弹性力学双语版-西安交通大学-8

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ELASTICITY 弹性力学常用专业名词中英文对照修改

中文英文英文中文艾利应力函数Airy stress function Airy stress function艾利应力函数板plate anti-sysmetric tensor反对称张量板边bounday of plate applied elasticity应用弹性力学板的抗弯强度flexural rigidity of plate axisymmetry轴对称板的内力internal force of plate base vector基矢量板的中面middle plane of plate basic assumptions ofelasticity弹性力学基本假定贝尔特拉米-米歇尔方程Beltrami-Michellequationbasic equation for thebending of thin plate薄板弯曲的基本方程贝蒂互换定理Betti reciprocal theorem Beltrami consistencyequation贝尔特拉米相容方程变温temperature change Beltrami-Michellequation 贝尔特拉米-米歇尔方程表层波surface wave Betti reciprocal theorem贝蒂互换定理半逆解法semi-inverse method body force体力薄板thin plate boundary condition边界条件薄板弯曲的基本方程basic equation for thebending of thin platebounday of plate板边薄膜比拟membrage analogy Boussinesq problem布西内斯克问题布西内斯克问题Boussinesq problem Boussinesq solution布西内斯克解答布西内斯克解答Boussinesq solution Boussinesq solution布西内斯克解答布西内斯克-伽辽金通解Boussinesq-Galerkingeneral solutionBoussinesq-Galerkingeneral solution布西内斯克-伽辽金通解半空间体semi-infinite body bulk modulus体积模量半平面体semi-infinite plane Castigliano formula卡斯蒂利亚诺公式贝尔特拉米相容方程Beltrami consistencyequationCauchy equation柯西方程边界条件boundary condition Cerruti problem塞路蒂问题变分法（能量法）variationalmethod,energy method characteristic equationof stress state应力状态特征方程薄板内力internal forces of thinplate coefficient of lateralpressure侧压力系数薄板弹性曲面elatic surface of thinplate complex potential复位势薄板弹性曲面微分方程differential equation ofelastic surface of thinplatecondition of single-value displacement位移单值条件薄板弯曲刚度flexural rigidity of thinplateconsistency equation相容方程布西内斯克解答Boussinesq solution contact problem接触问题产熵entropy prodction continuity连续性沉陷settlement continuous hypothesis连续性假设侧压力系数coefficient of lateralpressure coordinate curves坐标曲线ELASTICITY(弹性力学)常用专业名词中英文对照差分法finite-differencemethord coordinate surface坐标曲面差分公式finite-differencefromulate coupling耦合重三角级数double triangle series curvilinear coordinates曲线坐标大挠度问题large deflection problem deflection挠度单位张量unit tensor deformation形变单元分析element analysis density of comlementarystrain energy应变余能密度单元刚度矩阵element stiffness matrix density of internalenergy 内能密度等容波equivoluminal wave diaplacement位移等容的位移场equivoluminaldisplacement field diaplacementcomponents位移分量叠加原理superposition principle diaplacement method位移解法度量张量metric tensor diaplacement method位移法对称张量symmetric tensor diaplacement shapefunction位移的形函数单连体simply connected body diaplacement variationalequation位移变分方程单三角级数解single triangle series differential equation ofelastic surface弹性曲面的微分方程单元节点载荷列阵elemental nodal loadmatrix differential equation ofelastic surface of thinplate薄板弹性曲面微分方程单元劲度矩阵elemental stiffnessmatrix differential equation ofequilibrium平衡微分方程多连体multiply connected body differential equation ofequilibrium in terms ofdisplacement 以位移表示的平衡微分方程二阶张量second order tensor dilatation wave膨胀波反对称张量anti-sysmetric tensor discretization离散化符拉芒解答Flamant soluton discretization structure离散化结构反射reflection displacement boundarycondition位移边界条件傅里叶变换Fourier transform displacement model位移模式傅里叶积分Fourier integral distrotion wave畸变波复位势complex potential double triangle series重三角级数格林公式Green formula dummy index哑指标各向同性假设isotropic hypothesis elastic body弹性体供熵entropy supply elastic constants弹性常数广义变分原理generanized variatianalprincipleelastic matrix弹性矩阵广义胡克定律generanized Hooke law elastic principledirection 弹性主方向刚体位移rigid body displacement elastic symmetric plane弹性对称面各向同性isotropy elastic wave弹性波哈密顿变分原理Hamiton varitionalprincipleelasticity弹性哈密顿作用量Hamiton action elasticity弹性力学赫林格-赖斯纳变分原理Hellinger-Reissnervariational principleelatic surface of thinplate薄板弹性曲面亥姆霍兹定理Helmholtz theorem element analysis单元分析横观各向同性弹性体transverse isotropicelastic bodyelement stiffness matrix单元刚度矩阵横波transverse wave elemental nodal loadmatrix单元节点载荷列阵厚板thick plate elemental stiffnessmatrix 单元劲度矩阵胡海昌-鹫津久一郎变分原理Hu Haichang-Washizuvariational principleenergy method能量法混合边值问题mixed boundary-valueproblementropy prodction产熵胡克定律Hooke law entropy supply供熵混合边界条件mixed boundarycondition equation of stresscompatibility应力协调方程畸变波distrotion wave equivalent shear forcetorsional moment扭矩等效剪力基尔霍夫假设Kirchhoff hypothesis equivoluminaldisplacement field等容的位移场基矢量base vector equivoluminal wave等容波几何方程geometrical equation Euler method欧拉法几何可能的位移geometrically possibledisplacementEuler strain components欧拉应变分量几何可能的应变geometrically possiblestriainexternal force外力几何线性的假设geometrically linearhypothesisfinite element有限元伽辽金法Galerkin method finite element method有限单元法伽辽金矢量Galerkin vector finite-differencefromulate 差分公式结点node finite-differencemethord 差分法结点荷载nodal load first law ofthermodynamics热力学第一定律结点力nodal force first(second,third)kindboundary-value problemof elasticity 弹性力学的第一（第二、第三）类边值条件结点位移nodal displacement Flamant soluton符拉芒解答解的唯一性定理theorem of uniquenesssolutionflexural rigidity of plate板的抗弯强度静力可能的应力statically possible stress flexural rigidity of thinplate薄板弯曲刚度均匀性假设homogeneoushypothesis Fourier integral傅里叶积分局部编码local coding Fourier transform傅里叶变换基尔斯解答Kirsch solution free energy density自由能密度极小势能原理princile of minimumpotential energyfree index自由指标接触问题contact problem Galerkin method伽辽金法均匀性homogeneity Galerkin vector伽辽金矢量卡斯蒂利亚诺公式Castigliano formula generanized Hooke law广义胡克定律开尔文问题Kelvin problem generanized variatianalprinciple广义变分原理扭转刚度torsional rigidity geometrical equation几何方程柯西方程Cauchy equation geometrically linearhypothesis几何线性的假设克罗内克δ符号Kroneckerdelta symbol geometrically possibledisplacement几何可能的位移空间轴对称问题spatial axisymmetryproblem geometrically possiblestriain几何可能的应变孔口应力集中stress concentration ofholesglobal analysis整体分析拉梅解答Lame slution global analysis整体分析离散化结构discretization structure global coding总体编码理想弹性体perfect elastic body global equivalent nodalload vector整体等效结点荷载列阵连续性continuity global nodaldisplacement vector整体结点位移列阵拉格朗日法Lagrange method global stiffness matrix总刚度矩阵拉格朗日函数Lagrange function global stiffness matrix整体劲度矩阵拉格朗日应变函数Lagrange straincomponentsGreen formula格林公式拉梅常数Lamé constants Hamiton action哈密顿作用量拉梅系数Lamé coefficient Hamiton varitionalprinciple哈密顿变分原理拉梅方程Lamé equation heat-conductionequation 热传导方程拉梅应变势Lamé strain potential Hellinger-Reissnervariational principle 赫林格-赖斯纳变分原理莱维方程Lévy equation Helmholtz theorem亥姆霍兹定理勒夫应变函数Love strain function homogeneity均匀性离散化discretization homogeneoushypothesis 均匀性假设连续性假设continuous hypothesis Hooke law胡克定律梁的纯弯曲pure bending of beam Hooke's law of volume体应变胡克定律莱维解Lévy solution Hu Haichang-Washizuvariational principle 胡海昌-鹫津久一郎变分原理面力surface force infinitesimaldeformation hypothesis小变形假设膜板membrane plate internal force内力米歇尔相容方程Michell consistencyequationinternal force of plate板的内力挠度deflection internal forces of thinplate 薄板内力内力internal force inverse method逆解法能量法energy method irrotationaldisplacement field无旋的位移场逆解法inverse method irrotational wave无旋波扭矩等效剪力equivalent shear forcetorsional momentisotropic hypothesis各向同性假设扭转torsion isotropy各向同性纳维解Navier solution Kelvin problem开尔文问题内能密度density of internalenergy Kirchhoff hypothesis基尔霍夫假设纽勃-巴博考维奇通解Neuber-Papkovichgeneral solutionKirsch solution基尔斯解答欧拉法Euler method Kroneckerdelta symbol克罗内克δ符号欧拉应变分量Euler strain components Lagrange function拉格朗日函数耦合coupling Lagrange method拉格朗日法膨胀波dilatation wave Lagrange straincomponents拉格朗日应变函数平衡微分方程differential equation ofequilibriumLamé coefficient拉梅系数平面波plane wave Lamé constants拉梅常数平面应力问题plane stress problem Lamé equation拉梅方程平面应变问题plane strain problem Lame slution拉梅解答泊松比Poisson ratio Lamé strain potential拉梅应变势普朗特比拟Prandtl analogy large deflection problem大挠度问题普朗特应力函数Prandtl stress function Lévy equation莱维方程切变模量shear modulus Lévy solution莱维解切应变shear strain linear elasticity线性弹性力学切应力shear stress linear expansioncoefficient线膨胀系数切应力互等定理reciprocal theorem ofshear stresslinear thermal elasticity线性热弹性力学切应力线shear stress lines local coding局部编码求和约定summation convention longitudinal wave纵波球面波spherical wave Love strain function勒夫应变函数曲线坐标curvilinear coordinates mathematical elasticity数学弹性力学热力学第一定律first law ofthermodynamicsmembrage analogy薄膜比拟热力学第二定律second law ofthermodynamicsmembrane plate膜板热弹性应变势thermal elastic strainpotentialmetric tensor度量张量热应力thermal stress Michell consistencyequation米歇尔相容方程热传导方程heat-conductionequation middle plane of plate板的中面瑞利波Rayleigh wave mixed boundarycondition 混合边界条件瑞利-里茨法Rayleigh-Ritz method mixed boundary-valueproblem混合边值问题三阶张量third order tensor multiply connected body多连体塞路蒂问题Cerruti problem Navier solution纳维解圣维南扭转函数Saint-Venant torsionfunction Neuber-Papkovichgeneral solution纽勃-巴博考维奇通解圣维南方程Saint-Venant equation no initial stresshypothesis 无初始应力的假设圣维南原理Saint-Venant principle nodal displacement结点位移数学弹性力学mathematical elasticity nodal force结点力弹性elasticity nodal load结点荷载弹性波elastic wave node结点弹性常数elastic constants normal strain线应变弹性对称面elastic symmetric plane normal strain正应变弹性力学的平面问题plane problem ofelasticitynormal stress正应力弹性力学的第一（第二、第三）类边值条件first(second,third)kindboundary-value problemof elasticityorthotropic elastic body正交各向异性弹性体弹性曲面的微分方程differential equation ofelastic surfaceperfect elastic body理想弹性体弹性体elastic body perfect elasticity完全弹性弹性体的虚功原理principle of virtual workfor elastic solidperfectly elastic body完全弹性体弹性主方向elastic principledirection perfectly elastichypothesis完全弹性的假设弹性矩阵elastic matrix permulation tensor置换张量体力body force physical equation物理方程体应变胡克定律Hooke's law of volume physically linerhypothesis 物理线性的假设弹性力学elasticity plane problem ofelasticity 弹性力学的平面问题弹性力学基本假定basic assumptions ofelasticityplane strain problem平面应变问题体积模量bulk modulus plane stress problem平面应力问题体积应力volumetric strain plane wave平面波体应变volumetric strain plate板完全弹性的假设perfectly elastichypothesisPoisson ratio泊松比完全弹性体perfectly elastic body potential energy ofexternal force外力势能位移边界条件displacement boundarycondition potential functiondecomposition ofdisplacement field位移场的势函数分解式位移变分方程diaplacement variationalequationPrandtl analogy普朗特比拟位移场的势函数分解式potential functiondecomposition ofdisplacement fieldPrandtl stress function普朗特应力函数位移分量diaplacementcomponentspressure tunnel压力隧道位移解法diaplacement method princile of minimumpotential energy极小势能原理位移的形函数diaplacement shapefunctionprincipal plane主平面无初始应力的假设no initial stresshypothesisprincipal shear stress主切应力无旋波irrotational wave principal strain主应变无旋的位移场irrotationaldisplacement fieldprincipal stress主应力物理线性的假设physically linerhypothesis principle direction ofstrain应变主方向外力external force principle direction ofstress应力主方向外力功work of external force principle of least work最小功原理外力势能potential energy ofexternal force principle of minimum complementary energy最小余能原理完全弹性perfect elasticity principle of minimumpotential energy最小势能原理位移diaplacement principle of virtual workfor elastic solid弹性体的虚功原理位移单值条件condition of single-value displacementprinciple plane of stress应力主面位移法diaplacement method pure bending of beam梁的纯弯曲位移模式displacement model quadratic surface ofstrain 应变二次曲面物理方程physical equation quadratic surface ofstress 应力二次曲面线膨胀系数linear expansioncoefficientRayleigh wave瑞利波线性弹性力学linear elasticity Rayleigh-Ritz method瑞利-里茨法线性热弹性力学linear thermal elasticity reciprocal theorem ofshear stress切应力互等定理相对位移张量relative displacementtensorreflection反射小变形假设infinitesimaldeformation hypothesisrefraction折射小挠度问题small deflection matrix relative displacementtensor相对位移张量形函数矩阵shape function matrix rigid body displacement刚体位移虚位移virtual displacement rotation components转动分量虚位移方程virtual displacementequationrotation vector转动矢量虚应变virtual strain Saint-Venant equation圣维南方程虚应力virtual stress Saint-Venant principle圣维南原理虚应力方程virtual stress equation Saint-Venant torsionfunction圣维南扭转函数线应变normal strain second law ofthermodynamics热力学第二定律相容方程consistency equation second order tensor二阶张量形变deformation semi-infinite body半空间体形变势能strain erergy semi-infinite plane半平面体形函数shape function semi-inverse method半逆解法虚功方程virtual work equation settlement沉陷哑指标dummy index shape function形函数杨氏模量Young modulus shape function matrix形函数矩阵一点的应变状态state of strain at a point shear modulus切变模量一点的应力状态state of stress at a point shear strain切应变以位移表示的平衡微分方程differential equation ofequilibrium in terms ofdisplacementshear stress切应力应变二次曲面quadratic surface ofstrain shear stress lines切应力线应变分量strain components simply connected body单连体应变能密度strain energy density single triangle series单三角级数解应变矩阵strain matrix small deflection matrix小挠度问题应变协调方程strain compatibilityequation spatial axisymmetryproblem空间轴对称问题应变余能密度density of comlementarystrain energyspherical wave球面波应变张量strain tensor state of strain at a point一点的应变状态应变张量不变量strain tensor invariant state of stress at a point一点的应力状态应变主方向principle direction ofstrain statically possible stress静力可能的应力应力变分方程stress variationalequation strain compatibilityequation应变协调方程应力边界条件stress boundarycondition strain components应变分量应力二次曲面quadratic surface ofstress strain energy density应变能密度应力分量stress components strain erergy形变势能应力环量stress circulation strain matrix应变矩阵应力解法stress method strain tensor应变张量应力矩阵stress matrix strain tensor invariant应变张量不变量应力协调方程equation of stresscompatibility stress boundarycondition应力边界条件应力张量stress tensor stress circulation应力环量应力张量不变量stress tensor invariant stress components应力分量应力主方向principle direction ofstress stress concentration ofholes孔口应力集中应力状态特征方程characteristic equationof stress statestress matrix应力矩阵应用弹性力学applied elasticity stress method应力解法有限元finite element stress method应力法圆柱体扭转torsion of circular bar stress tensor应力张量压力隧道pressure tunnel stress tensor invariant应力张量不变量应力法stress method stress variationalequation 应力变分方程应力主面principle plane of stress summation convention求和约定有限单元法finite element method superposition principle叠加原理折射refraction surface force面力整体等效结点荷载列阵global equivalent nodalload vectorsurface wave表层波整体结点位移列阵global nodaldisplacement vectorsymmetric tensor对称张量整体分析global analysis temperature change变温正应变normal strain theorem of uniquenesssolution解的唯一性定理正应力normal stress thermal elastic strainpotential热弹性应变势正交各向异性弹性体orthotropic elastic body thermal stress热应力置换张量permulation tensor thick plate厚板主应变principal strain thin plate薄板主应力principal stress third order tensor三阶张量主平面principal plane torsion扭转主切应力principal shear stress torsion of circular bar圆柱体扭转转动矢量rotation vector torsional rigidity扭转刚度转动分量rotation components total complementaryenergy总余能自由能密度free energy density total potential energy总势能自由指标free index transverse isotropicelastic body横观各向同性弹性体纵波longitudinal wave transverse wave横波总刚度矩阵global stiffness matrix unit tensor单位张量总势能total potential energy variationalmethod,energy method变分法（能量法）总余能total complementaryenergyvirtual displacement虚位移总体编码global coding virtual displacementequation虚位移方程最小功原理principle of least work virtual strain虚应变最小势能原理principle of minimumpotential energyvirtual stress虚应力最小余能原理principle of minimumcomplementary energyvirtual stress equation虚应力方程坐标曲面coordinate surface virtual work equation虚功方程坐标曲线coordinate curves volumetric strain体积应力整体分析global analysis volumetric strain体应变整体劲度矩阵global stiffness matrix work of external force外力功轴对称axisymmetry Young modulus杨氏模量。

英汉双语弹性力学ppt课件

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第二章平面问题的基本理论
§2-1 平面应力问题与平面应变问题 §2-2 平衡微分方程 §2-3 斜面上的应力主应力 §2-4 几何方程刚体位移 §2-5 物理方程 §2-6 边界条件 §2-7 圣维南原理 §2-8 按位移求解平面问题 §2-9 按应力求解平面问题。相容方程 §2-10 常体力情况下的简化 §2-11 应力函数逆解法与半逆解法习题课
无外力作用。
y
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注意：平面应力问题z =0，但问题相反。
ቤተ መጻሕፍቲ ባይዱz 0，这与平面应变
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2.Plane strain problem Very long column bears the face force in parallel with plate face and doesn’t change
Elasticity
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Chapter 2 The Basic theory of the Plane Problem
§2-1 Plane stress problem and plane strain problem
§2-2 Differential equation of equilibrium §2-3 The stress on the incline.Principal stress §2-4 Geometrical equation.The displacement of the rigid body §2-5 Physical equation §2-6 Boundary conditions §2-7 Saint-Venant’s principle §2-8 Solving the plane problem according to the displacement §2-9 Solving the plane problem according to the patible equation

弹性力学专业英语英汉互译词汇

elasticitytheory of elasticity homogeneous state ofstressstress invariant strain invariant strain ellipsoid homogeneous state ofstrainequation of strain compatibilityLame constants isotropic elasticityrotating circular diskwedgeKelvin problemBoussinesq problemAiry stress functionKolosoff-Muskhelishvili methodKirchhoff hypothesisPlateRectangular plate Circular plate Annular plate Corrugated plate Stiffened plate,reinforced弹性力学弹性理论均匀应力状态应力不变量应变不变量应变椭球均匀应变状态应变协调方程拉梅常量各向同性弹性旋转圆盘楔开尔文问题布西内斯克问题艾里应力函数克罗索夫―穆斯赫利什维利法基尔霍夫假设板矩形板圆板环板波纹板加劲板PlatePlate of moderate thickness Stress function of bendingShell Shallow shell Revolutionary shell Spherical shell Cylindrical shell Conical shell Toroidal shell Closed shell Corrugated shell Stress function of torsionWarping function semi-inverse method Rayleigh-Ritz method Relaxation methodLevy method Relaxation Dimensional analysis self-similarity Influence surface Contact stress Hertz theory Conforming contact Sliding contact Rolling contact中厚板弯［曲］应力函数壳扁壳旋转壳球壳［圆］柱壳锥壳环壳封闭壳波纹壳扭［转］应力函数翘曲函数半逆解法瑞利―里茨法松弛法莱维法松弛量纲分析自相似［性］影响面接触应力赫兹理论协调接触压入Indentation各向异性弹性Anisotropic elasticity 颗粒材料Granular material散体力学Mechanics of granular media 热弹性Thermoelasticity超弹性Hyperelasticity粘弹性Viscoelasticity对应原理Correspondence principle 褶皱Wrinkle塑性全量理论Total theory of plasticity 滑动Sliding微滑Microslip粗糙度Roughness非线性弹性Nonlinear elasticity 大挠度Large deflection突弹跳变snap-through有限变形Finite deformation格林应变Green strain阿尔曼西应变Almansi strain弹性动力学Dynamic elasticity运动方程Equation of motion准静态的Quasi-static气动弹性Aeroelasticity水弹性Hydroelasticity颤振Flutter弹性波Elastic wave简单波Simple wave柱面波Cylindrical wave水平剪切波Horizontal shear wave 竖直剪切波Vertical shear wave 体波body wave无旋波Irrotational wave 畸变波Distortion wave膨胀波Dilatation wave瑞利波Rayleigh wave等容波Equivoluminal wave 勒夫波Love wave界面波Interfacial wave 边缘效应edge effect塑性力学Plasticity可成形性Formability金属成形Metal forming耐撞性Crashworthiness结构抗撞毁性Structural crashworthiness 拉拔Drawing破坏机构Collapse mechanism回弹Springback挤压Extrusion冲压Stamping穿透Perforation层裂Spalling塑性理论Theory of plasticity 安定［性］理论Shake-down theory 运动安定定理kinematic shake-downtheoremStatic shake-down theorem rate dependent theoremload factor Loading criterion Loading function Loading surface Plastic loading Plastic loading waveSimple loading Proportional loadingUnloading Unloading wave Impulsive load step load pulse load limit load nentral loading instability in tension acceleration wave constitutive equation complete solution nominal stress over-stress true stress equivalent stressflow stress stress discontinuity静力安定定理率相关理论载荷因子加载准则加载函数加载面塑性加载塑性加载波简单加载比例加载卸载卸载波冲击载荷阶跃载荷脉冲载荷极限载荷中性变载拉抻失稳加速度波本构方程完全解名义应力过应力真应力等效应力流动应力应力间断stress space principal stress space hydrostatic state of stresslogarithmic strain engineering strain equivalent strain strain localizationstrain ratestrain rate sensitivitystrain space finite strain plastic strain incrementaccumulated plastic strainpermanent deformationinternal variable strain-softening rigid-perfectly plasticMaterialrigid-plastic materialperfectl plastic material stability of material deviatoric tensor of strain deviatori tensor of stress spherical tensor of strain spherical tensor of stresspath-dependency linear strain-hardening应力空间主应力空间静水应力状态对数应变工程应变等效应变应变局部化应变率应变率敏感性应变空间有限应变塑性应变增量累积塑性应变永久变形内变量应变软化理想刚塑性材料刚塑性材料理想塑性材料材料稳定性应变偏张量应力偏张量应变球张量应力球张量路径相关性strain-hardening kinematic hardening isotropic hardening strain-hardening moduluspower hardening plastic limit bendingMomentplastic limit torque elastic-plastic bending elastic-plastic interface elastic-plastic torsionViscoplasticityInelasticityelastic-perfectly plasticMaterial limit analysislimit design limit surface upper bound theorem upper yield point lower bound theorem lower yield point bound theorem initial yield surface subsequent yield surface convexity of yield surface shape factor of cross-section应变强化随动强化各向同性强化强化模量幕强化塑性极限弯矩塑性极限扭矩弹塑性弯曲弹塑性交界面弹塑性扭转粘塑性非弹性理想弹塑性材料极限分析极限设计极限面上限定理上屈服点下限定理下屈服点界限定理初始屈服面后继屈服面屈服面［的］外沙堆比拟屈服屈服条件屈服准则屈服函数屈服面塑性势能量吸收装置能量耗散率塑性动力学塑性动力屈曲塑性动力响应塑性波运动容许场静力容许场流动法则速度间断滑移线滑移线场移行塑性铰塑性增量理论米泽斯屈服准则普朗特―罗伊斯关系特雷斯卡屈服准则sand heap analogyYieldyield conditionyield criterionyield functionyield surfaceplastic potential energy absorbing device energy absorbing device dynamic plasticity dynamic plastic buckling dynamic plastic response plastic wave kinematically admissibleFieldstatically admissibleFieldflow rule velocity discontinuityslip-linesslip-lines field travelling plastic hinge incremental theory ofPlasticityMises yield criterion prandtl- Reuss relation Tresca yield criterion洛德应力参数莱维―米泽斯关系亨基应力方程赫艾一韦斯特加德应力空间洛德应变参数德鲁克公设盖林格速度方程结构力学结构分析结构动力学拱三铰拱抛物线拱圆拱穹顶空间结构空间桁架雪载［荷］风载［荷］土压力地震载荷弹簧支座支座位移支座沉降Lode stress parameterLevy-Mises relation Hencky stress equation Haigh-Westergaardstress space Lode strain parameter Drucker postulateGeiringer velocityEquation structural mechanics structural analysis structural dynamicsArchthree-hinged archparabolic archcircular archDomespace structurespace trusssnow loadwind loadearth pressureearthquake loadingspring support support displacementsupport settlementdegree of indeterminacy kinematic analysis method of joints method of sectionsjoint forces conjugate displacementinfluence line three-moment equation unit virtual force stiffness coefficient flexibility coefficientmoment distributionmoment distribution methodmoment redistribution distribution factor matri displacement method element stiffness matrix element strain matrix global coordinates Betti theorem Gauss-Jordan eliminationMethod buckling mode mechanics of compositescomposite materialfibrous composite unidirectional composite超静定次数机动分析结点法截面法结点力共轭位移影响线三弯矩方程单位虚力刚度系数柔度系数力矩分配力矩分配法力矩再分配分配系数矩阵位移法单元刚度矩阵单元应变矩阵总体坐标贝蒂定理高斯一若尔当消去法屈曲模态复合材料力学复合材料foamed composite particulate compositeLaminate sandwich panel cross-ply laminate angle-ply laminatePlycellular solid ExpansionDebulk Degradation DelaminationDebond fiber stress ply stress ply strain interlaminar stress specific strength strength reduction factor strength -stress ratio transverse shear modulustransverse isotropyOrthotropyshear lag analysis chopped fiber continuous fiber fiber direction泡沫复合材料颗粒复合材料层板夹层板正交层板斜交层板层片多胞固体膨胀压实劣化脱层脱粘纤维应力层应力层应变层间应力比强度强度折减系数强度应力比横向剪切模量横观各向同性正交各向异剪滞分析短纤维长纤维fiber break fiber pull-out fiber reinforcementDensification optimum weight design netting analysis rule of mixture failure criterion Tsai-W u failure criterionDugdale model fracture mechanics probabilistic fractureMechanicsGriffith theory linear elastic fracturemechanics, LEFMelastic-plastic fracturemecha-nics, EPFMFracture brittle fracturecleavage fracture creep fracture ductile fracture inter-granular fracture quasi-cleavage fracture trans-granular fractureCrack纤维断裂纤维拔脱纤维增强致密化最小重量设计网格分析法混合律失效准则蔡一吴失效准则达格代尔模型断裂力学概率断裂力学格里菲思理论线弹性断裂力学弹塑性断裂力学断裂脆性断裂解理断裂蠕变断裂延性断裂晶间断裂准解理断裂裂纹Flaw Defect Slit MicrocrackKinkelliptical crack embedded crack penny-shape crackPrecrack short crack surface crack crack blunting crack branching crack closure crack front crack mouthcrack opening angle,COAcrack opening displacement,CODcrack resistancecrack surfacecrack tipcrack tip opening angle,CTOAcrack tip openingdisplacement, CTOD crack tip singularity裂缝缺陷割缝微裂纹折裂椭圆裂纹深埋裂纹［钱］币状裂纹预制裂纹短裂纹表面裂纹裂纹钝化裂纹分叉裂纹闭合裂纹前缘裂纹嘴裂纹张开角裂纹张开位移裂纹阻力裂纹面裂纹尖端裂尖张角裂尖张开位移Fieldcrack growth rate stable crack growth steady crack growth subcritical crack growthcrack retardation crack arrest arrest toughness fracture mode sliding mode opening mode tearing mode mixed mode Tearingtearing modulus fracture criterionJ-integral J-resistance curve fracture toughness stress intensity factor Hutchinson-Rice-RosengrenFieldconservation integraleffective stress tensor strain energy density energy release ratecohesive zone裂纹扩展速率稳定裂纹扩展定常裂纹扩展亚临界裂纹扩展裂纹［扩展］减速止裂止裂韧度断裂类型滑开型张开型撕开型复合型撕裂撕裂模量断裂准则 J 积分 J 阻力曲线断裂韧度应力强度因子HRR 场守恒积分有效应力张量应变能密度能量释放率塑性区plastic zone张拉区stretched zone热影响区heat affected zone, HAZ延脆转变温度brittle-ductile transitiontempe- rature剪切带shear band 剪切唇shear lip无损检测non-destructive inspection双边缺口试件double edge notchedspecimen, DEN specimen 单边缺口试件single edge notchedspecimen, SEN specimen 三点弯曲试件three point bendingspecimen, TPB specimen 中心裂纹拉伸试件center cracked tensionspecimen, CCT specimen 中心裂纹板试件center cracked panelspecimen, CCP specimen 紧凑拉伸试件compact tension specimen,CT specimen 大范围屈服large scale yielding 小范围攻屈服small scale yielding 韦布尔分布Weibull distribution 帕里斯公式paris formula空穴化Cavitation应力腐蚀stress corrosion概率风险判定probabilistic riskassessment, PRAdamage mechanicsDamagecontinuum damage mechanics microscopic damage mechanicsaccumulated damage brittle damage ductile damage macroscopic damage microscopic damage microscopic damagedamage criteriondamage evolution equationdamage softeningdamage strengtheningdamage tensor damage threshold damage variable damage vector damage zone Fatigue low cycle fatigue stress fatigue random fatigue creep fatigue corrosion fatigue fatigue damage 损伤力学损伤连续介质损伤力学细观损伤力学累积损伤脆性损伤延性损伤宏观损伤细观损伤微观损伤损伤准则损伤演化方程损伤软化损伤强化损伤张量损伤阈值损伤变量损伤矢量损伤区疲劳低周疲劳应力疲劳随机疲劳蠕变疲劳腐蚀疲劳fatigue failure fatigue fracture fatigue crack fatigue life fatigue rupture fatigue strength fatigue striations fatigue threshold alternating load alternating stress stress amplitudestrain fatiguestress cyclestress ratio safe life overloading effect cyclic hardening cyclic softening environmental effectcrack gage crack growth, crackPropagation crack initiationcycle ratio experimental stressAnalysisactive[strain] gage疲劳失效疲劳断裂疲劳裂纹疲劳寿命疲劳破坏疲劳强度疲劳辉纹疲劳阈值交变载荷交变应力应力幅值应变疲劳应力循环应力比安全寿命过载效应循环硬化循环软化环境效应裂纹片裂纹扩展裂纹萌生循环比工作［应变］片backing material stress gage zero shift, zero drift strain measurementstrain gage strain indicator strain rosette strain sensitivity mechanical strain gage rectangular rosetteExtensometertelemetering of strain transverse gage factor transverse sensitivity weldable strain gage balanced bridge bonded strain gage bonded foiled gage bonded wire gage bridge balancing capacitance strain gage compensation technique compensation techniquereference bridge resistance strain gageself-temperature compensating gage基底材料应力计零［点］飘移应变测量应变计应变指示器应变花应变灵敏度机械式应变仪直角应变花弓I 伸仪应变遥测横向灵敏系数横向灵敏度焊接式应变计平衡电桥粘贴式应变计粘贴箔式应变计粘贴丝式应变计桥路平衡电容应变计补偿片补偿技术基准电桥电阻应变计semiconductor strainGageslip ring strain amplifier fatigue life gage inductance [strain] gagePhotomechanics Photoelasticity Photoplasticity Young fringe birefrigent effect contour of equal Displacement dark fringefringe multiplication interference fringeIsochromatic Isoclinic isopachic stress- optic lawIsostatic light fringe optical path differencephoto-thermo -elasticityphotoelastic coatingMethodphotoelastic sandwich半导体应变计集流器应变放大镜疲劳寿命计电感应变计光［测］力学光弹性光塑性杨氏条纹双折射效应等位移线暗条纹条纹倍增干涉条纹等差线等倾线等和线应力光学定律主应力迹线亮条纹光程差热光弹性光弹性贴片法Methoddynamic photo-elasticityspatial filtering spatial frequencyPolarizerreflection polariscope residual birefringentEffectstrain fringe valuestrain-optic sensitivitystress freezing effectstress fringe valuestress-optic pattern temporary birefringentEffect pulsed holographytransmission polariscope real-time holographic interfero - metrygrid methodholo-photoelasticityHologram Holographholographic interferometry holographic moire techniqueHolography whole-field analysis动态光弹性空间滤波空间频率起偏镜反射式光弹性仪残余双折射效应应变条纹值应变光学灵敏度应力冻结效应应力条纹值应力光图暂时双折射效应脉冲全息法透射式光弹性仪实时全息干涉法网格法全息光弹性法全息图全息照相全息干涉法全息云纹法全息术散斑干涉法speckle interferometry 散斑Speckle错位散斑干涉法speckle-shearinginterferometry,shearography散斑图Specklegram 白光散斑法white-light speckle method 云纹干涉法moire interferometry ［叠栅］云纹moire fringe［叠栅］云纹法moire method 云纹图moire pattern离面云纹法off-plane moire method 参考栅reference grating试件栅specimen grating分析栅analyzer grating面内云纹法in-plane moire method脆性涂层法brittle-coating method 条带法strip coating method坐标变换transformation ofCoordinates计算结构力学computational structuralmecha-nics加权残量法weighted residual method 有限差分法finite difference method 有限［单］元法finite element method 配点法point collocation里茨法Ritz method广义变分原理generalized variationalPrinciple 最小二乘法least square method胡［海昌］一鹫津原理Hu-Washizu principle赫林格-赖斯纳原理Hellinger-ReissnerPrinciple修正变分原理modified variationalPrinciple约束变分原理constrained variationalPrinciple混合法mixed method杂交法hybrid method边界解法boundary solution method有限条法finite strip method半解析法semi-analytical method协调兀conforming element非协调兀non-conforming element混合元mixed element杂交元hybrid element边界元boundary element强迫边界条件forced boundary condition自然边界条件natural boundary condition离散化Discretization离散系统discrete system连续问题continuous problem广义位移generalized displacement广义载荷generalized load广义应变generalized straingeneralized stress interface variable node, nodal pointElement corner node mid-side node internal node nodeless variablebar element truss element beam elementtwo-dimensional elementone-dimensional elementthree-dimensional element axisymmetric elementplate element shell elementthick plate element triangular element quadrilateral element tetrahedral element curved element quadratic element linear element cubic element quartic element isoparametric element广义应力界面变量节点［单］元角节点边节点内节点无节点变量杆元桁架杆元梁元二维元一维元三维元轴对称元厚板元三角形元四边形元四面体元曲线元二次元线性元三次元四次元等参［数］super-parametric element sub-parametric element variable-number-nodeelement Lagrange element Lagrange family serendipity element serendipity family infinite element element analysis element characteristicsstiffness matrixgeometric matrixequivalent nodal forcenodal displacementnodal load displacement vectorload vector mass matrix lumped mass matrix consistent mass matrixdamping matrix Rayleigh damping assembly of stiffnessMatricesconsistent mass matrix assembly of mass matrices assembly of elements超参数元亚参数元节点数可变元拉格朗日元拉格朗日族巧凑边点元巧凑边点族无限元单元分析单元特性刚度矩阵几何矩阵等效节点力节点位移节点载荷位移矢量载荷矢量质量矩阵集总质量矩阵相容质量矩阵阻尼矩阵瑞利阻尼刚度矩阵的组集载荷矢量的组集质量矩阵的组集local coordinate systemlocal coordinate area coordinates volume coordinates curvilinear coordinates static condensation contragradienttransformation shape function trial function test function weight function spline function substitute function reduced integration zero-energy mode p-convergenceh-convergenceblended interpolation isoparametric mapping bilinear interpolationpatch test incompatible modenode number element number band width banded matrix profile matrix局部坐标系局部坐标面积坐标体积坐标曲线坐标静凝聚合同变换形状函数试探函数检验函数权函数样条函数代用函数降阶积分零能模式P 收敛H 收敛掺混插值等参数映射双线性插值小块检验非协调模式节点号 M 二口. 单兀号minimization of band widthfrontal method subspace iteration method determinant search methodstep-by-step methodNewmark Wilsonquasi-Newton method Newton-Raphson method incremental method initial straininitial stresstangent stiffness matrixsecant stiffness matrix mode superposition method equilibrium iterationSubstructure substructure techniquesuper-element mesh generationstructural analysis programpre-processing post-processing mesh refinement stress smoothing composite structure带宽最小化波前法子空间迭代法行列式搜索法逐步法纽马克法威尔逊法拟牛顿法牛顿-拉弗森法增量法初应变初应力切线刚度矩阵割线刚度矩阵模态叠加法平衡迭代子结构子结构法超单元网格生成结构分析程序前处理后处理网格细化应力光顺。

奥鹏西安交通大学2020年3月课程考试《弹性力学》参考资料答案

奥鹏西安交通大学2020年3月课程考试《弹性力学》参考资料答案西安交通大学课程考试复习资料单选题1.所谓“应力状态”是指( )。

A.斜截面应力矢量与横截面应力矢量不同B.一点不同截面的应力随着截面方位变化而改变C.3个主应力作用平面相互垂直D.不同截面的应力不同，因此应力矢量是不可确定的答案: B2.所谓“应力状态”是指（）。

A.A、斜截面应力矢量与横截面应力矢量不同B.B、一点不同截面的应力随着截面方位变化而改变C.C、个主应力作用平面相互垂直D.D、不同截面的应力不同，因此应力矢量是不可确定的答案: B3.圆弧曲梁纯弯时,( )A.横截面上有正应力和剪应力B.横截面上只有正应力且纵向纤维互不挤压C.横截面上只有正应力且纵向纤维互相挤压D.横截面上有正应力和剪应力，且纵向纤维互相挤压答案: C4.用应变分量表示的相容方程等价于( )。

A.平衡微分方程B.几何方程C.物理方程D.几何方程和物理方程答案: B5.用应力分量表示的相容方程等价于( )。

A.平衡微分方程B.几何方程和物理方程C.用应变分量表示的相容方程D.平衡微分方程、几何方程和物理方程答案: B6.在常体力情况下,用应力函数表示的相容方程等价于( )。

A.平衡微分方程B.几何方程C.物理关系D.平衡微分方程、几何方程和物理关系答案: D7.平面应变问题的微元体处于( )A.单向应力状态B.双向应力状态C.三向应力状态D.纯剪切应力状态答案: C8.下列关于“刚体转动”的描述,认识正确的是( )。

A.刚性转动描述了微分单元体的方位变化，与变形位移一起构成弹性体的变形B.刚性转动分量描述的是一点的刚体转动位移，因此与弹性体的变形无关C.刚性转动位移也是位移的导数，因此它描述了一点的变形D.刚性转动分量可以确定弹性体的刚体位移。

答案: A9.设有平面应力状态,σx=ax+by,σy=cx+dy,τxy=?dx?ay?γx,其中a,b,c,d均为常数,γ为容重。

弹性力学英语

弹性力学 elasticity弹性理论 theory of elasticity均匀应力状态 homogeneous state of stress 应力不变量 stress invariant应变不变量 strain invariant应变椭球strain ellipsoid均匀应变状态 homogeneous state of strain 应变协调方程 equation of strain compatibility拉梅常量 Lame constants各向同性弹性 isotropic elasticity旋转圆盘 rotating circular disk楔 wedge开尔文问题Kelvin problem布西内斯克问题 Boussinesq problem艾里应力函数 Airy stress function克罗索夫--穆斯赫利什维利法 Kolosoff- Muskhelishvili method基尔霍夫假设 Kirchhoff hypothesis板 Plate矩形板 Rectangular plate圆板 Circular plate环板 Annular plate波纹板 Corrugated plate加劲板 Stiffened plate,reinforced Plate 中厚板 Plate of moderate thickness弯[曲]应力函数 Stress function of bending 壳 Shell扁壳 Shallow shell旋转壳 Revolutionary shell球壳 Spherical shell[圆]柱壳 Cylindrical shell锥壳 Conical shell环壳 Toroidal shell封闭壳 Closed shell波纹壳 Corrugated shell扭[转]应力函数 Stress function of torsion 翘曲函数 Warping function半逆解法 semi-inverse method瑞利--里茨法 Rayleigh-Ritz method松弛法 Relaxation method莱维法 Levy method松弛 Relaxation量纲分析 Dimensional analysis自相似[性] self-similarity影响面 Influence surface接触应力 Contact stress赫兹理论 Hertz theory协调接触 Conforming contact滑动接触 Sliding contact滚动接触 Rolling contact压入 Indentation 各向异性弹性 Anisotropic elasticity颗粒材料 Granular material散体力学 Mechanics of granular media热弹性 Thermoelasticity超弹性 Hyperelasticity粘弹性Viscoelasticity对应原理 Correspondence principle褶皱 Wrinkle塑性全量理论 Total theory of plasticity 滑动 Sliding微滑 Microslip粗糙度 Roughness非线性弹性 Nonlinear elasticity大挠度 Large deflection突弹跳变 snap-through有限变形 Finite deformation格林应变 Green strain阿尔曼西应变 Almansi strain弹性动力学 Dynamic elasticity运动方程 Equation of motion准静态的 Quasi-static气动弹性 Aeroelasticity水弹性 Hydroelasticity颤振 Flutter弹性波 Elastic wave简单波 Simple wave柱面波 Cylindrical wave水平剪切波 Horizontal shear wave竖直剪切波 Vertical shear wave体波 body wave无旋波Ir rotational wave畸变波 Distortion wave膨胀波 Dilatation wave瑞利波 Rayleigh wave等容波 Equivoluminal wave勒夫波 Love wave界面波 Interfacial wave边缘效应 edge effect塑性力学Plasticity可成形性 Formability金属成形 Metal forming耐撞性 Crashworthiness结构抗撞毁性 Structural crashworthiness 拉拔 Drawing破坏机构 Collapse mechanism回弹 Springback挤压 Extrusion冲压 Stamping穿透 Perforation层裂 Spalling塑性理论 Theory of plasticity安定[性]理论 Shake-down theory运动安定定理 kinematic shake-down theorem 静力安定定理 Static shake-down theorem率相关理论 rate dependent theorem载荷因子 load factor加载准则 Loading criterion加载函数 Loading function加载面 Loading surface塑性加载 Plastic loading塑性加载波Plastic loading wave简单加载 Simple loading比例加载 Proportional loading卸载 Unloading卸载波 Unloading wave冲击载荷 Impulsive load阶跃载荷 step load脉冲载荷 pulse load极限载荷 limit load中性变载 nentral loading拉抻失稳 instability in tension加速度波 acceleration wave本构方程constitutive equation完全解 complete solution名义应力 nominal stress过应力 over-stress真应力 true stress等效应力 equivalent stress流动应力 flow stress应力间断 stress discontinuity应力空间 stress space主应力空间 principal stress space静水应力状态 hydrostatic state of stress 对数应变 logarithmic strain工程应变 engineering strain等效应变 equivalent strain应变局部化 strain localization应变率 strain rate应变率敏感性 strain rate sensitivity应变空间 strain space有限应变 finite strain塑性应变增量 plastic strain increment累积塑性应变 accumulated plastic strain 永久变形 permanent deformation内变量 internal variable应变软化 strain-softening理想刚塑性材料 rigid-perfectly plastic Material刚塑性材料 rigid-plastic material理想塑性材料 perfectl plastic material材料稳定性 stability of material应变偏张量 deviatoric tensor of strain应力偏张量deviatori tensor of stress应变球张量 spherical tensor of strain 应力球张量 spherical tensor of stress路径相关性 path-dependency线性强化 linear strain-hardening应变强化 strain-hardening随动强化 kinematic hardening各向同性强化 isotropic hardening强化模量 strain-hardening modulus幂强化 power hardening塑性极限弯矩 plastic limit bending Moment 塑性极限扭矩 plastic limit torque弹塑性弯曲 elastic-plastic bending弹塑性交界面 elastic-plastic interface弹塑性扭转elastic-plastic torsion粘塑性 Viscoplasticity非弹性 Inelasticity理想弹塑性材料 elastic-perfectly plastic Material极限分析 limit analysis极限设计 limit design极限面 limit surface上限定理 upper bound theorem上屈服点 upper yield point下限定理lower bound theorem下屈服点 lower yield point界限定理 bound theorem初始屈服面 initial yield surface后继屈服面 subsequent yield surface屈服面[的]外凸性 convexity of yield surface 截面形状因子 shape factor of cross-section 沙堆比拟 sand heap analogy屈服 Yield屈服条件 yield condition屈服准则 yield criterion屈服函数 yield function屈服面 yield surface塑性势 plastic potential能量吸收装置 energy absorbing device能量耗散率 energy absorbing device塑性动力学 dynamic plasticity塑性动力屈曲 dynamic plastic buckling塑性动力响应 dynamic plastic response塑性波 plastic wave运动容许场 kinematically admissible Field 静力容许场 statically admissible Field流动法则 flow rule速度间断 velocity discontinuity滑移线slip-lines滑移线场 slip-lines field移行塑性铰 travelling plastic hinge塑性增量理论 incremental theory ofPlasticity米泽斯屈服准则 Mises yield criterion普朗特--罗伊斯关系 prandtl- Reuss relation 特雷斯卡屈服准则 Tresca yield criterion洛德应力参数 Lode stress parameter莱维--米泽斯关系 Levy-Mises relation亨基应力方程 Hencky stress equation赫艾--韦斯特加德应力空间Haigh-Westergaard stress space洛德应变参数 Lode strain parameter德鲁克公设 Drucker postulate盖林格速度方程 Geiringer velocity Equation 结构力学 structural mechanics结构分析 structural analysis结构动力学 structural dynamics拱 Arch三铰拱 three-hinged arch抛物线拱 parabolic arch圆拱 circular arch穹顶 Dome空间结构 space structure空间桁架 space truss雪载[荷] snow load风载[荷] wind load土压力 earth pressure地震载荷 earthquake loading弹簧支座 spring support支座位移 support displacement支座沉降 support settlement超静定次数degree of indeterminacy机动分析 kinematic analysis结点法 method of joints截面法 method of sections结点力 joint forces共轭位移 conjugate displacement影响线 influence line三弯矩方程 three-moment equation单位虚力 unit virtual force刚度系数 stiffness coefficient柔度系数flexibility coefficient力矩分配 moment distribution力矩分配法moment distribution method力矩再分配 moment redistribution分配系数 distribution factor矩阵位移法 matri displacement method单元刚度矩阵 element stiffness matrix单元应变矩阵 element strain matrix总体坐标 global coordinates贝蒂定理 Betti theorem高斯--若尔当消去法 Gauss-Jordan elimination Method屈曲模态 buckling mode复合材料力学 mechanics of composites复合材料 composite material 纤维复合材料 fibrous composite单向复合材料 unidirectional composite泡沫复合材料 foamed composite颗粒复合材料 particulate composite层板 Laminate夹层板 sandwich panel正交层板 cross-ply laminate斜交层板 angle-ply laminate层片 Ply多胞固体 cellular solid膨胀 Expansion压实 Debulk劣化 Degradation脱层 Delamination脱粘 Debond纤维应力 fiber stress层应力 ply stress层应变 ply strain层间应力 interlaminar stress比强度 specific strength强度折减系数strength reduction factor强度应力比strength -stress ratio横向剪切模量 transverse shear modulus横观各向同性 transverse isotropy正交各向异 Orthotropy剪滞分析 shear lag analysis短纤维 chopped fiber长纤维 continuous fiber纤维方向 fiber direction纤维断裂 fiber break纤维拔脱 fiber pull-out纤维增强 fiber reinforcement致密化 Densification最小重量设计 optimum weight design网格分析法netting analysis混合律 rule of mixture失效准则 failure criterion蔡--吴失效准则 Tsai-W u failure criterion 达格代尔模型 Dugdale model断裂力学 fracture mechanics概率断裂力学 probabilistic fracture Mechanics格里菲思理论 Griffith theory线弹性断裂力学 linear elastic fracture mechanics, LEFM弹塑性断裂力学 elastic-plastic fracture mecha-nics, EPFM断裂 Fracture脆性断裂 brittle fracture解理断裂 cleavage fracture蠕变断裂 creep fracture延性断裂 ductile fracture晶间断裂 inter-granular fracture准解理断裂 quasi-cleavage fracture穿晶断裂 trans-granular fracture裂纹 Crack裂缝 Flaw缺陷 Defect割缝 Slit微裂纹 Microcrack折裂 Kink椭圆裂纹elliptical crack深埋裂纹 embedded crack币状裂纹penny-shape crack预制裂纹 Precrack短裂纹 short crack表面裂纹 surface crack裂纹钝化crack blunting裂纹分叉 crack branching裂纹闭合 crack closure裂纹前缘 crack front裂纹嘴 crack mouth裂纹张开角 crack opening angle,COA裂纹张开位移crack opening displacement, COD 裂纹阻力 crack resistance裂纹面 crack surface裂纹尖端 crack tip裂尖张角 crack tip opening angle, CTOA裂尖张开位移 crack tip opening displacement, CTOD裂尖奇异场 crack tip singularity Field裂纹扩展速率 crack growth rate稳定裂纹扩展 stable crack growth定常裂纹扩展 steady crack growth亚临界裂纹扩展 subcritical crack growth裂纹[扩展]减速 crack retardation止裂 crack arrest止裂韧度 arrest toughness断裂类型 fracture mode滑开型 sliding mode张开型 opening mode撕开型 tearing mode复合型 mixed mode撕裂 Tearing撕裂模量 tearing modulus断裂准则 fracture criterionJ积分 J-integralJ阻力曲线 J-resistance curve断裂韧度 fracture toughness应力强度因子stress intensity factorHRR场 Hutchinson-Rice-Rosengren Field守恒积分 conservation integral有效应力张量 effective stress tensor应变能密度 strain energy density 能量释放率 energy release rate内聚区 cohesive zone塑性区 plastic zone张拉区 stretched zone热影响区 heat affected zone, HAZ延脆转变温度 brittle-ductile transition tempe- rature剪切带 shear band剪切唇 shear lip无损检测non-destructive inspection双边缺口试件double edge notched specimen, DEN specimen单边缺口试件 single edge notched specimen, SEN specimen三点弯曲试件 three point bending specimen, TPB specimen中心裂纹拉伸试件 center cracked tension specimen, CCT specimen中心裂纹板试件 center cracked panel specimen, CCP specimen紧凑拉伸试件 compact tension specimen, CT specimen大范围屈服 large scale yielding小范围攻屈服 small scale yielding韦布尔分布 Weibull distribution帕里斯公式 paris formula空穴化 Cavitation应力腐蚀 stress corrosion概率风险判定 probabilistic risk assessment, PRA损伤力学 damage mechanics损伤 Damage连续介质损伤力学 continuum damage mechanics 细观损伤力学 microscopic damage mechanics 累积损伤 accumulated damage脆性损伤 brittle damage延性损伤 ductile damage宏观损伤 macroscopic damage细观损伤 microscopic damage微观损伤 microscopic damage损伤准则 damage criterion损伤演化方程 damage evolution equation损伤软化 damage softening损伤强化 damage strengthening损伤张量 damage tensor损伤阈值 damage threshold损伤变量 damage variable损伤矢量 damage vector损伤区 damage zone疲劳 Fatigue低周疲劳 low cycle fatigue应力疲劳 stress fatigue随机疲劳 random fatigue蠕变疲劳 creep fatigue腐蚀疲劳 corrosion fatigue疲劳损伤 fatigue damage疲劳失效 fatigue failure疲劳断裂 fatigue fracture疲劳裂纹 fatigue crack疲劳寿命 fatigue life疲劳破坏 fatigue rupture疲劳强度 fatigue strength疲劳辉纹 fatigue striations疲劳阈值 fatigue threshold交变载荷 alternating load交变应力 alternating stress应力幅值 stress amplitude应变疲劳 strain fatigue应力循环 stress cycle应力比 stress ratio安全寿命 safe life过载效应 overloading effect循环硬化 cyclic hardening循环软化 cyclic softening环境效应 environmental effect裂纹片 crack gage裂纹扩展 crack growth, crack Propagation 裂纹萌生 crack initiation循环比 cycle ratio实验应力分析 experimental stress Analysis 工作[应变]片 active[strain] gage基底材料 backing material应力计 stress gage零[点]飘移zero shift, zero drift应变测量 strain measurement应变计 strain gage应变指示器 strain indicator应变花 strain rosette应变灵敏度 strain sensitivity机械式应变仪 mechanical strain gage直角应变花 rectangular rosette引伸仪 Extensometer应变遥测 telemetering of strain横向灵敏系数 transverse gage factor横向灵敏度 transverse sensitivity焊接式应变计weldable strain gage平衡电桥 balanced bridge粘贴式应变计 bonded strain gage粘贴箔式应变计 bonded foiled gage粘贴丝式应变计bonded wire gage桥路平衡 bridge balancing电容应变计 capacitance strain gage补偿片 compensation technique补偿技术 compensation technique 基准电桥 reference bridge电阻应变计 resistance strain gage温度自补偿应变计 self-temperature compensating gage半导体应变计 semiconductor strain Gage集流器 slip ring应变放大镜 strain amplifier疲劳寿命计 fatigue life gage电感应变计inductance [strain] gage光[测]力学 Photomechanics光弹性 Photoelasticity光塑性 Photoplasticity杨氏条纹 Young fringe双折射效应 birefrigent effect等位移线 contour of equal Displacement暗条纹 dark fringe条纹倍增 fringe multiplication干涉条纹 interference fringe等差线 Isochromatic等倾线 Isoclinic等和线 isopachic应力光学定stress- optic law主应力迹线 Isostatic亮条纹 light fringe光程差 optical path difference热光弹性 photo-thermo -elasticity光弹性贴片法 photoelastic coating Method光弹性夹片法 photoelastic sandwich Method 动态光弹性 dynamic photo-elasticity空间滤波 spatial filtering空间频率 spatial frequency起偏镜 Polarizer反射式光弹性仪 reflection polariscope残余双折射效应 residual birefringent Effect 应变条纹值 strain fringe value应变光学灵敏度 strain-optic sensitivity应力冻结效应 stress freezing effect应力条纹值 stress fringe value应力光图 stress-optic pattern暂时双折射效应 temporary birefringentEffect脉冲全息法 pulsed holography透射式光弹性仪 transmission polariscope实时全息干涉法 real-time holographic interfero - metry网格法 grid method全息光弹性法 holo-photoelasticity全息图 Hologram全息照相 Holograph全息干涉法 holographic interferometry全息云纹法 holographic moire technique全息术 Holography全场分析法 whole-field analysis散斑干涉法 speckle interferometry散斑 Speckle错位散斑干涉法 speckle-shearing interferometry, shearography散斑图 Specklegram白光散斑法 white-light speckle method云纹干涉法 moire interferometry[叠栅]云纹 moire fringe[叠栅]云纹法 moire method云纹图 moire pattern离面云纹法 off-plane moire method参考栅 reference grating试件栅specimen grating分析栅 analyzer grating面内云纹法in-plane moire method脆性涂层法 brittle-coating method条带法 strip coating method坐标变换 transformation of Coordinates计算结构力学 computational structuralmecha-nics加权残量法 weighted residual method有限差分法 finite difference method有限[单]元法 finite element method配点法 point collocation里茨法 Ritz method广义变分原理 generalized variational Principle最小二乘法 least square method胡[海昌]一鹫津原理 Hu-Washizu principle赫林格-赖斯纳原理 Hellinger-Reissner Principle修正变分原理 modified variational Principle 约束变分原理 constrained variational Principle混合法 mixed method杂交法 hybrid method边界解法 boundary solution method有限条法 finite strip method半解析法 semi-analytical method协调元 conforming element非协调元 non-conforming element混合元 mixed element杂交元 hybrid element边界元 boundary element强迫边界条件 forced boundary condition自然边界条件 natural boundary condition离散化 Discretization离散系统 discrete system连续问题 continuous problem广义位移 generalized displacement广义载荷 generalized load 广义应变 generalized strain广义应力 generalized stress界面变量 interface variable节点 node, nodal point[单]元 Element角节点 corner node边节点 mid-side node内节点 internal node无节点变量 nodeless variable杆元 bar element桁架杆元 truss element梁元 beam element二维元 two-dimensional element一维元 one-dimensional element三维元 three-dimensional element轴对称元 axisymmetric element板元 plate element壳元 shell element厚板元 thick plate element三角形元 triangular element四边形元 lateral element四面体元 tetrahedral element曲线元 curved element二次元 quadratic element线性元 linear element三次元 cubic element四次元 quartic element等参[数]元 isoparametric element超参数元 super-parametric element亚参数元 sub-parametric element节点数可变元 variable-number-node element 拉格朗日元 Lagrange element拉格朗日族 Lagrange family巧凑边点元 serendipity element巧凑边点族 serendipity family无限元 infinite element单元分析 element analysis单元特性 element characteristics刚度矩阵 stiffness matrix几何矩阵 geometric matrix等效节点力 equivalent nodal force节点位移 nodal displacement节点载荷 nodal load位移矢量 displacement vector载荷矢量 load vector质量矩阵 mass matrix集总质量矩阵 lumped mass matrix相容质量矩阵 consistent mass matrix阻尼矩阵 damping matrix瑞利阻尼 Rayleigh damping刚度矩阵的组集 assembly of stiffness Matrices载荷矢量的组集 consistent mass matrix质量矩阵的组集 assembly of mass matrices 单元的组集 assembly of elements局部坐标系 local coordinate system局部坐标 local coordinate面积坐标 area coordinates体积坐标 volume coordinates曲线坐标 curvilinear coordinates静凝聚 static condensation合同变换contragradient transformation形状函数 shape function试探函数 trial function检验函数 test function权函数 weight function样条函数 spline function代用函数 substitute function降阶积分 reduced integration零能模式 zero-energy modeP收敛 p-convergenceH收敛 h-convergence掺混插值 blended interpolation等参数映射 isoparametric mapping双线性插值 bilinear interpolation小块检验 patch test非协调模式 incompatible mode节点号 node number单元号 element number带宽 band width带状矩阵 banded matrix变带状矩阵 profile matrix带宽最小化 minimization of band width波前法 frontal method子空间迭代法 subspace iteration method 行列式搜索法 determinant search method 逐步法 step-by-step method纽马克法 Newmark威尔逊法 Wilson拟牛顿法 quasi-Newton method牛顿-拉弗森法 Newton-Raphson method增量法 incremental method初应变 initial strain初应力 initial stress切线刚度矩阵 tangent stiffness matrix割线刚度矩阵 secant stiffness matrix模态叠加法 mode superposition method平衡迭代 equilibrium iteration子结构 Substructure子结构法 substructure technique超单元 super-element网格生成 mesh generation结构分析程序 structural analysis program 前处理 pre-processing 后处理 post-processing网格细化 mesh refinement应力光顺 stress smoothing组合结构 composite structure。

弹性力学第4章

5Formulation and Solution StrategiesThe previous chapters have now developed the basicﬁeld equations of elasticity theory.Theseresults comprise a system of differential and algebraic relations among the stresses,strains,anddisplacements that express particular physics at all points within the body under investigation.In this chapter we now wish to complete the general formulation byﬁrst developing boundaryconditions appropriate for use with theﬁeld equations.These conditions specify the physicsthat occur on the boundary of body,and generally provide the loading inputs that physicallycreate the interior stress,strain,and displacementﬁelds.Although theﬁeld equations are thesame for all problems,boundary conditions are different for each problem.Therefore,properdevelopment of boundary conditions is essential for problem solution,and thus it is importantto acquire a good understanding of such development bining theﬁeldequations with boundary conditions then establishes the fundamental boundary value problemsof the theory.This eventually leads us into two different formulations,one in terms ofdisplacements and the other in terms of stresses.Because these boundary value problems aredifﬁcult to solve,many different strategies have been developed to aid in problem solution.Wereview in a general way several of these strategies,and later chapters incorporate many ofthese into the solution of speciﬁc problems.5.1Review of Field EquationsBefore beginning our discussion on boundary conditions we list here the basicﬁeld equationsfor linear isotropic elasticity.Appendix A includes a more comprehensive listing of allﬁeldequations in Cartesian,cylindrical,and spherical coordinate systems.Because of its ease of useand compact properties,our formulation uses index notation.Strain-displacement relations:e ij¼12(u i,jþu j,i)(5:1:1)Compatibility relations:e ij,klþe kl,ijÀe ik,jlÀe jl,ik¼0(5:1:2)83Equilibrium equations:s ij,jþF i¼0(5:1:3) Elastic constitutive law(Hooke’s law):s ij¼l e kk d ijþ2m e ije ij¼1þnEs ijÀnEs kk d ij(5:1:4)As mentioned in Section2.6,the compatibility relations ensure that the displacements arecontinuous and single-valued and are necessary only when the strains are arbitrarily speciﬁed.If,however,the displacements are included in the problem formulation,the solution normallygenerates single-valued displacements and strain compatibility is automatically satisﬁed.Thus,in discussing the general system of equations of elasticity,the compatibility relations(5.1.2)are normally set aside,to be used only with the stress formulation that we discuss shortly.Therefore,the general system of elasticityﬁeld equations refers to the15relations(5.1.1),(5.1.3),and(5.1.4).It is convenient to deﬁne this entire system using a generalized operatornotation asJ{u i,e ij,s ij;l,m,F i}¼0(5:1:5) This system involves15unknowns including3displacements u i,6strains e ij,and6stresses s ij.The terms after the semicolon indicate that the system is also dependent on two elastic materialconstants(for isotropic materials)and on the body force density,and these are to be given apriori with the problem formulation.It is reassuring that the number of equations matches thenumber of unknowns to be determined.However,this general system of equations is of suchcomplexity that solutions by using analytical methods are essentially impossible and furthersimpliﬁcation is required to solve problems of interest.Before proceeding with development ofsuch simpliﬁcations,it is usefulﬁrst to discuss typical boundary conditions connected with theelasticity model,and this leads us to the classiﬁcation of the fundamental problems.5.2Boundary Conditions and Fundamental ProblemClassiﬁcationsSimilar to otherﬁeld problems in engineering science(e.g.,ﬂuid mechanics,heat conduction,diffusion,electromagnetics),the solution of system(5.1.5)requires appropriate boundaryconditions on the body under study.The common types of boundary conditions for elasticityapplications normally include speciﬁcation of how the body is being supported or loaded.Thisconcept is mathematically formulated by specifying either the displacements or tractions atboundary points.Figure5-1illustrates this general idea for three typical cases includingtractions,displacements,and a mixed case for which tractions are speciﬁed on boundary S tand displacements are given on the remaining portion S u such that the total boundary is givenby S¼S tþS u.Another type of mixed boundary condition can also occur.Although it is generally not possible to specify completely both the displacements and tractions at the same boundarypoint,it is possible to prescribe part of the displacement and part of the traction.Typically,this 84FOUNDATIONS AND ELEMENTARY APPLICATIONStype of mixed condition involves the speciﬁcation of a traction and displacement in two different orthogonal directions.A common example of this situation is shown in Figure 5-2for a case involving a surface of problem symmetry where the condition is one of a rigid-smooth boundary with zero normal displacement and zero tangential traction.Notice that in this example the body under study was subdivided along the symmetry line,thus creating a new boundary surface and resulting in a smaller region to analyze.Because boundary conditions play a very essential role in properly formulating and solving elasticity problems,it is important to acquire a clear understanding of their speciﬁcation and use.Improper speciﬁcation results in either no solution or a solution to a different problem than what was originally sought.Boundary conditions are normally speciﬁed using the coordinate system describing the problem,and thus particular components of the displacements and tractions are set equal to prescribed values.For displacement-type conditions,such a speciﬁ-cation is straightforward,and a common example includes ﬁxed boundaries where the dis-placements are to be zero.For traction boundary conditions,the speciﬁcation can be a bit more complex.Figure 5-3illustrates particular cases in which the boundaries coincide with Cartesian or polar coordinate surfaces.By using results from Section 3.2,the traction speciﬁcation can be reduced to a stress speciﬁcation.For the Cartesian example in which y ¼constant ,Displacement Conditions Mixed ConditionsTraction ConditionsFIGURE 5-1Typical boundary conditions.T (n)y u Rigid-SmoothFIGURE 5-2Line of symmetry boundary condition.Formulation and Solution Strategies 85the normal traction becomes simply the stress component s y ,while the tangential traction reduces to t xy .For this case,s x exists only inside the region,and thus this component of stress cannot be speciﬁed on the boundary surface y ¼constant .A similar situation exists on the vertical boundary x ¼constant ,where the normal traction is now s x ,the tangential traction is t xy and the stress component s y exists inside the domain.Similar arguments can be made for polar coordinate boundary surfaces as shown.Drawing the appropriate element along the boundary as illustrated allows a clear visualization of the particular stress components that act on the surface in question.Such a sketch also allows determination of the positive directions of these boundary stresses,and this is useful to properly match with boundary loadings that might be prescribed.It is recommended that sketches similar to Figure 5-3be used to aid in the proper development of boundary conditions during problem formulation.Consider the pair of two-dimensional example problems with mixed conditions as shown in Figure 5-4.For the rectangular plate problem,all four boundaries are coordinate surfaces,andr(Cartesian Coordinate Boundaries)(Polar Coordinate Boundaries)xFIGURE 5-3Boundary stress components on coordinatesurfaces.(n)(n)(n)= σy = 0= t xy = 0(n)T x (n)T y = t xy =0,Traction Condition (Non-Coordinate Surface Boundary)(Coordinate Surface Boundaries)FIGURE 5-4Example boundary conditions.86FOUNDATIONS AND ELEMENTARY APPLICATIONSthis simpliﬁes speciﬁcation of particular boundary conditions.Theﬁxed conditions on the left edge simply require that x and y displacement components vanish on x¼0,and this speciﬁca-tion does not change even if this were not a coordinate surface.However,as per our previous discussion,the traction conditions on the other three boundaries simplify because they are coordinate surfaces.These simpliﬁcations are shown in theﬁgure for each of the traction speciﬁed surfaces.The second problem of a tapered cantilever beam has an inclined face that is not a coordinate surface.For this problem,theﬁxed end and top surface follow similar procedures as in theﬁrst example and are speciﬁed in theﬁgure.However,on the inclined face,the traction is to be zero and this does not reduce to a simple speciﬁcation of the vanishing of individual stress components.On this face each traction component is set to zero,giving the resultT(n)x¼s x n xþt xy n y¼0T(n)y¼t xy n xþs y n y¼0where n x and n y are the components of the unit normal vector to the inclined face.This is the more general type of speciﬁcation,and it should be clearly noted that none of the individual stress components in the x,y system will vanish along this surface.It should also be pointed out for this problem that the unit normal vector components are constants for all points on the inclined face.However,for curved boundaries the normal vector changes with surface position.Although these examples provide some background on typical boundary conditions,many other types will be encountered throughout the text.Several exercises at the end of this chapter provide additional examples that will prove to be useful for students new to the elasticity formulation.We are now in the position to formulate and classify the three fundamental boundary-value problems in the theory of elasticity that are related to solving the general system ofﬁeld equations(5.1.5).Our presentation is limited to the static case.Problem1:Traction problemDetermine the distribution of displacements,strains,and stresses in the interior of an elastic body in equilibrium when body forces are given and the distribution of the tractions are prescribed over the surface of the body,T(n)i(x(s)i)¼f i(x(s)i)(5:2:1) where x(s)i denotes boundary points and f i(x(s)i)are the prescribed traction values. Problem2:Displacement problemDetermine the distribution of displacements,strains,and stresses in the interior of an elastic body in equilibrium when body forces are given and the distribution of the displacements are prescribed over the surface of the body,u i(x(s)i)¼g i(x(s)i)(5:2:2) where x(s)i denotes boundary points and g i(x(s)i)are the prescribed displacement values.Formulation and Solution Strategies87Problem3:Mixed problemDetermine the distribution of displacements,strains,and stresses in the interior of an elasticbody in equilibrium when body forces are given and the distribution of the tractions areprescribed as per(5.2.1)over the surface S t and the distribution of the displacementsare prescribed as per(5.2.2)over the surface S u of the body(see Figure5-1).As mentioned previously,the solution to any of these types of problems is formidable,andfurther reduction and simpliﬁcation of(5.1.5)is required for the development of analyticalsolution methods.Based on the description of Problem1with only traction boundary condi-tions,it would appear to be desirable to express the fundamental system solely in terms ofstress,that is,J(t){s ij;l,m,F i}thereby reducing the number of unknowns in the system.Likewise for Problem2,a displacement-only formulation of the form J(u){u i;l,m,F i}wouldappear to simplify the problem.We now pursue such specialized formulations and explicitlydetermine these reducedﬁeld equation systems.5.3Stress FormulationFor theﬁrst fundamental problem in elasticity,the boundary conditions are to be given only interms of the tractions or stress components.In order to develop solution methods for this case,it is very helpful to reformulate the general system(5.1.5)by eliminating the displacementsand strains and thereby cast a new system solely in terms of the stresses.We now develop thisreformulated system.By eliminating the displacements,we must now include the compatibil-ity equations in the fundamental system ofﬁeld equations.We therefore start by using Hooke’slaw(5.1.4)2and eliminate the strains in the compatibility relations(5.1.2)to gets ij,kkþs kk,ijÀs ik,jkÀs jk,ik¼n 1þn (s mm,kk d ijþs mm,ij d kkÀs mm,jk d ikÀs mm,ik d jk)(5:3:1)where we have used the arguments of Section2.6,that the six meaningful compatibility relations are found by setting k¼l in(5.1.2).Although equations(5.3.1)represent the compatibility in terms of stress,a more useful result is found by incorporating the equilibrium equations into the system.Recall that from(5.1.3),s ij,j¼ÀF i,and also note that d kk¼3. Substituting these results into(5.3.1)givess ij,kkþ11þns kk,ij¼n1þns mm,kk d ijÀF i,jÀF j,i(5:3:2)For the case i¼j,relation(5.3.2)reduces to s ii,kk¼À1þn1ÀnF i,i.Substituting this result backinto(5.3.2)gives the desired relations ij,kkþ11þns kk,ij¼Àn1Ànd ij F k,kÀF i,jÀF j,i(5:3:3)This result is the compatibility relations in terms of the stress and is commonly called theBeltrami-Michell compatibility equations.For the case with no body forces,these relations canbe expressed as the following six scalar equations:88FOUNDATIONS AND ELEMENTARY APPLICATIONS(1þn)r2s xþ@2@x(s xþs yþs z)¼0(1þn)r2s yþ@2@y(s xþs yþs z)¼0(1þn)r2s zþ@2@z(s xþs yþs z)¼0(1þn)r2t xyþ@2@x@y(s xþs yþs z)¼0(1þn)r2t yzþ@2@y@z(s xþs yþs z)¼0(1þn)r2t zxþ@2(s xþs yþs z)¼0(5:3:4)Recall that the six developed relations(5.3.3)or(5.3.4)actually represent three independentresults as per our discussion in Section2.6.Thus,combining these results with the threeequilibrium equations(5.1.3)provides the necessary six relations to solve for the six unknownstress components for the general three-dimensional case.This system constitutes the stressformulation for elasticity theory and is appropriate for use with traction boundary conditionproblems.Once the stresses have been determined,the strains may be found from Hooke’s law(5.1.4)z,and the displacements can be then be computed through integration of(5.1.1).As perour previous discussion in Section2.2,such an integration process determines the displace-ments only up to an arbitrary rigid-body motion,and the displacements obtained are single-valued only if the region under study is simply connected.The system of equations for the stress formulation is still rather complex,and analytical solutions are commonly determined for this case by making use of stress functions.Thisconcept establishes a representation for the stresses that automatically satisﬁes the equilibriumequations.For the two-dimensional case,this concept represents the in-plane stresses in termsof a single function.The representation satisﬁes equilibrium,and the remaining compatibilityequations yield a single partial differential equation(biharmonic equation)in terms of thestress function.Having reduced the system to a single equation then allows us to employ manyanalytical methods toﬁnd solutions of interest.Further discussion on these techniques ispresented in subsequent chapters.5.4Displacement FormulationWe now wish to develop the reduced set ofﬁeld equations solely in terms of the displacements.This system is referred to as the displacement formulation and is most useful when combinedwith displacement-only boundary conditions found in the Problem2statement.This develop-ment is somewhat more straightforward than our previous discussion for the stress formulation.For this case,we wish to eliminate the strains and stresses from the fundamental system(5.1.5).This is easily accomplished by using the strain-displacement relations in Hooke’s lawto gives ij¼l u k,k d ijþm(u i,jþu j,i)(5:4:1) which can be expressed as six scalar equationsFormulation and Solution Strategies89s x¼l@u@xþ@n@yþ@w@zþ2m@u@xs y¼l@u@xþ@v@yþ@w@zþ2m@v@ys z¼l@u@xþ@v@yþ@w@zþ2m@w@zt xy¼m @u@yþ@v@x,t yz¼m @v@zþ@w@y,t zx¼m @w@xþ@u@z(5:4:2)Using these relations in the equilibrium equations gives the resultm u i,kkþ(lþm)u k,kiþF i¼0(5:4:3)which are the equilibrium equations in terms of the displacements and are referred to as Navier’s or Lame´’s equations.This system can be expressed in vector form asm r2uþ(lþm),(,Áu)þF¼0(5:4:4) or written out in terms of the three scalar equationsm r2uþ(lþm)@@x@u@xþ@v@yþ@w@zþF x¼0m r2vþ(lþm)@@y@u@xþ@v@yþ@w@zþF y¼0m r2wþ(lþm)@@z@u@xþ@v@yþ@w@zþF z¼0(5:4:5)where the Laplacian is given by r2¼(@2=@x2)þ(@2=@y2)þ(@2=@z2).Navier’s equations arethe desired formulation for the displacement problem,and the system represents three equa-tions for the three unknown displacement components.Similar to the stress formulation,thissystem is still difﬁcult to solve,and additional mathematical techniques have been developedto further simplify these equations for problem mon methods normally employthe use of displacement potential functions.It is shown in Chapter13that several suchschemes can be developed that allow the displacement vector to be expressed in terms ofparticular potentials.These schemes generally simplify the problem by yielding uncoupledgoverning equations in terms of the displacement potentials.This then allows several analyt-ical methods to be employed to solve problems of interest.Several of these techniques arediscussed in later sections of the text.To help acquire a general understanding of these results,a summaryﬂow chart of the developed stress and displacement formulations is shown in Figure5-5.Note that for thestress formulation,the resulting system J(t){s ij;l,m,F i}is actually dependent onlyon the single material constant Poisson’s ratio,and thus it could be expressed asJ(t){s ij;n,F i}.90FOUNDATIONS AND ELEMENTARY APPLICATIONS5.5Principle of SuperpositionA very useful tool for the solution to many problems in engineering science is the principle ofsuperposition.This technique applies to any problem that is governed by linear equations.Under the assumption of small deformations and linear elastic constitutive behavior,allelasticityﬁeld equations(see Figure5-5)are linear.Furthermore,the usual boundary condi-tions speciﬁed by relations(5.2.1)and(5.2.2)are also linear.Thus,under these conditions allgoverning equations are linear,and the superposition concept can be applied.It can be easilyproved(see Chou and Pagano1967)that the general statement of the principle can beexpressed as follows:Principle of Superposition:For a given problem domain,if the state{s(1)ij,e(1)ij,u(1)i}is asolution to the fundamental elasticity equations with prescribed body forces F(1)i andsurface tractions T(1)i,and the state{s(2)ij,e(2)ij,u(2)i}is a solution to the fundamentalequations with prescribed body forces F(2)i and surface tractions T(2)i,then the sta-te{s(1)ijþs(2)ij,e(1)ijþe(2)ij,u(1)iþu(2)i}will be a solution to the problem with body forcesF(1)iþF(2)i and surface tractions T(1)iþT(2)i.In order to see a more direct application of this principle,consider a simple two-dimensionalcase with no body forces as shown in Figure5-6.It can be observed that the solution to themore complicated biaxial loading case(1)þ(2)is thus found by adding the two simplerproblems.This is a common use of the superposition principle,and we make repeated use ofthis application throughout the text.Thus,once the solutions to some simple problems aregenerated,we can combine these results to generate a solution to a more complicated case withsimilar geometry.Formulation and Solution Strategies915.6Saint-Venant’s PrincipleConsider the set of three identical rectangular strips under compressive loadings as shown in Figure 5-7.As indicated,the only difference between each problem is the loading.Because the total resultant load applied to each problem is identical (statically equivalent loadings),it is expected that the resulting stress,strain,and displacement ﬁelds near the bottom of each strip would be approximately the same.This behavior can be generalized by considering an elastic solid with an arbitrary loading T (n )over a boundary portion S *,as shown in Figure 5-8.Based on experience from other ﬁeld problems in engineering science,it seems logical that the particular boundary loading would produce detailed and characteristic effects only in the vicinity of S *.In other words,we expect that at points far away from S *the stresses generally depend more on the resultant F R of the tractions rather than on the exact distribution.Thus,the characteristic signature of the generated stress,strain,and displacement ﬁelds from a given boundary loading tend to disappear as we move away from the boundary loading points.These concepts form the principle of Saint-Venant ,which can be stated as follows:Saint-Venant’s Principle:The stress,strain,and displacement ﬁelds caused by two different statically equivalent force distributions on parts of the body far away from the loading points are approximately the same.=+ ij ij i ij ij i {s (1)ij + s (2) ij , e (1) ij , + e (2) ij , u (1) i + u (2) i }FIGURE 5-6Two-dimensional superposition example.2P 2P3P 3P 3P FIGURE 5-7Statically equivalent loadings.92FOUNDATIONS AND ELEMENTARY APPLICATIONSThis statement of the principle includes qualitative terms such as far away and approxi-mately the same ,and thus does not provide quantitative estimates of the differences between the two elastic ﬁelds in question.Quantitative results have been developed by von Mises (1945),Sternberg (1954),and Toupin (1965),while Horgan (1989)has presented a recent review of related work.Some of this work is summarized in Boresi and Chong (2000).If we restrict our solution to points away from the boundary loading,Saint-Venant’s principle allows us to change the given boundary conditions to a simpler statically equivalent statement and not affect the resulting solution.Such a simpliﬁcation of the boundary conditions greatly increases our chances of ﬁnding an analytical solution to the problem.This concept therefore proves to be very useful,and we formally outline this solution scheme in the next section.5.7General Solution StrategiesHaving completed our formulation and related solution principles,we now wish to examine some general solution strategies commonly used to solve elasticity problems.At this stage we categorize particular methods and outline only typical techniques that are commonly used.As we move further along in the text,many of these methods are developed in detail and are applied in speciﬁc problem solution.We ﬁrst distinguish three general methods of solution called direct,inverse ,and semi-inverse .5.7.1Direct MethodThis method seeks to determine the solution by direct integration of the ﬁeld equations (5.1.5)or equivalently the stress and/or displacement formulations given in Figure 5-5.Boundary conditions are to be satisﬁed exactly.This method normally encounters signiﬁcant mathemat-ical difﬁculties,thus limiting its application to problems with simple geometry.EXAMPLE 5-1:Direct Integration Example:Stretching of Prismatic Bar Under Its Own WeightAs an example of a simple direct integration problem,consider the case of a uniform prismatic bar stretched by its own weight,as shown in Figure 5-9.The body forces forContinuedFIGURE 5-8Saint-Venant concept.5.7.2Inverse MethodFor this technique,particular displacements or stresses are selected that satisfy the basicﬁeld equations.A search is then conducted to identify a speciﬁc problem that would be solved by this solutionﬁeld.This amounts to determine appropriate problem geometry,boundary conditions,and body forces that would enable the solution to satisfy all conditions on the ing this scheme it is sometimes difﬁcult to construct solutions to a speciﬁc problem of practical interest.5.7.3Semi-Inverse MethodIn this scheme part of the displacement and/or stressﬁeld is speciﬁed,and the other remaining portion is determined by the fundamentalﬁeld equations(normally using direct integration) and the boundary conditions.It is often the case that constructing appropriate displacement and/or stress solutionﬁelds can be guided by approximate strength of materials theory.The usefulness of this approach is greatly enhanced by employing Saint-Venant’s principle, whereby a complicated boundary condition can be replaced by a simpler statically equivalent distribution.EXAMPLE5-3:Semi-Inverse Example:Torsion of Prismatic BarsA simple semi-inverse example may be borrowed from the torsion problem that isdiscussed in detail in Chapter9.Skipping for now the developmental details,we propose the following displacementﬁeld:ContinuedThere are numerous mathematical techniques used to solve the elasticity ﬁeld equations.Many techniques involve the development of exact analytical solutions ,while others involve the construction of approximate solution schemes .A third procedure involves the establishment of numerical solution methods .We now brieﬂy provide an overview of each of these techniques.5.7.4Analytical Solution ProceduresA variety of analytical solution methods are used to solve the elasticity ﬁeld equations.The following sections outline some of the more common methods.Power Series MethodFor many two-dimensional elasticity problems,the stress formulation leads to the use of a stress function f (x ,y ).It is shown that the entire set of ﬁeld equations reduces to a single partial differential equation (biharmonic equation)in terms of this stress function.A general mathematical scheme to solve this equation is to look for solutions in terms of a power series in the independent variables,that is,f (x ,y )¼P C mn x m y n (see Neou 1957).Use of the boundary conditions determines the coefﬁcients and number of terms to be used in the series.This method is employed to develop two-dimensional solutions in Section 8.1.Fourier MethodA general scheme to solve a large variety of elasticity problems employs the Fourier method.This procedure is normally applied to the governing partial differential equations by using。

弹性力学双语讲义(chapter1)

弹性力学 Elasticity The lectures will be given both in English and Chinese 采用中英文双语讲授
extbook: Applied Elasticity 徐芝纶中文教材：中文教材：弹性力学简明教程徐芝纶
Chapter 1. Introduction 第一章绪论
•A prismatical tension member with a small hole •It is assumed in mechanics of materials that the tensile stresses are uniformly distributed across the net section of the member. •The analysis in elasticity shows that the stresses are by no means uniform, but are concentrated near the hole.
Three branches of solid mechanics 固体力学的三个分枝固体力学的三个分枝
• Mechanics of materials 材料力学, 材料力学, Structural Mechanics 结构力学 Elasticity 弹性力学
•
•
What does the Elasticity deal with? It deals with the stresses, deformations and displacements in elastic solids produced by external forces or changes in temperature. 研究弹性体由于外力和温度改变而引起的应力，由于外力和温度改变而引起的应力研究弹性体由于外力和温度改变而引起的应力，形变和位移。形变和位移。 It analyzes the stresses, deformations and displacements of structural elements within the elastic range and thereby to check the sufficiency of their strength, stiffness and stability. 分析结构的应力，形变和位移，分析结构的应力，形变和位移，检查是否满足强刚度和稳定性条件。度，刚度和稳定性条件。

弹性力学

弹性力学网络课程第一章绪论内容介绍知识点弹性力学的特点弹性力学的基本假设弹性力学的发展弹性力学的任务弹性力学的研究方法内容介绍：一. 内容介绍本章作为弹性力学课程的引言，主要介绍课程的研究对象、基本分析方法和特点；课程分析的基本假设和课程学习的意义以及历史和发展。

弹性力学的研究对象是完全弹性体，因此分析从微分单元体入手，基本方程为偏微分方程。

偏微分方程边值问题在数学上求解困难，使得弹性力学的基本任务是研究弹性体由于外力载荷或者温度改变，物体内部所产生的位移、变形和应力分布等，为解决工程结构的强度，刚度和稳定性问题作准备，但是并不直接作强度和刚度分析。

本章介绍弹性力学分析的基本假设。

弹性力学分析中，必须根据已知物理量，例如外力、结构几何形状和约束条件等，通过静力平衡、几何变形和本构关系等，推导和确定基本未知量，位移、应变和应力等与已知物理量的关系。

由于工程实际问题的复杂性是由多方面因素构成的，如果不分主次地考虑所有因素，问题是十分复杂的，数学推导将困难重重，以至于不可能求解。

课程分析中使用张量符号描述物理量和基本方程。

目前，有关弹性力学的文献和工程资料都是使用张量符号的。

如果你没有学习过张量概念，请进入附录一学习，或者查阅参考资料。

二. 重点1.课程的研究对象；2.基本分析方法和特点；3.弹性力学的基本假设；4.课程的学习意义；5.弹性力学的发展。

特点：弹性力学，又称弹性理论。

作为固体力学学科的一个分支，弹性力学的基本任务是研究弹性体由于外力载荷或者温度改变，物体内部所产生的位移、变形和应力分布等，为解决工程结构的强度，刚度和稳定性问题作准备，但是并不直接作强度和刚度分析。

构件承载能力分析是固体力学的基本任务，但是对于不同的学科分支，研究对象和方法是不同的。

弹性力学的研究对象是完全弹性体，包括构件、板和三维弹性体，比材料力学和结构力学的研究范围更为广泛。

弹性是变形固体的基本属性，而“完全弹性”是对弹性体变形的抽象。

弹性力学双语版-西安交通大学-8

Elasticity
1
2Leabharlann Chapter8 Space Problem
§8-1 Introduction §8-2 The Basic Equation unde Rectangular Coordinate §8-3 The Axially Symmetric Problem of Space
§8-4 The Spherical Symmetric Problem of Space
P
x x
y z y z
Axial Symmetric Problem
Ball Symmetric Problem
5
§8-1
概述
本章首先给出空间问题直角坐标下的平衡方程、几何方程和物理方程。针对空间问题的解析解一般只能在特殊边界条件下才可以得到，我们着重讨论空间轴对称问题和空间球对称问题。
P
y e 2G y z e 2G z
where：
zx G zx xy G xy
e x y z

E 1 1 2
11
三物理方程对于各向同性体，形变分量与应力分量之间的关系如下：
1 x y z E 1 y y z x E 1 z z x y E
化简并略去高阶微量，得
8
Similarly,we get
y z zy zx x z xy yx from X 0, Y 0, Z 0
Here we prove the relation of the equality of cross shears again
yx x zx X 0 x y z zy xy y Y 0 y z x yz xz z Z 0 z x y

弹性力学专业英语英汉互译词汇

弹性力学elasticity弹性理论theory of elasticity 均匀应力状态homogeneous state of stress 应力不变量stress invariant应变不变量strain invariant应变椭球strain ellipsoid 均匀应变状态homogeneous state ofstrain 应变协调方程equation of straincompatibility 拉梅常量Lame constants 各向同性弹性isotropic elasticity 旋转圆盘rotating circular disk 楔wedge开尔文问题Kelvin problem 布西内斯克问题Boussinesq problem艾里应力函数Airy stress function克罗索夫--穆斯赫利什维Kolosoff-利法Muskhelishvili method 基尔霍夫假设Kirchhoff hypothesis 板Plate矩形板Rectangular plate圆板Circular plate环板Annular plate波纹板Corrugated plate加劲板Stiffened plate,reinforcedPlate 中厚板Plate of moderate thickness 弯[曲]应力函数Stress function of bending 壳Shell扁壳Shallow shell旋转壳Revolutionary shell球壳Spherical shell [圆]柱壳Cylindrical shell 锥壳Conical shell环壳Toroidal shell封闭壳Closed shell波纹壳Corrugated shell扭[转]应力函数Stress function of torsion 翘曲函数Warping function半逆解法semi-inverse method瑞利--里茨法Rayleigh-Ritz method 松弛法Relaxation method莱维法Levy method松弛Relaxation 量纲分析Dimensional analysis自相似[性] self-similarity 影响面Influence surface接触应力Contact stress赫兹理论Hertz theory协调接触Conforming contact滑动接触Sliding contact滚动接触Rolling contact压入Indentation各向异性弹性Anisotropic elasticity 颗粒材料Granular material散体力学Mechanics of granular media 热弹性Thermoelasticity超弹性Hyperelasticity粘弹性Viscoelasticity对应原理Correspondence principle 褶皱Wrinkle塑性全量理论Total theory of plasticity 滑动Sliding微滑Microslip粗糙度Roughness非线性弹性Nonlinear elasticity 大挠度Large deflection突弹跳变snap-through有限变形Finite deformation格林应变Green strain阿尔曼西应变Almansi strain弹性动力学Dynamic elasticity运动方程Equation of motion准静态的Quasi-static气动弹性Aeroelasticity水弹性Hydroelasticity颤振Flutter弹性波Elastic wave简单波Simple wave柱面波Cylindrical wave水平剪切波Horizontal shear wave竖直剪切波Vertical shear wave 体波body wave无旋波Irrotational wave畸变波Distortion wave膨胀波Dilatation wave瑞利波Rayleigh wave等容波Equivoluminal wave勒夫波Love wave界面波Interfacial wave边缘效应edge effect塑性力学Plasticity可成形性Formability金属成形Metal forming耐撞性Crashworthiness结构抗撞毁性Structural crashworthiness 拉拔Drawing 破坏机构Collapse mechanism 回弹Springback挤压Extrusion冲压Stamping穿透Perforation层裂Spalling 塑性理论Theory of plasticity安定[性]理论Shake-down theory运动安定定理kinematic shake-down theorem静力安定定理Static shake-down theorem 率相关理论rate dependent theorem 载荷因子load factor加载准则Loading criterion加载函数Loading function加载面Loading surface塑性加载Plastic loading塑性加载波Plastic loading wave 简单加载Simple loading比例加载Proportional loading 卸载Unloading卸载波Unloading wave冲击载荷Impulsive load阶跃载荷step load脉冲载荷pulse load极限载荷limit load中性变载nentral loading拉抻失稳instability in tension 加速度波acceleration wave本构方程constitutive equation 完全解complete solution名义应力nominal stress过应力over-stress真应力true stress等效应力equivalent stress流动应力flow stress应力间断stress discontinuity应力空间stress space主应力空间principal stress space静水应力状态hydrostatic state of stress 对数应变logarithmic strain工程应变engineering strain等效应变equivalent strain应变局部化strain localization 应变率strain rate应变率敏感性strain rate sensitivity 应变空间strain space有限应变finite strain塑性应变增量plastic strain increment 累积塑性应变accumulated plastic strain 永久变形permanent deformation内变量internal variable应变软化strain-softening理想刚塑性材料rigid-perfectly plasticMaterial刚塑性材料rigid-plastic material理想塑性材料perfectl plastic material 材料稳定性stability of material应变偏张量deviatoric tensor of strain 应力偏张量deviatori tensor of stress 应变球张量spherical tensor of strain 应力球张量spherical tensor of stress 路径相关性path-dependency线性强化linear strain-hardening应变强化strain-hardening随动强化kinematic hardening各向同性强化isotropic hardening 强化模量strain-hardening modulus幂强化power hardening塑性极限弯矩plastic limit bendingMoment塑性极限扭矩plastic limit torque弹塑性弯曲elastic-plastic bending弹塑性交界面elastic-plastic interface 弹塑性扭转elastic-plastic torsion 粘塑性Viscoplasticity非弹性Inelasticity理想弹塑性材料elastic-perfectly plasticMaterial 极限分析limit analysis极限设计limit design极限面limit surface上限定理upper bound theorem上屈服点upper yield point下限定理lower bound theorem下屈服点lower yield point界限定理bound theorem初始屈服面initial yield surface后继屈服面subsequent yield surface屈服面[的]外凸性convexity of yield surface 截面形状因子shape factor of cross-section沙堆比拟sand heap analogy 屈服Yield 屈服条件yield condition屈服准则yield criterion屈服函数yield function屈服面yield surface塑性势plastic potential 能量吸收装置energy absorbing device 能量耗散率energy absorbing device 塑性动力学dynamic plasticity 塑性动力屈曲dynamic plastic buckling 塑性动力响应dynamic plastic response 塑性波plastic wave 运动容许场kinematically admissibleField 静力容许场statically admissibleField 流动法则flow rule速度间断velocity discontinuity滑移线slip-lines滑移线场slip-lines field移行塑性铰travelling plastic hinge 塑性增量理论incremental theory ofPlasticity 米泽斯屈服准则Mises yield criterion 普朗特--罗伊斯关系prandtl- Reuss relation 特雷斯卡屈服准则Tresca yield criterion洛德应力参数Lode stress parameter莱维--米泽斯关系Levy-Mises relation亨基应力方程Hencky stress equation赫艾--韦斯特加德应力空Haigh-Westergaard 间stress space洛德应变参数Lode strain parameter德鲁克公设Drucker postulate盖林格速度方程Geiringer velocityEquation结构力学structural mechanics结构分析structural analysis结构动力学structural dynamics拱Arch三铰拱three-hinged arch抛物线拱parabolic arch圆拱circular arch穹顶Dome空间结构space structure空间桁架space truss雪载[荷] snow load风载[荷] wind load土压力earth pressure地震载荷earthquake loading弹簧支座spring support支座位移support displacement支座沉降support settlement超静定次数degree of indeterminacy机动分析kinematic analysis结点法method of joints截面法method of sections结点力joint forces共轭位移conjugate displacement影响线influence line 三弯矩方程three-moment equation单位虚力unit virtual force刚度系数stiffness coefficient柔度系数flexibility coefficient力矩分配moment distribution力矩分配法moment distribution method 力矩再分配moment redistribution分配系数distribution factor矩阵位移法matri displacement method 单元刚度矩阵element stiffness matrix 单元应变矩阵element strain matrix 总体坐标global coordinates贝蒂定理Betti theorem高斯--若尔当消去法Gauss-Jordan eliminationMethod 屈曲模态buckling mode 复合材料力学mechanics of composites 复合材料composite material 纤维复合材料fibrous composite单向复合材料unidirectional composite泡沫复合材料foamed composite颗粒复合材料particulate composite 层板Laminate夹层板sandwich panel正交层板cross-ply laminate 斜交层板angle-ply laminate 层片Ply 多胞固体cellular solid 膨胀Expansion压实Debulk劣化Degradation脱层Delamination脱粘Debond 纤维应力fiber stress层应力ply stress层应变ply strain层间应力interlaminar stress比强度specific strength强度折减系数strength reduction factor 强度应力比strength -stress ratio 横向剪切模量transverse shear modulus 横观各向同性transverse isotropy正交各向异Orthotropy剪滞分析shear lag analysis短纤维chopped fiber长纤维continuous fiber纤维方向fiber direction纤维断裂fiber break纤维拔脱fiber pull-out纤维增强fiber reinforcement致密化Densification最小重量设计optimum weight design网格分析法netting analysis 混合律rule of mixture失效准则failure criterion蔡--吴失效准则Tsai-W u failure criterion 达格代尔模型Dugdale model 断裂力学fracture mechanics概率断裂力学probabilistic fractureMechanics格里菲思理论Griffith theory线弹性断裂力学linear elastic fracturemechanics, LEFM弹塑性断裂力学elastic-plastic fracturemecha-nics, EPFM 断裂Fracture 脆性断裂brittle fracture解理断裂cleavage fracture蠕变断裂creep fracture延性断裂ductile fracture晶间断裂inter-granular fracture 准解理断裂quasi-cleavage fracture 穿晶断裂trans-granular fracture 裂纹Crack裂缝Flaw缺陷Defect割缝Slit微裂纹Microcrack折裂Kink 椭圆裂纹elliptical crack深埋裂纹embedded crack[钱]币状裂纹penny-shape crack 预制裂纹Precrack短裂纹short crack表面裂纹surface crack裂纹钝化crack blunting裂纹分叉crack branching裂纹闭合crack closure裂纹前缘crack front裂纹嘴crack mouth裂纹张开角crack opening angle,COA 裂纹张开位移crack opening displacement,COD 裂纹阻力crack resistance裂纹面crack surface裂纹尖端crack tip裂尖张角crack tip opening angle,CTOA裂尖张开位移crack tip openingdisplacement, CTOD裂尖奇异场crack tip singularityField裂纹扩展速率crack growth rate稳定裂纹扩展stable crack growth定常裂纹扩展steady crack growth亚临界裂纹扩展subcritical crack growth 裂纹[扩展]减速crack retardation 止裂crack arrest 止裂韧度arrest toughness断裂类型fracture mode滑开型sliding mode张开型opening mode撕开型tearing mode复合型mixed mode撕裂Tearing 撕裂模量tearing modulus断裂准则fracture criterionJ积分J-integral J阻力曲线J-resistance curve断裂韧度fracture toughness应力强度因子stress intensity factor HRR场Hutchinson-Rice-RosengrenField 守恒积分conservation integral 有效应力张量effective stress tensor 应变能密度strain energy density 能量释放率energy release rate 内聚区cohesive zone塑性区plastic zone张拉区stretched zone热影响区heat affected zone, HAZ 延脆转变温度brittle-ductile transitiontempe- rature 剪切带shear band剪切唇shear lip无损检测non-destructive inspection 双边缺口试件double edge notchedspecimen, DEN specimen 单边缺口试件single edge notchedspecimen, SEN specimen 三点弯曲试件three point bendingspecimen, TPB specimen 中心裂纹拉伸试件center cracked tensionspecimen, CCT specimen 中心裂纹板试件center cracked panelspecimen, CCP specimen 紧凑拉伸试件compact tension specimen,CT specimen 大范围屈服large scale yielding小范围攻屈服small scale yielding 韦布尔分布Weibull distribution 帕里斯公式paris formula 空穴化Cavitation应力腐蚀stress corrosion概率风险判定probabilistic riskassessment, PRA 损伤力学damage mechanics 损伤Damage连续介质损伤力学continuum damage mechanics 细观损伤力学microscopic damage mechanics 累积损伤accumulated damage脆性损伤brittle damage延性损伤ductile damage宏观损伤macroscopic damage细观损伤microscopic damage微观损伤microscopic damage损伤准则damage criterion损伤演化方程damage evolution equation 损伤软化damage softening损伤强化damage strengthening损伤张量damage tensor损伤阈值damage threshold损伤变量damage variable损伤矢量damage vector损伤区damage zone疲劳Fatigue 低周疲劳low cycle fatigue应力疲劳stress fatigue随机疲劳random fatigue蠕变疲劳creep fatigue腐蚀疲劳corrosion fatigue疲劳损伤fatigue damage疲劳失效fatigue failure 疲劳断裂fatigue fracture 疲劳裂纹fatigue crack 疲劳寿命fatigue life疲劳破坏fatigue rupture 疲劳强度fatigue strength 疲劳辉纹fatigue striations 疲劳阈值fatigue threshold 交变载荷alternating load 交变应力alternating stress 应力幅值stress amplitude 应变疲劳strain fatigue 应力循环stress cycle应力比stress ratio安全寿命safe life过载效应overloading effect 循环硬化cyclic hardening 循环软化cyclic softening 环境效应environmental effect 裂纹片crack gage裂纹扩展crack growth, crackPropagation 裂纹萌生crack initiation 循环比cycle ratio实验应力分析experimental stressAnalysis工作[应变]片active[strain] gage基底材料backing material应力计stress gage 零[点]飘移zero shift, zero drift 应变测量strain measurement应变计strain gage 应变指示器strain indicator 应变花strain rosette 应变灵敏度strain sensitivity机械式应变仪mechanical strain gage 直角应变花rectangular rosette 引伸仪Extensometer应变遥测telemetering of strain 横向灵敏系数transverse gage factor 横向灵敏度transverse sensitivity 焊接式应变计weldable strain gage 平衡电桥balanced bridge粘贴式应变计bonded strain gage粘贴箔式应变计bonded foiled gage粘贴丝式应变计bonded wire gage 桥路平衡bridge balancing电容应变计capacitance strain gage 补偿片compensation technique 补偿技术compensation technique 基准电桥reference bridge电阻应变计resistance strain gage 温度自补偿应变计self-temperaturecompensating gage半导体应变计semiconductor strainGage 集流器slip ring应变放大镜strain amplifier疲劳寿命计fatigue life gage电感应变计inductance [strain] gage 光[测]力学Photomechanics 光弹性Photoelasticity光塑性Photoplasticity杨氏条纹Young fringe双折射效应birefrigent effect 等位移线contour of equalDisplacement 暗条纹dark fringe条纹倍增fringe multiplication 干涉条纹interference fringe 等差线Isochromatic等倾线Isoclinic等和线isopachic应力光学定律stress- optic law主应力迹线Isostatic 亮条纹light fringe光程差optical path difference 热光弹性photo-thermo -elasticity 光弹性贴片法photoelastic coatingMethod光弹性夹片法photoelastic sandwichMethod动态光弹性dynamic photo-elasticity 空间滤波spatial filtering空间频率spatial frequency起偏镜Polarizer反射式光弹性仪reflection polariscope残余双折射效应residual birefringentEffect应变条纹值strain fringe value应变光学灵敏度strain-optic sensitivity 应力冻结效应stress freezing effect应力条纹值stress fringe value应力光图stress-optic pattern暂时双折射效应temporary birefringentEffect脉冲全息法pulsed holography透射式光弹性仪transmission polariscope 实时全息干涉法real-time holographicinterfero - metry 网格法grid method全息光弹性法holo-photoelasticity 全息图Hologram全息照相Holograph全息干涉法holographic interferometry 全息云纹法holographic moire technique 全息术Holography全场分析法whole-field analysis散斑干涉法speckle interferometry 散斑Speckle错位散斑干涉法speckle-shearinginterferometry, shearography 散斑图Specklegram白光散斑法white-light speckle method 云纹干涉法moire interferometry [叠栅]云纹moire fringe[叠栅]云纹法moire method 云纹图moire pattern 离面云纹法off-plane moire method 参考栅reference grating试件栅specimen grating分析栅analyzer grating面内云纹法in-plane moire method脆性涂层法brittle-coating method 条带法strip coating method坐标变换transformation ofCoordinates计算结构力学computational structuralmecha-nics加权残量法weighted residual method 有限差分法finite difference method 有限[单]元法finite element method 配点法point collocation里茨法Ritz method广义变分原理generalized variationalPrinciple 最小二乘法least square method胡[海昌]一鹫津原理Hu-Washizu principle赫林格-赖斯纳原理Hellinger-ReissnerPrinciple 修正变分原理modified variationalPrinciple 约束变分原理constrained variationalPrinciple 混合法mixed method杂交法hybrid method边界解法boundary solution method 有限条法finite strip method半解析法semi-analytical method协调元conforming element非协调元non-conforming element混合元mixed element杂交元hybrid element边界元boundary element 强迫边界条件forced boundary condition 自然边界条件natural boundary condition 离散化Discretization离散系统discrete system连续问题continuous problem广义位移generalized displacement 广义载荷generalized load广义应变generalized strain广义应力generalized stress界面变量interface variable 节点node, nodal point[单]元Element角节点corner node边节点mid-side node内节点internal node无节点变量nodeless variable 杆元bar element桁架杆元truss element 梁元beam element二维元two-dimensional element 一维元one-dimensional element 三维元three-dimensional element 轴对称元axisymmetric element 板元plate element壳元shell element厚板元thick plate element三角形元triangular element四边形元quadrilateral element 四面体元tetrahedral element 曲线元curved element二次元quadratic element线性元linear element三次元cubic element四次元quartic element等参[数]元isoparametric element超参数元super-parametric element 亚参数元sub-parametric element节点数可变元variable-number-node element 拉格朗日元Lagrange element拉格朗日族Lagrange family巧凑边点元serendipity element巧凑边点族serendipity family 无限元infinite element单元分析element analysis单元特性element characteristics 刚度矩阵stiffness matrix几何矩阵geometric matrix等效节点力equivalent nodal force 节点位移nodal displacement节点载荷nodal load位移矢量displacement vector载荷矢量load vector质量矩阵mass matrix集总质量矩阵lumped mass matrix相容质量矩阵consistent mass matrix 阻尼矩阵damping matrix瑞利阻尼Rayleigh damping刚度矩阵的组集assembly of stiffnessMatrices载荷矢量的组集consistent mass matrix质量矩阵的组集assembly of mass matrices 单元的组集assembly of elements局部坐标系local coordinate system局部坐标local coordinate面积坐标area coordinates体积坐标volume coordinates曲线坐标curvilinear coordinates 静凝聚static condensation合同变换contragradient transformation 形状函数shape function试探函数trial function检验函数test function权函数weight function样条函数spline function代用函数substitute function降阶积分reduced integration零能模式zero-energy modeP收敛p-convergenceH收敛h-convergence掺混插值blended interpolation等参数映射isoparametric mapping双线性插值bilinear interpolation小块检验patch test非协调模式incompatible mode 节点号node number单元号element number带宽band width带状矩阵banded matrix变带状矩阵profile matrix带宽最小化minimization of band width 波前法frontal method子空间迭代法subspace iteration method 行列式搜索法determinant search method 逐步法step-by-step method 纽马克法Newmark威尔逊法Wilson拟牛顿法quasi-Newton method牛顿-拉弗森法Newton-Raphson method 增量法incremental method初应变initial strain初应力initial stress切线刚度矩阵tangent stiffness matrix 割线刚度矩阵secant stiffness matrix 模态叠加法mode superposition method 平衡迭代equilibrium iteration子结构Substructure子结构法substructure technique 超单元super-element网格生成mesh generation结构分析程序structural analysis program 前处理pre-processing后处理post-processing网格细化mesh refinement应力光顺stress smoothing组合结构composite structure。

弹性力学基础-中英

The actual point of yield is often difficult to identify. A number of techniques are used to locateσy. The tangent method <or knee method> locates the yield strength at the intersection of the elastic slope and the initial portion of the plastic region <not reliably>. The preferred method is the percentage offset method where yield strength is obtained by drawing a line parallel to the initial elastic region data at 0.2% strain <0.002> offset. Where this line intersects the stress-strain curve then becomes known as the 0.2% yield strength.
Plastic means permanent!
Plastic deformation---it is irreversible or permanent.
O
A
B
C
D
E
elastic region
yield strength 屈服应力屈服强度
plastic region
ultimate tensile strength 抗拉强度

弹性力学(双语版)-西安交通大学-3

h32determinationofdisplacementstakethepurebendingofrectangularforexampletoexplainhowtodeterminethedisplacementbythestresscomponents1inthestateoftwodimensionalstressputthestresscomponentputthestresscomponentintothephysicalequation10000????????yym????????15yxxyyxi??????????e?????xyxyxyyyxxe12e1???????????32位移分量的求出以矩形梁的纯弯曲问题为例说明如何由应力分量求出位移分量
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第三章平面问题的直角坐标解答
§3-1 §3-2 §3-3 §3-4 §3-5 §3-6 习题课
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多项式解答位移分量的求出简支梁受均布载荷楔形体受重力和液体压力级数式解答简支梁受任意横向载荷
§3-1 Solution by Polynomials
1.The Stress Function in the form of a Polynomial of the First Degree
Elasticity
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Chapter 3 Two-dimensional Problem in Rectangular Coordinates
§3-1 Solution by Polynomials §3-2 Determination of Displacements §3-3 Bending of a Simply Supported Beam by Uniform Load
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弹性力学

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刘璐璐，能源与动力学院
Chapter 1
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1.1 弹性力学概要
建筑工程
水利
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刘璐璐，能源与动力学院
Chapter 1
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1.1 弹性力学概要航空航天工程
2019/11/5
刘璐璐，能源与动力学院
Chapter 1
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1.1 弹性力学概要船舶机械工程
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1.1.2 研究方法 (Research method ) 弹性体区域内部，考虑静力学、几何学和
物理学三方面的条件，建立三套方程；结合应
平衡微分方程几何方程物理方程
力边界条件和位移边界条件进行求解。
寻求适当的数学方法求出问题的解，从而得到弹性体的应力、形变和位移.
应力，应变位移
•弹性力学的基本方程——偏微分方程的边值问题，求解的方法有解析法和近似解法。
chapter12弹性力学发展史能源与动力学院132015121412弹性力学发展史16001700启蒙时代17001880大师的耕耘18801950体系形成1950学科的发展chapter16001700启蒙时代12弹性力学发展史能源与动力学院1420151214leonardodavinci14521519直升机飞机以弹簧为动力的汽车弹簧驱动的钟表力学是数学科学的天堂因为我们在这里获得数学的成果chapter16001700启蒙时代12弹性力学发展史能源与动力学院1520151214galileogalilei15641642伽利略是第一个把实验引进力学的科学家倡导数学与实验相结合的研究方法是他对近代科学的最重要贡献
1.2 弹性力学发展史
Saint Venant的研究领域主要集中于固体力学和流体力学，特别是在材料力学和弹性力学方面作出很大贡献。重视理论研究成果应用于工程实际。

奥鹏西安交通大学2020年3月课程考试《弹性力学》参考资料答案

西安交通大学课程考试复习资料单选题1.所谓“应力状态”是指( )。

A.平衡微分方程B.几何方程C.物理方程D.几何方程和物理方程答案: B5.用应力分量表示的相容方程等价于( )。

答案: A9.设有平面应力状态,σx=ax+by,σy=cx+dy,τxy=−dx−ay−γx,其中a,b,c,d均为常数,γ为容重。

该应力状态满足平衡微分方程,其体力是( )A.fx=0，fy=0B.fx≠0，fy=0C.fx≠0，fy≠0D.fx=0，fy≠0答案: D10.平面问题的平衡微分方程表述的是( )之间的关系。

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奥鹏西安交通大学2020年3月课程考试《弹性力学》参考资料答案

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弹性力学第4章

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弹性力学

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奥鹏西安交通大学2020年3月课程考试《弹性力学》参考资料答案

ELASTICITY 弹性力学常用专业名词中英文对照修改