平面问题基本理论 - Theory of Elasticity.ppt

TheoryofElasticity弹性力学 Chapter7Two DimensionalFormulation平面问题基本理论 Content 内容 1 1 Introduction 概述 MathematicalPreliminaries 数学基础 StressandEquilibrium 应力与平衡 DisplacementsandStrains 位移与应变 MaterialBehavior LinearElasticSolids 弹性应力应变关系 FormulationandSolutionStrategies 弹性力学问题求解 Two DimensionalFormulation 平面问题基本理论 Two DimensionalSolution 平面问题的直角坐标求解 Two DimensionalSolution 平面问题的极坐标求解 Three DimensionalProblems 三维空间问题 BendingofThinPlates 薄板弯曲 Plasticdeformation Introduction 塑性力学基础 IntroductiontoFiniteElementMechod 有限元方法介绍 Two DimensionalFormulation 7 1PlaneStressandPlaneStrain 平面应力和平面应变 7 2DisplacementFormulation 位移求解 7 3StressFormulationandAiryStressFunction 应力求解与应力函数 7 4Photoelasticstressmeasurement 光弹应力测试 7 2 7 1PlaneStress 平面应力 z h arestressfree h issmallincomparisontootherdimensions Notonlyonthesurface butalsothroughouttheentiredomain 整个实体 7 3 Example thinelasticplate 弹性薄板 7 1PlaneStress 平面应力 Hooke slaw strain displacementequations Theequilibriumequations 平衡方程 7 4 Fieldequations 基本方程 7 1PlaneStrain 平面应变 allcross sectionshaveidenticaldisplacements 横截面位移相同 Aprismaticbodywhoselengthismuchlargerthananyin planedimension In planeloadsareindependentoftheout of planecoordinatez Absenceofnormalstrain inadirectionperpendiculartotheplane 7 Example longcylindricalbody 长圆柱体 7 1PlaneStrain 平面应变 PlainStrainExamples 7 7 1PlaneStrain 平面应变 Hooke slaw strain displacementequations theequilibriumequations 7 7 Fieldequations 基本方程 7 1PlaneStressandPlaneStrain x y xy x y xy Plane Stress 6component 3arezero Plane Strain 6component 3arezero Difference 7 8 7 1PlaneStressandPlaneStrain PlainStress平面应力问题 PlainStrain平面应变问题 非平面问题NotPlainProblem 7 9 Problems 7 2DisplacementFormulation 位移法 DisplacementsFormulation Navierequationsforplanestress 7 10 B C 7 11 DisplacementsFormulation Navierequationsforplanestrain 7 2DisplacementFormulation 位移法 B C 7 3StressFormulation 应力法 StressFormulation forplanestress or 7 12 B C 7 3StressFormulation 应力法 StressFormulation forplanestrain or 7 13 B C 7 3StressFormulation 应力法 Differenceinsolution theequilibriumequations 平衡方程 CompatibilityEquations 相容方程 Whichfactorcausesthedifference 7 14 PlainStrain PlainStress 7 3StressFormulation 应力法 ThedifferenceinPhysicalEquationbetweenPlainStressandPlainStrain 7 15 PlainStress PlainStrain 7 3StressFormulation 应力法 7 16 7 3AiryStressFunction 应力函数 Solutionofplainproblems 平面问题的应力求解 SingleConnected 单连通域 7 17 PlainStrain PlainStress 3unknownsSolutionisnoteasy employstheAirystressfunctionSingleunknown 7 3AiryStressFunction 按应力求解 方程的解 非齐次方程的特解 齐次方程通解 7 18 全解 齐次方程通解 非齐次方程的特解 7 3AiryStressFunction 应力函数 由微分方程理论 必存在一函数A x y 使得 也必存在一函数B x y 使得 由微分方程理论 必存在一函数 x y 使得 齐次方程的通解 7 19 7 3AiryStressFunction 应力函数 通解 特解 满足相容方程 边界条件 单值条件 biharmonicequation 7 20 7 3AiryStressFunction 应力函数 7 21 7 4PhotoelasticstressMeasurement 光弹应力测试 Solutionofplainproblems 平面问题的应力求解 SingleConnected 单连通域 Stressdistributiondoesn tdependonmaterialconstantsPhotoelasticstressmeasurement 光弹应力测试 7 22 7 4PhotoelasticstressMeasurement 光弹应力测试 Photoelasticexperiment 光弹性实验 7 23 7 4PhotoelasticstressMeasurement 光弹应力测试 7 24 Example 7 4PhotoelasticstressMeasurement 光弹应力测试 7 25 7 4PhotoelasticstressMeasurement 光弹应力测试 7 26 Example indirecttensiontest ASTMD 41231987 bituminousandotherbrittlematerialssuchasconcrete asphalt rock andceramics 7 4PhotoelasticstressMeasurement 光弹应力测试 7 27 Example 7 4PhotoelasticstressMeasurement 光弹性测试 7 28 Example FEM 7 4PhotoelasticstressMeasurement 光弹性测试 7 29 Example granular 颗粒状 materials 7 4PhotoelasticstressMeasurement 光弹性测试 7 30 Example Photoelasticstudiesofthestressdist