新型有限元論——結構工程中的高等有限元方法

基本介紹

  • 書名： 新型有限元論——結構工程中的高等有限元方法  
  • 作者：Yu-Qiu long Song Cen Zhi-Fei l 
  • ISBN：9787302188896 
  • 定價：138元 
出版信息,內容簡介,目錄,

出版信息

作者：Yu-Qiu long Song Cen Zhi-Fei l
定價：138元
印次：1-1
ISBN：9787302188896
出版日期：2009.03.01
印刷日期：2009.02.25

    內容簡介

    本書是在中文專著《新型有限元論》（2004年版）的基礎上補充了2004年至2008年期間的新成果所撰寫的英文專著，是龍馭球院士、岑松博士和龍志飛教授及其研究組多年來在新型有限元方面研究成果的系統論述。全書分為20章。除首尾兩章外，其餘18章分為3篇：第1篇是變分原理進展，介紹分區和含參變分原理2項成果；它們為構造新型有限元起到理論指導作用。第2篇是有限元法進展初論，重點介紹廣義協調元；這是在協調元與非協調元之間另闢的新路，使協調問題和收斂問題得到合理解決，單元構造方案可以靈活優選，學科內容得到充實更新；廣義協調元是新型有限元方面的主要成果，在本書中起核心作用。第3篇是有限元法進展續論，補充介紹4項成果，包括分區混合元法、解析試函式法、第一和第二類四邊形面積坐標法和樣條函式有限元法，在本書中起錦上添花作用。本書還結合7項成果的論述，介紹了總共108個相關的新單元。
    本書可作為高等學校力學、土木、機械等專業研究生和高年級本科生的教材和參考書，也可供相關領域教師和科技人員參考。

    目錄

    Chapter1　Introduction-TheEvolutiveFiniteElementMethod 1
    1.1　BriefReviewoftheFeaturesofFiniteElementMethod 1
    1.2　FiniteElementMethodandVariationalPrinciples 3
    1.3　ResearchAreasofFEM 5
    1.4　AdvancesinFEMandOutlineofThisBook 6
    References 9
    PARTⅠ　AdvancesinVariationalPrinciples
    Chapter2　TheSub-RegionVariationalPrinciples 15
    2.1　Introduction 15
    2.2　TheSub-RegionVariationalPrincipleforElasticity 16
    2.3　TheSub-RegionVariationalPrincipleforElasticThinPlate 28
    2.4　TheSub-RegionVariationalPrincipleforElasticThickPlate 40
    2.5　TheSub-RegionVariationalPrincipleforElasticShallowShell 51
    2.6　TheSub-RegionMixedEnergyPartialDerivativeTheorem 58
    References 64
    Chapter3　VariationalPrincipleswithSeveralAdjustableParameters 66
    3.1　Introduction 66
    3.2　SeveralPatternsofFunctionalTransformation 67
    3.3　GeneralizedVariationalPrincipleInvolvingSeveralAdjustable
    Parameters 75
    3.4　Variable-Substitution-MultiplierMethod 83
    References 85
    PARTⅡ　AdvancesinFiniteElementMethod—
    GeneralizedConformingElements
    Chapter4　GeneralizedConformingElementTheory 89
    4.1　Introduction 89
    4.2　ConformingandNonconformingElements-SomeConsideration
    about"Conforming" 90
    4.3　TheFirstPatternofGeneralizedConformingElement-Replacing
    NodalConformingbyLineConformingConditions 91
    4.4　TheVariationalBasisofGeneralizedConformingElement-Duality 94
    4.5　TheSynthesisofEnergyMethodandWeightedResidualMethod
    -Flexibility 97
    4.6　TheConvergenceofGeneralizedConformingElement 99
    References 99
    Chapter5　GeneralizedConformingThinPlateElementⅠ
    -Introduction 101
    5.1　Introduction 101
    5.2　TheGeneralizedConformingConditionsandTheirEquivalent
    FormsforThinPlateElements 102
    5.3　GeneralFormulationsoftheGeneralizedConformingThinPlate
    Elements 105
    5.4　SeveralConstructionSchemesoftheGeneralizedConforming
    ThinPlateElements 107
    5.5　ACollectionoftheRecentGeneralizedConformingThinPlate
    Elements 111
    References 118
    Chapter6　GeneralizedConformingThinPlateElementⅡ
    -Line-PointandSemiLoofConformingSchemes 120
    6.1　LineConformingScheme-ElementsTGC-9andTGC-9-1 120
    6.2　Line-PointConformingScheme-RectangularElements 130
    6.3　Line-PointConformingScheme-TriangularElements 146
    6.4　Super-BasisLine-PointConformingScheme-ElementsGCⅢ-R12
    andGCⅢ-T9 155
    6.5　Super-BasisPointConformingScheme-ElementsMB1-T9
    andMB2-T9 164
    6.6　SemiLoofConformingScheme 167
    References 174
    Chapter7　GeneralizedConformingThinPlateElementⅢ
    -Perimeter-PointandLeast-SquareConformingSchemes 176
    7.1　Perimeter-PointConformingScheme-ElementsLR12-1
    andLR12-2 176
    7.2　TheApplicationofPerimeterConformingConditions-Verification
    fortheConvergenceoftheElementACM 181
    7.3　Super-BasisPerimeter-PointConformingScheme-Verificationand
    ImprovementoftheElementBCIZ 187
    7.4　Least-squareScheme-ElementsLSGC-R12andLSGC-T9 198
    References 202
    Chapter8　GeneralizedConformingThickPlateElement 203
    8.1　SummaryoftheThickPlateTheory 203
    8.2　ComparisonoftheTheoriesforThickPlatesandThinPlates 215
    8.3　Thick/ThinBeamElement 232
    8.4　ReviewofDisplacement-basedThick/ThinPlateElements 235
    8.5　GeneralizedConformingThick/ThinPlateElements(1)
    -StartingwithAssuming 237
    8.6　GeneralizedConformingThick/ThinPlateElements(2)
    -StartingwithAssuming 249
    8.7　GeneralizedConformingThin/ThickPlateElements
    -FromThintoThickPlateElements 260
    References 266
    Chapter9　GeneralizedConformingElementfortheAnalysisof
    theLaminatedCompositePlates 268
    9.1　Introduction 268
    9.2　FundamentalTheory 270
    9.3　NewElementCTMQ20fortheAnalysisofLaminated
    CompositePlates 275
    9.4　TheHybrid-EnhancedPost-ProcessingProcedureforElement
    Stresses 286
    9.5　VibrationAnalysisofLaminatedCompositePlates 290
    9.6　NumericalExamples 292
    References 301
    Chapter10　GeneralizedConformingElementfortheAnalysisof
    PiezoelectricLaminatedCompositePlates 304
    10.1　Introduction 304
    10.2　TheFirst-OrderShearDeformationTheoryofPiezoelectric
    LaminatedCompositePlate 306
    10.3　NewPiezoelectricLaminatedCompositePlateElementCTMQE 309
    10.4　The"PartialHybrid"-EnhancedPost-ProcessingProcedurefor
    ElementStresses 314
    10.5　NumericalExamples 318
    References 323
    Chapter11　GeneralizedConformingMembraneandShellElements 325
    11.1　Introduction 325
    11.2　GeneralizedConformingIsoparametricMembraneElement 326
    11.3　MembraneElementswithDrillingFreedoms-Definitionofthe
    DrillingFreedomandtheCorrespondingRectangularand
    QuadrilateralElements 334
    11.4　MembraneElementswithDrillingFreedoms-TriangularElements 346
    11.5　Flat-ShellElements-TriangularThick/ThinShellElement
    GMST18 357
    11.6　ShallowShellElement-VariationalPrincipleandMembrane
    LockingProblem 370
    11.7　ShallowShellElement-TriangularElementSST21with
    Mid-SideNodes 375
    11.8　ShellElementforGeometricallyNonlinearAnalysis
    -TriangularFlat-ShellElementGMST18 382
    11.9　ShellElementforGeometricallyNonlinearAnalysis
    -RectangularShallowShellElementSSR28 386
    References 398
    PARTⅢ　OtherAdvancesinFiniteElementMethod
    Chapter12　Sub-RegionMixedElementⅠ-FundamentalTheory
    andCrackProblem 405
    12.1　ReviewoftheSub-RegionMixedElementMethod 405
    12.2　BasicEquationsoftheSub-RegionMixedElementMethod 408
    12.3　2DCrackProblem 411
    12.4　CrackedThickPlateProblem 418
    12.5　SurfaceCrackProblemina3DBody 426
    References 435
    Chapter13　Sub-RegionMixedElementⅡ-V-NotchProblem 438
    13.1　Introduction 438
    13.2　PlaneV-NotchProblem 438
    13.3　PlaneV-NotchProbleminaBi-Material 450
    13.4　Anti-PlaneV-NotchProbleminaBi-Material 457
    13.5　V-NotchProbleminReissnerPlate 463
    13.6　3DV-NotchProblem 481
    References 493
    Chapter14　AnalyticalTrialFunctionMethodⅠ-Membraneand
    PlateBendingElements 495
    14.1　RecognitionoftheAnalyticalTrialFunctionMethod 495
    14.2　4-NodeMembraneElementsBasedontheAnalyticalTrial
    FunctionMethod 498
    14.3　AvoidingTrapezoidalLockingPhenomenonbyATFElements 500
    14.4　TheBasicAnalyticalSolutionsoftheThickPlateTheoryand
    ATFElementsFreeofShearLocking 504
    14.5　DevelopmentofQuadrilateralThin-ThickPlateElementBased
    ontheAnalyticalTrialFunctionMethod 506
    14.6　AnalyticalTrialFunctionMethodforDevelopingaTriangular
    ThickPlateElementBasedonaThinPlateElement 510
    References 516
    Chapter15　AnalyticalTrialFunctionMethodⅡ-SingularElements
    withCrackandNotch 518
    15.1　Introduction 518
    15.2　TheBasicAnalyticalSolutionsofthePlaneCrackProblem 519
    15.3　ElementATF-MSwithCrackFormulatedbytheAnalytical
    TrialFunctionMethod 523
    15.4　ErrorAnalysisofElementATF-MSwithCrack 525
    15.5　AnalysisofZeroEnergyModeinElementandinStructural
    System 529
    15.6　TheBasicAnalyticalSolutionsofthePlaneNotchProblem 535
    15.7　ElementATF-VNwithNotchFormulatedbytheAnalytical
    TrialFunctionMethod 538
    15.8　ErrorAnalysisofElementATF-VNwithNotch 542
    References 545
    Chapter16　QuadrilateralAreaCoordinateSystems,PartⅠ
    -TheoryandFormulae 546
    16.1　Introduction 546
    16.2　TheIsoparametricCoordinateMethodandtheAreaCoordinate
    Method 547
    16.3　TwoShapeCharacteristicParametersofaQuadrilateral 549
    16.4　TheDefinitionofQuadrilateralAreaCoordinates(QACM-Ⅰ) 553
    16.5　TwoIdenticalRelationsAmongAreaCoordinates(QACM-Ⅰ) 556
    16.6　TransformationRelationsBetweentheAreaCoordinateSystem
    (QACM-Ⅰ)andtheCartesianorIsoparametricCoordinateSystem 558
    16.7　DifferentialFormulae(QACM-Ⅰ) 560
    16.8　IntegralFormulae(QACM-Ⅰ) 562
    16.9　TheProofoftheBasicFormulae(A)and(B)(QACM-Ⅰ) 565
    16.10　TheProofoftheBasicFormulae(C)(QACM-Ⅰ) 569
    16.11　TheQuadrilateralAreaCoordinateSystemwithOnly
    TwoComponents(QACM-Ⅱ) 570
    References 580
    Chapter17　QuadrilateralAreaCoordinateSystems,PartⅡ
    -NewToolsforConstructingQuadrilateralElements 582
    17.1　Introduction 582
    17.2　SensitivityAnalysisofIsoparametricElementstoMeshDistortion 583
    17.3　BriefReviewoftheFiniteElementModelsFormulatedby
    QuadrilateralAreaCoordinateMethods 586
    17.4　4-NodeQuadrilateralMembraneElementsFormulatedby
    theAreaCoordinateMethod 589
    17.5　GeometricallyNonlinearAnalysisUsingElementAGQ6-Ⅰ 601
    17.6　QuadrilateralMembraneElementswithDrillingDegreesof
    FreedomFormulatedbytheAreaCoordinateMethod 606
    17.7　8-NodeQuadrilateralMembraneElementsFormulatedbythe
    AreaCoordinateMethod 613
    17.8　QuadrilateralThinPlateElementFormulatedbytheArea
    CoordinateMethod 620
    17.9　QuadrilateralThickPlateElementFormulatedbytheArea
    CoordinateMethod 628
    17.10　QuadrilateralLaminatedCompositePlateElementFormulated
    bytheAreaCoordinateMethod 635

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