有限元方法基础论第6版

图书标准信息

• 作者 [英]监凯维奇 著
• 出版社 世界图书出版公司
• 出版时间 2008-09
• 版次 1
• ISBN 9787506292542
• 定价 115.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 733页
• 正文语种 英语

【内容简介】

《有限元方法基础论第6版》是一套在国际上颇具权威性的经典著作（共三卷），由有限元法的创始人Zienkiewicz教授和美国加州大学Taylor教授合作撰写，初版于1967年，多次修订再版，深受力学界和工程界科技人员的欢迎。《有限元方法基础论第6版》的特点是理论可靠，内容全面，既有基础理论，又有其具体应用。第1卷目次：标准的离散系统和有限元方法的起源；弹性力学问题的直接方法；有限元概念的推广，Galerkin加权残数和变分法；‘标准的’和‘晋级的’单元形函数：Co连续性单元族；映射单元和数值积分—无限元和奇异元；线性弹性问题；场问题—热传导、电磁势、流体流动；自动网格生成；拼法试验，简缩积分和非协调元；混合公式和约束—完全场方法；不可压缩材料，混合方法和其它解法；多区域混合逼近-区域分解和“框架”方法；误差、恢复过程和误差估计；自适应有限元细分；以点为基础和单元分割的近似，扩展的有限元方法；时间维-场的半离散化、动力学问题以及分析解方法；时间维—时间的离散化近似；耦合系统；有限元分析和计算机处理。

【目录】

Preface
1Thestandarddiscretesystemandoriginsofthefiniteelementmethod
1.1Introduction
1.2Thestruraalelementandthestructuralsystem
1.3Assemblyandanalysisofastructure
1.4Theboundaryconditions
1.5Electricalandfluidnetworks
1.6Thegeneralpattern
1.7Thestandarddiscretesystem
1.8Transformationofcoordinates
1.9Problems

2Adirectphysicalapproachtoproblemsinelasticity：planestress
2.1Introduction
2.2Directformulationoffiniteelementcharacteristics
2.3Generalizationtothewholeregion-internalnodalforceconceptabandoned
2.4Displacementapproachasaminimizationoftotalpotentialenergy
2.5Convergencecriteria
2.6Discretizationerrorandconvergencerate
2.7Displacementfunctionswithdiscontinuitybetweenelementsnon-conformingelementsandthepatchtest
2.8Finiteelementsolutionprocess
2.9Numericalexamples
2.10Concludingremarks
2.11Problems

3Generalizationofthefiniteelementconcepts.Galerkin-weightedresidualandvariationalapproaches
3.1Introduction
3.2Integralorweakstatementsequivalenttothedifferentialequations
3.3Approximationtointegralformulations：theweightedresidualGalerkinmethod
3.4Virtualworkastheweakformofequilibriumequationsforanalysisofsolidsorfluids
69
3.5Partialdiscretization
3.6Convergence
3.7Whatarevariationalprinciples？
3.8Naturalvariationalprinciplesandtheirrelationtogoverningdifferentialequations
3.9Establishmentofnaturalvariationalprinciplesforlinear，self-adjoint，differentialequations
3.10Maximum，minimum，orasaddlepoint？
3.11Constrainedvariationalprinciples.Lagrangemultipliers
3.12Constrainedvariationalprinciples.Penaltyfunctionandperturbedlagrangianmethods
88
3.13Leastsquaresapproximations
3.14Concludingremarks-finitedifferenceandboundarymethods
3.15Problems

4Standardandhierarchicalelementshapefunctions：somegeneralfamiliesofCocontinuity
4.1Introduction
4.2Standardandhierarchicalconcepts
4.3Rectangularelements-somepreliminaryconsiderations
4.4Completenessofpolynomials
4.5Rectangularelements-Lagrangefamily
4.6Rectangularelements-serendipityfamily
4.7Triangularelementfamily
4.8Lineelements
4.9Rectangularprisms-Lagrangefamily
4.10Rectangularprisms-serendipityfamily
4.11Tetrahedralelements
4.12Othersimplethree-dimensionalelements
4.13Hierarchicpolynomialsinonedimension
4.14Two-andthree-dimensional，hierarchicalelementsoftherectangleorbricktype
4.15Triangleandtetrahedronfamily
4.16Improvementofconditioningwithhierarchicalforms
4.17Globalandlocalfiniteelementapproximation
4.18Eliminationofinternalparametersbeforeassembly-substructures
4.19Concludingremarks
4.20Problems

5Mappedelementsandnumericalintegrationinfiniteandsingularityelements
5.1Introduction
5.2Useofshapefunctionsintheestablishmentofcoordinatetransformations
5.3Geometricalconformityofelements
5.4Variationoftheunknownfunctionwithindistorted，curvilinearelements.Continuityrequirements
5.5Evaluationofelement-matrices.Transformationincoordinates
5.6Evaluationofelementmatrices.Transformationinareaandvolumecoordinates
5.7Orderofconvergenceformappedelements
5.8Shapefunctionsbydegeneration
5.9Numericalintegration-onedimensional
5.10Numericalintegration-rectangular（2D）orbrickregions（3D）
5.11Numericalintegration-triangularortetrahedralregions
5.12Requiredorderofnumericalintegration
5.13Generationoffiniteelementmeshesbymapping.Blendingfunctions
5.14Infinitedomainsandinfiniteelements
5.15Singularelementsbymapping-useinfracturemechanics，etc.
5.16Computationaladvantageofnumericallyintegratedfiniteelements
5.17Problems

6Problemsinlinearelasticity
6.1Introduction
6.2Governingequations
6.3Finiteelementapproximation
6.4Reportingofresults：displacements，strainsandstresses
6.5Numericalexamples
6.6Problems

7Fieldproblems-heatconduction，electricandmagneticpotentialandfluidflow
7.1Introduction
7.2Generalquasi-harmonicequation
7.3Finiteelementsolutionprocess
7.4Partialdiscretization-transientproblems
7.5Numericalexamples-anassessmentofaccuracy
7.6Concludingremarks
7.7Problems

8Automaticmeshgeneration
8.1Introduction
8.2Two-dimensionalmeshgeneration-advancingfrontmethod
8.3Surfacemeshgeneration
8.4Three-dimensionalmeshgeneration-Delaunaytriangulation
8.5Concludingremarks
8.6Problems

9Thepatchtest，reducedintegration，andnon-conformingelements
9.1Introduction
9.2Convergencerequirements
9.3Thesimplepatchtest（testsAandB）-anecessaryconditionforconvergence
332
9.4Generalizedpatchtest（testC）andthesingle-elementtest
9.5Thegeneralityofanumericalpatchtest
9.6Higherorderpatchtests
9.7Applicationofthepatchtesttoplaneelasticityelementswithstandardandreducedquadrature
9.8Applicationofthepatchtesttoanincompatibleelement
9.9Higherorderpatchtest-assessmentofrobustness
9.10Concludingremarks
9.11Problems

10Mixedformulationandconstraints-completefieldmethods
10.1Introduction
10.2Discretizationofmixedforms-somegeneralremarks
10.3Stabilityofmixedapproximation.Thepatchtest
10.4Two-fieldmixedformulationinelasticity
10.5Three-fieldmixedformulationsinelasticity
10.6Complementaryformswithdirectconstraint
10.7Concludingremarks-mixedformulationoratestofelementrobustness
10.8Problems

11Incompressibleproblems，mixedmethodsandotherproceduresofsolution
11.1Introduction
11.2Deviatoricstressandstrain，pressureandvolumechange
11.3Two-fieldincompressibleelasticity（upform）
11.4Three-fieldnearlyincompressibleelasticity（u-p-form）
11.5Reducedandselectiveintegrationanditsequivalencetopenalizedmixedproblems
11.6Asimpleiterativesolutionprocessformixedproblems：Uzawamethod
11.7Stabilizedmethodsforsomemixedelementsfailingtheincompressibilitypatchtest
11.8Concludingremarks
11.9Problems

12Multidomainmixedapproximations-domaindecompositionandframemethods
12.1Introduction
12.2LinkingoftwoormoresubdomainsbyLagrangemultipliers
12.3Linkingoftwoormoresubdomainsbyperturbedlagrangianandpenaltymethods
12.4Interfacedisplacementframe
12.5Linkingofboundary（orTrefftz）-typesolutionbytheframeofspecifieddisplacements
12.6Subdomainswithstandardelementsandglobalfunctions
12.7Concludingremarks
12.8Problems

13Errors，recoveryprocessesanderrorestimates
13.1Definitionoferrors
13.2Superconvergenceandoptimalsamplingpoints
13.3Recoveryofgradientsandstresses
13.4Superconvergentpatchrecovery-=SPR
13.5Recoverybyequilibrationofpatches-REP
13.6Errorestimatesbyrecovery
13.7Residual-basedmethods
13.8Asymptoticbehaviourandrobustnessoferrorestimators-theBabuskapatchtest
13.9Boundsonquantitiesofinterest
13.10Whicherrorsshouldconcernus7
13.11Problems

14Adaptivefiniteelementrefinement
14.1Introduction
14.2Adaptiveh-refinement
14.3p-refinementandhp-refinement
14.4Concludingremarks
14.5Problems

15Point-basedandpartitionofunityapproximations.Extendedfiniteelementmethods
15.1Introduction
15.2Functionapproximation
15.3Movingleastsquaresapproximations-restorationofcontinuityofapproximation
15.4Hierarchicalenhancementofmovingleastsquaresexpansions
15.5Pointcollocation-finitepointmethods
15.6Galerkinweightingandfinitevolumemethods
15.7Useofhierarchicandspecialfunctionsbasedonstandardfiniteelementssatisfyingthepartitionofunityrequirement
15.8Concludingremarks
15.9Problems

16Thetimedimension-semi-discretizationoffieldanddynamicproblemsandanalyticalsolutionprocedures
16.1Introduction
16.2Directformulationoftime-dependentproblemswithspatialfiniteelementsubdivision
16.3Generalclassification
16.4Freeresponse-eigenvaluesforsecond-orderproblemsanddynamicvibration
16.5Freeresponse-eigenvaluesforfirst-orderproblemsandheatconduction，etc.
16.6Freeresponse-dampeddynamiceigenvalues
16.7Forcedperiodicresponse
16.8Transientresponsebyanalyticalprocedures
16.9Symmetryandrepeatability
16.10Problems

17Thetimedimension-discreteapproximationintime
17.1Introduction
17.2Simpletime-stepalgorithmsforthefirst-orderequation
17.3Generalsingle-stepalgorithmsforfirst-andsecond-orderequations
17.4Stabilityofgeneralalgorithms
17.5Multisteprecurrencealgorithms
17.6Someremarksongeneralperformanceofnumericalalgorithms
17.7TimediscontinuousGalerkinapproximation
17.8Concludingremarks
17.9Problems

18Coupledsystems
18.1Coupledproblems-definitionandclassification
18.2Fluid-structureinteraction（ClassIproblems）
18.3Soil-porefluidinteraction（ClassIIproblems）
18.4Partitionedsingle-phasesystems-implicit-explicitpartitions（ClassIproblems）
18.5Staggeredsolutionprocesses
18.6Concludingremarks

19Computerproceduresforfiniteelementanalysis
19.1Introduction
19.2Pre-processingmodule：meshcreation
19.3Solutionmodule
19.4Post-processormodule
19.5Usermodules

AppendixA：Matrixalgebra
AppendixB：Tensor-indicialnotationintheapproximationofelasticityproblems
AppendixC：Solutionofsimultaneouslinearalgebraicequations
AppendixD：Someintegrationformulaeforatriangle
AppendixE：Someintegrationformulaeforatetrahedron
AppendixF：Somevectoralgebra
AppendixG：Integrationbypartsintwoorthreedimensions（Greenstheorem）
AppendixH：Solutionsexactatnodes
AppendixI：Matrixdiagonalizationorlumping
Authorindex
Subjectindex