
| physical | XVI, 766 S. graph. Darst. 24 cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
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| publisher | McGraw-Hill |
| record_format | marc |
| series2 | McGraw-Hill series in mechanical engineering |
| spelling | Reddy, Junuthula Narasimha 1945- Verfasser (DE-588)108393232 aut An introduction to the finite element method J. N. Reddy 3. ed., Internat. ed., [Nachdr.] Boston [u.a.] McGraw-Hill 2009 XVI, 766 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier McGraw-Hill series in mechanical engineering Literaturangaben Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021113437&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reddy, Junuthula Narasimha 1945- An introduction to the finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4017233-8 |
| title | An introduction to the finite element method |
| title_auth | An introduction to the finite element method |
| title_exact_search | An introduction to the finite element method |
| title_full | An introduction to the finite element method J. N. Reddy |
| title_fullStr | An introduction to the finite element method J. N. Reddy |
| title_full_unstemmed | An introduction to the finite element method J. N. Reddy |
| title_short | An introduction to the finite element method |
| title_sort | an introduction to the finite element method |
| topic | Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021113437&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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