张量分析及其在力学中的应用

图书标准信息

• 作者 [俄]L.P.乐博德夫（Leonid P.Lebedev）、[俄]Michael J、[俄]Victor A Eremeyev 著
• 出版社 世界图书出版公司
• 出版时间 2015-01
• 版次 1
• ISBN 9787510084539
• 定价 69.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 363页
• 正文语种 简体中文

【内容简介】

　　《张量分析及其在力学中的应用》张量分析是研究连续介质力学的重要数学工具。张量分析及其在连续介质力学中的应用紧密结合工程力学来介绍张量分析的基本理论和实用计算。《张量分析及其在力学中的应用》共分七章，内容包括：矢量与张量，笛卡尔张量，张量场论，张量场函数的导数，张量分析在线弹性理论中的应用，张量分析在流体力学中的应用。

【目录】

Foreword
Preface
TensorAnalysis
1.Preliminaries
1.1TheVectorConceptRevisited
1.2AFirstLookatTensors
1.3AssumedBackground
1.4MoreontheNotionofaVector
1.5Problems

2.TransformationsandVectors
2.1ChangeofBasis
2.2DualBases
2.3TransformationtotheReciprocalFrame
2.4TransformationBetweenGeneralFrames
2.5CovariantandContravariantComponents
2.6TheCrossProductinIndexNotation
2.7NormsontheSpaceofVectors
2.8ClosingRemarks
2.9Problems

3.Tensors
3.1DyadicQuantitiesandTensors
3.2TensorsFromanOperatorViewpoint
3.3DyadicComponentsUnderTransformation
3.4MoreDyadicOperations
3.5PropertiesofSecond—OrderTensors
3.6EigenvaluesandEigenvectorsofaSecond—OrderSymmelricTensor
3.7TheCayley—HamiltonTheorem
3.8OtherPropertiesofSecond—OrderTensors
3.9ExtendingtheDyadIdea
3.10TensorsoftheFourthandHigherOrders
3.11FunctionsofTensorialArguments
3.12NormsforTensors，andSomeSpaces
3.13DifferentiationofTensorialFunctions
3.14Problems

4.TensorFields
4.1VectorFields
4.2DifferentialsandtheNablaOperator
4.3DifferentiationofaVectorFunction
4.4DerivativesoftheFrameVectors
4.5ChristoffelCoefficientsandtheirProperties
4.6CovariantDifferentiation
4.7CovariantDerivativeofaSecond—OrderTensor
4.8DifferentialOperations
4.9OrthogonalCoordinateSystems
4.10SomeFormulasoflntegration
4.11Problems

5.ElementsofDifferentialGeometry
5.1ElementaryFactsfromtheTheoryofCurves
5.2TheTorsionofaCurve
5.3Frenet—SerretEquations
5.4ElementsoftheTheoryofSurfaces
5.5TheSecondFundamentalFormofaSurface
5.6DerivationFormulas
5.7ImplicitR，epresentationofaCurve；ContactofCurves
5.8OsculatingParaboloid
5.9ThePrincipalCurvaturesofaSurface
5.10SurfacesofRevolution
5.11NaturalEquationsofaCurve
5.12AWordAboutRigor
5.13Conclusion
5.14Problems
ApplicationsinMechanics

6.LinearElasticity
6.1StressTensor
6.2StrainTensor
6.3EquationofMotion
6.4Hooke'sLaw
6.5EqrulibriumEquationsinDisplacements
6.6BoundaryConditionsandBoundaryValueProblems
6.7EquilibriumEquationsinStresses
6.8UniquenessofSolutionfortheBoundaryValueProblemsofElasticity
6.9Betti'sReciprocityTheorem
6.10MuumumTotalEnergyPrinciple
6.11Ritz'sMethod
6.12Rayleigh'sVariationalPrinciple
6.13PlaneWaves
6.14PlaneProblemsofElasticity
6.15Problems

7.LinearElasticShells
7.1SomeUsefulFormulasofSurfaceTheory
7.2KinematicsinaNeighborhoodof∑
7.3ShellEqrulibriumEquations
7.4ShellDeformationandStrains；Kirchhoff'sHypotheses
7.5ShellEnergy
7.6BoundaryConditions
7.7AFewRemarksontheKirchhoff—LoveTheory
7.8PlateTheory
7.9OnNon—ClassicalTheoriesofPlatesandShells
AppendixAFormulary
AppendixBHintsandAnswers
Bibliography
Index