英汉双语弹性力学3

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力学中英文辞汇

通类名词力学mechanics牛顿力学Newtonian mechanics经典力学classical mechanics静力学statics运动学kinematics动力学dynamics动理学kinetics宏观力学macroscopic mechanics,macromechanics 细观力学mesomechanics微观力学microscopic mechanics,micromechanics 一般力学general mechanics固体力学solid mechanics流体力学fluid mechanics理论力学theoretical mechanics应用力学applied mechanics工程力学engineering mechanics实验力学experimental mechanics计算力学computational mechanics理性力学rational mechanics物理力学physical mechanics地球动力学geodynamics力force作用点point of action作用线line of action力系system of forces力系的简化reduction of force system 等效力系equivalent force system刚体rigid body力的可传性transmissibility of force平行四边形定则parallelogram rule力三角形force triangle力多边形force polygon零力系null-force system平衡equilibrium力的平衡equilibrium of forces平衡条件equilibrium condition平衡位置equilibrium position平衡态equilibrium state分析力学analytical mechanics拉格朗日乘子Lagrange multiplier拉格朗日[量] Lagrangian拉格朗日括号Lagrange bracket循环坐标cyclic coordinate循环积分cyclic integral哈密顿[量] Hamiltonian哈密顿函数Hamiltonian function正则方程canonical equation正则摄动canonical perturbation正则变换canonical transformation正则变量canonical variable哈密顿原理Hamilton principle作用量积分action integral哈密顿--雅可比方程Hamilton-Jacobi equation 作用--角度变量action-angle variables阿佩尔方程Appell equation劳斯方程Routh equation拉格朗日函数Lagrangian function诺特定理Noether theorem泊松括号poisson bracket边界积分法boundary integral method并矢dyad运动稳定性stability of motion轨道稳定性orbital stability李雅普诺夫函数Lyapunov function渐近稳定性asymptotic stability结构稳定性structural stability久期不稳定性secular instability弗洛凯定理Floquet theorem倾覆力矩capsizing moment自由振动free vibration固有振动natural vibration暂态transient state环境振动ambient vibration反共振anti-resonance衰减attenuation库仑阻尼Coulomb damping同相分量in-phase component非同相分量out-of -phase component超调量overshoot参量[激励]振动parametric vibration模糊振动fuzzy vibration临界转速critical speed of rotation阻尼器damper半峰宽度half-peak width集总参量系统lumped parameter system相平面法phase plane method相轨迹phase trajectory等倾线法isocline method跳跃现象jump phenomenon负阻尼negative damping达芬方程Duffing equation希尔方程Hill equationKBM方法KBM method, Krylov-Bogoliu-bov-Mitropol'skii method 马蒂厄方程Mathieu equation平均法averaging method组合音调combination tone解谐detuning耗散函数dissipative function硬激励hard excitation硬弹簧hard spring, hardening spring谐波平衡法harmonic balance method久期项secular term自激振动self-excited vibration分界线separatrix亚谐波subharmonic软弹簧soft spring ,softening spring软激励soft excitation邓克利公式Dunkerley formula瑞利定理Rayleigh theorem分布参量系统distributed parameter system优势频率dominant frequency模态分析modal analysis固有模态natural mode of vibration同步synchronization超谐波ultraharmonic范德波尔方程van der pol equation频谱frequency spectrum基频fundamental frequencyWKB方法WKB method, Wentzel-Kramers-Brillouin method 缓冲器buffer风激振动aeolian vibration嗡鸣buzz倒谱cepstrum颤动chatter蛇行hunting阻抗匹配impedance matching机械导纳mechanical admittance机械效率mechanical efficiency机械阻抗mechanical impedance随机振动stochastic vibration, random vibration隔振vibration isolation减振vibration reduction应力过冲stress overshoot喘振surge摆振shimmy起伏运动phugoid motion起伏振荡phugoid oscillation驰振galloping陀螺动力学gyrodynamics陀螺摆gyropendulum陀螺平台gyroplatform陀螺力矩gyroscoopic torque陀螺稳定器gyrostabilizer陀螺体gyrostat惯性导航inertial guidance姿态角attitude angle方位角azimuthal angle舒勒周期Schuler period机器人动力学robot dynamics多体系统multibody system多刚体系统multi-rigid-body system机动性maneuverability凯恩方法Kane method转子[系统]动力学rotor dynamics转子[一支承一基础]系统rotor-support-foundation system静平衡static balancing动平衡dynamic balancing静不平衡static unbalance动不平衡dynamic unbalance现场平衡field balancing不平衡unbalance不平衡量unbalance互耦力cross force挠性转子flexible rotor分频进动fractional frequency precession半频进动half frequency precession油膜振荡oil whip转子临界转速rotor critical speed自动定心self-alignment亚临界转速subcritical speed涡动whirl固体力学弹性力学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 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 of Plasticity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[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 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 temperature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 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 birefringent Effect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 interferometry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 structural mechanics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 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流体力学流体动力学fluid dynamics连续介质力学mechanics of continuous media 介质medium流体质点fluid particle无粘性流体nonviscous fluid, inviscid fluid连续介质假设continuous medium hypothesis流体运动学fluid kinematics水静力学hydrostatics液体静力学hydrostatics支配方程governing equation伯努利方程Bernoulli equation伯努利定理Bernonlli theorem毕奥-萨伐尔定律Biot-Savart law欧拉方程Euler equation亥姆霍兹定理Helmholtz theorem开尔文定理Kelvin theorem涡片vortex sheet库塔-茹可夫斯基条件Kutta-Zhoukowski condition 布拉休斯解Blasius solution达朗贝尔佯廖d'Alembert paradox雷诺数Reynolds number施特鲁哈尔数Strouhal number随体导数material derivative不可压缩流体incompressible fluid质量守恒conservation of mass动量守恒conservation of momentum 能量守恒conservation of energy动量方程momentum equation能量方程energy equation控制体积control volume液体静压hydrostatic pressure涡量拟能enstrophy压差differential pressure流[动] flow流线stream line流面stream surface流管stream tube迹线path, path line流场flow field流态flow regime流动参量flow parameter流量flow rate, flow discharge涡旋vortex涡量vorticity涡丝vortex filament涡线vortex line涡面vortex surface涡层vortex layer涡环vortex ring涡对vortex pair涡管vortex tube涡街vortex street卡门涡街Karman vortex street 马蹄涡horseshoe vortex对流涡胞convective cell卷筒涡胞roll cell涡eddy涡粘性eddy viscosity环流circulation环量circulation速度环量velocity circulation偶极子doublet, dipole驻点stagnation point总压[力] total pressure总压头total head静压头static head总焓total enthalpy能量输运energy transport速度剖面velocity profile库埃特流Couette flow单相流single phase flow单组份流single-component flow 均匀流uniform flow非均匀流nonuniform flow二维流two-dimensional flow三维流three-dimensional flow 准定常流quasi-steady flow非定常流unsteady flow, non-steady flow 暂态流transient flow周期流periodic flow振荡流oscillatory flow分层流stratified flow无旋流irrotational flow有旋流rotational flow轴对称流axisymmetric flow不可压缩性incompressibility不可压缩流[动] incompressible flow浮体floating body定倾中心metacenter阻力drag, resistance减阻drag reduction表面力surface force表面张力surface tension毛细[管]作用capillarity来流incoming flow自由流free stream自由流线free stream line外流external flow进口entrance, inlet出口exit, outlet扰动disturbance, perturbation分布distribution传播propagation色散dispersion弥散dispersion附加质量added mass ,associated mass 收缩contraction镜象法image method无量纲参数dimensionless parameter几何相似geometric similarity运动相似kinematic similarity动力相似[性] dynamic similarity平面流plane flow势potential势流potential flow速度势velocity potential复势complex potential复速度complex velocity流函数stream function源source汇sink速度[水]头velocity head拐角流corner flow空泡流cavity flow超空泡supercavity超空泡流supercavity flow空气动力学aerodynamics低速空气动力学low-speed aerodynamics 高速空气动力学high-speed aerodynamics气动热力学aerothermodynamics亚声速流[动] subsonic flow跨声速流[动] transonic flow超声速流[动] supersonic flow锥形流conical flow楔流wedge flow叶栅流cascade flow非平衡流[动] non-equilibrium flow细长体slender body细长度slenderness钝头体bluff body钝体blunt body翼型airfoil翼弦chord薄翼理论thin-airfoil theory构型configuration后缘trailing edge迎角angle of attack失速stall脱体激波detached shock wave波阻wave drag诱导阻力induced drag诱导速度induced velocity临界雷诺数critical Reynolds number 前缘涡leading edge vortex附着涡bound vortex约束涡confined vortex气动中心aerodynamic center气动力aerodynamic force气动噪声aerodynamic noise气动加热aerodynamic heating离解dissociation地面效应ground effect气体动力学gas dynamics稀疏波rarefaction wave热状态方程thermal equation of state喷管Nozzle普朗特-迈耶流Prandtl-Meyer flow瑞利流Rayleigh flow可压缩流[动] compressible flow可压缩流体compressible fluid绝热流adiabatic flow非绝热流diabatic flow未扰动流undisturbed flow等熵流isentropic flow匀熵流homoentropic flow兰金-于戈尼奥条件Rankine-Hugoniot condition 状态方程equation of state量热状态方程caloric equation of state完全气体perfect gas拉瓦尔喷管Laval nozzle马赫角Mach angle马赫锥Mach cone马赫线Mach line马赫数Mach number马赫波Mach wave当地马赫数local Mach number冲击波shock wave激波shock wave正激波normal shock wave斜激波oblique shock wave头波bow wave附体激波attached shock wave激波阵面shock front激波层shock layer压缩波compression wave反射reflection折射refraction散射scattering衍射diffraction绕射diffraction出口压力exit pressure超压[强] over pressure反压back pressure爆炸explosion爆轰detonation缓燃deflagration水动力学hydrodynamics液体动力学hydrodynamics泰勒不稳定性Taylor instability盖斯特纳波Gerstner wave斯托克斯波Stokes wave瑞利数Rayleigh number自由面free surface波速wave speed, wave velocity 波高wave height波列wave train波群wave group波能wave energy表面波surface wave表面张力波capillary wave规则波regular wave不规则波irregular wave浅水波shallow water wave深水波deep water wave重力波gravity wave椭圆余弦波cnoidal wave潮波tidal wave涌波surge wave破碎波breaking wave船波ship wave非线性波nonlinear wave孤立子soliton水动[力]噪声hydrodynamic noise 水击water hammer空化cavitation空化数cavitation number空蚀cavitation damage超空化流supercavitating flow水翼hydrofoil水力学hydraulics洪水波flood wave涟漪ripple消能energy dissipation海洋水动力学marine hydrodynamics谢齐公式Chezy formula欧拉数Euler number弗劳德数Froude number水力半径hydraulic radius水力坡度hvdraulic slope高度水头elevating head水头损失head loss水位water level水跃hydraulic jump含水层aquifer排水drainage排放量discharge壅水曲线back water curve压[强水]头pressure head过水断面flow cross-section明槽流open channel flow孔流orifice flow无压流free surface flow有压流pressure flow缓流subcritical flow急流supercritical flow渐变流gradually varied flow急变流rapidly varied flow临界流critical flow异重流density current, gravity flow堰流weir flow掺气流aerated flow含沙流sediment-laden stream降水曲线dropdown curve沉积物sediment, deposit沉[降堆]积sedimentation, deposition沉降速度settling velocity流动稳定性flow stability不稳定性instability奥尔-索末菲方程Orr-Sommerfeld equation 涡量方程vorticity equation泊肃叶流Poiseuille flow奥辛流Oseen flow剪切流shear flow粘性流[动] viscous flow层流laminar flow分离流separated flow二次流secondary flow近场流near field flow远场流far field flow滞止流stagnation flow尾流wake [flow]回流back flow反流reverse flow射流jet自由射流free jet管流pipe flow, tube flow内流internal flow拟序结构coherent structure猝发过程bursting process表观粘度apparent viscosity运动粘性kinematic viscosity动力粘性dynamic viscosity泊poise厘泊centipoise厘沱centistoke剪切层shear layer次层sublayer流动分离flow separation层流分离laminar separation湍流分离turbulent separation分离点separation point附着点attachment point再附reattachment再层流化relaminarization起动涡starting vortex驻涡standing vortex涡旋破碎vortex breakdown涡旋脱落vortex shedding压[力]降pressure drop压差阻力pressure drag压力能pressure energy型阻profile drag滑移速度slip velocity无滑移条件non-slip condition壁剪应力skin friction, frictional drag 壁剪切速度friction velocity磨擦损失friction loss磨擦因子friction factor耗散dissipation。

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
x
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

(整理)弹性力学专业英语英汉互译词汇

elasticity 弹性力学弹性理论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-integralJ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。

弹性力学第三章

Thus, Eqs.(3.1.2) become
σx 12M y, σ y 0, τ xy τ yx 0. 3 h
3.1.4
Since the moment of inertia of the beam section is I 1 h 12 , Eqs.(3.1.4) may be rewritten as
b
y
For a rectangular plate with its edges parallel to the coordinate axes, the stress function bxy can solve the problem of a rectangular plate in pure shear.
y
For a rectangular plate with its edges parallel to the coordinate axes, the stress function ax 2 can solve the problem of uniform tension (a>0) or uniform compression (a<0) of a rectangular plate in y direction.
• Identify the problem which the selected can solve确定所设定的能解决的问题
弹性力学第三章 3
s
Y.
§3.1 Solution by Polynomials [pɔli\nəumiəlz] §3.1.1 Take a polynomial of the first degree
In this section, we shall use the inverse method to obtain the solutions of some simple plane problems by stress functions in the form of polynomials, assuming that there are no body forces acting, i.e.,X=Y=0

《弹性力学与有限元法(双语课)》教学经验浅谈

《弹性力学与有限元法（双语课）》教学经验浅谈建筑工程学院沈新普.引言2005年土木工程02级的本科生的《弹性力学与有限元法》采用了中英双语教学，这门课是土木工程专业02级学生的考查课。

施行的教学方式是：《弹性力学》部分采用中文教材，讲课过程中仅介绍主要的专业术语的英文词汇；《有限元》部分采用英文教材，该教材是从美国科罗拉多大学航空系Fellipa教授撰写的有限元初步（《Introduction to Finite Element Method》）讲义中选择编辑而成的. 讲课时教师结合英文讲义用中文讲解课程内容，多媒体显示为英文。

教学目的是：使学生在学习专业知识的同时，学到必要的专业英语，争取通过该课程的学习，使学生达到基本读懂本专业方向的英文科技文献的水平。

更深层次的教学目的是使学生按照西方人的思维方式领会有限元的哲学思想。

有限元英文教材的原作者Fellipa教授在国际上很有威望。

他曾于1966年获得过有限元研究的博士学位，近40年来一直从事有限元理论与应用研究，他的有限元讲义全书写得通俗易懂，该教材是从Fellipa教授2004年正在使用的有限元课程的讲义中选择编辑的精华部分。

因此该课程讲义是与国际同类教学处于同步水平的。

该课程主讲教师沈新普曾在清华大学工程力学系担任有限元课程的教学工作，还曾在英国Sheffield大学工作两年，在欧洲的科研院所工作时间有6年之久，英语能力和专业能力均符合本课程要求，还曾于2000年和2001年两次主讲过东北大学《材料力学（90学时）》双语课程。

.学生的反应：在本课程开课的第五周，主讲教师对学生进行了一次随堂测试，同时进行了民意测验，检查教学效果以及学生对双语教学的看法。

考试结果的成绩统计分布情况见表1，民意测验统计分布情况结果见表2。

表1期中随堂测验成绩情况表 2 双语课民意测验结果（随堂进行，108人答卷）从表1的考试成绩看，情况基本正常，符合一般的教学规律。

chapter 3 Basics of fluid flow(revision)

大连理工大学Dalian University of Technology Fluid mechanics Chapter 3 Basics of Fluid Flow2.1 Lagrangian and Eulerian descriptions of fluid motionLagrangian descriptionLagrangian description of fluid flow tracks the position and velocity of individual particles.The path of a fluid particle is given by the vector r (t), and can be expressed in terms Cartesian coordinates as()()()()r t x t i y t j z t k=++Velocity field:(,,,)(,,,)(,,,)x a b c t u t y a b c t v t z a b c t w t ∂⎧=⎪∂⎪∂⎪=⎨∂⎪∂⎪=⎪∂⎩acceleration field :222222(,,,)(,,,)(,,,)x a b c t u t y a b c t v t z a b c t w t ⎧∂=⎪∂⎪∂⎪=⎨∂⎪⎪∂=⎪∂⎩大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow2.1 Lagrangian and Eulerian Descriptions offluid motionEulerian descriptionsA flow domain or control volume is defined by which fluid flows in and out.This method to describe fluid motion is to imagine an array of “windows”in the flow field, and have information for the velocity of fluid particles that pass each window for all timeVelocity field:(,,,)(,,,)(,,,)u u x y z t v v x y z t w w x y z t =⎧⎪=⎨⎪=⎩大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.3 Streamlines, pathlines and streaklinesStreamlinesA Streamline is a curve that is everywhere tangent to the instantaneous local velocity vector.Consider an arc lengthstreamline must be parallel to the local velocity vectorGeometric arguments results in the equation for a streamlinedr dxi dyj dzk =++V ui vj wk=++dr dx dy dz V u v w ===大连理工大学Dalian University of Technologystreamlines大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowPathlinesA Pathline is the actual path traveled by an individual fluid particle over some time period.Same as the fluid particle's material position vectorParticle location at time t:Particle Image Velocimetry (PIV) is a modern experimental technique to measure velocity field over a plane in the flow field.()()()(),,particleparticle particle xt y t z t starttstart t x x Vdt=+∫大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowExample 3.1A velocity field is given by where V 0and l areconstant, at what location in the flow field is the speed equal to V 0? Make a sketch of the velocity field in the first quadrant(x>0, y>0) by drawing arrows representing the fluid velocity at representative locations()0()V V l xi yj =−Solution:The fluid speed V, is()()1/21/2222220VV u v w x y l=++=+The speed is V=V 0at any location on the circle of radius l centered centered at the origin()1/222x y l+=The direction of the fluid velocity00tan V y l v y u V x l xθ−−===理工大学Dalian University of Technology)Stream function大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowExample 3.3Water flowing from the oscillating slit shown in figure produces a velocity field given bywhere u 0, v 0and ωare constants, Thus, the y component ofvelocity remains constant (v =v 0) and the x components of velocity at y=0 coincides with the velocity of the oscillating sprinkler head [u=u 0sin(wt) at y=0].()000sin V u t y v i v jω=−+⎡⎤⎣⎦(a ) determine the streamline that passes the through the origin at t=0; at t=π/2ω.(b) Determine the pathline of the particle that was at the origin at t=0; at t=π/2ω.(c) Discuss the shape of the streakline that pass through the origin大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowExample 3.3Solution: (streamline)The streamline are given by the solution of()000sin v dy vdx u u t y v ω==−⎡⎤⎣⎦In which the variables can be separated and the equation integrated to give()000sin u t y v dy v dxω−=⎡⎤⎣⎦∫∫()0000cos y u v t v x Cv ωω⎡⎤⎛⎞−=+⎢⎥⎜⎟⎝⎠⎣⎦x=0,y=0,t=0----------Æ00C u v ω=00cos 1u y x v ωω⎡⎤⎛⎞=−⎢⎥⎜⎟⎝⎠⎣⎦x=0,y=0,t=π/2ω----------ÆC=00cos 2u y x v πωω⎛⎞=−⎜⎟⎝⎠大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowExample 3.31020sin C x u t C v ω⎡⎤⎛⎞=−+⎢⎥⎜⎟⎝⎠⎣⎦Solution: (pathline)The pathline of a particle can beobtained from the velocity field and the definition of the velocity ()000sin dx dyu t y v and v dtdtω=−=⎡⎤⎣⎦The y equation can be integrated to givethe y coordinate of the pathline as 01y v t C =+0110000sin sin v t C C dxu t u dt v v ωω⎡⎤⎛⎞⎛⎞+=−=−⎢⎥⎜⎟⎜⎟⎝⎠⎝⎠⎣⎦X=y=0,t=0----ÆC 1=C 2=000x and y v t==X=y=0,t=π/2ω----ÆC 1=-πv 0/2ωC 2=-πu 0/2ω0022x u t and y v t ππωω⎛⎞⎛⎞=−=−⎜⎟⎜⎟⎝⎠⎝⎠0v y xu =大连理工大学Dalian University of TechnologySolution: (streakline)大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.4 One-, two, and three-dimensional flowsGenerally, a fluid flow is a rather complex three-dimensional, time-dependent phenomenon.It is possible to make simplify assumptions that allow a much easier understanding of the problem without sacrificing needed accuracy. One of these simplifications involves approximating a real flow as a simpler one-or two-dimensional flow.three-dimensional flow(,,,)V V x y z t ui vj wk==++大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowTwo-dimensional flowIn many situations one of the velocity components may be small (in some sense) relative to the two othercomponents.In situations of this kind it may be reasonable to neglect the smaller component and assume two dimensional flow. (,,)V V x y t ui vj==+Stream filament: the fluid in the stream tube大连理工大学Dalian University of Technologyfinite flow cross大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.5 Some fundamental conception for fluid flow Uniform flow: is one in which the velocity is the same on both magnitude and direction at a given instant at every point in the flow.This strict definition of uniform flow can have little meaning for the flow a real fluid where the velocity varies acrosssection. But when the size and shape of cross section areconstant along the length of channel under consideration. We say the flow is uniform.0V n∂=∂acceleration 大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.5 Some fundamental conception for fluid flow Non-uniform flow:is one in which the velocity is variable at a given instant at every point in the flow.the flow cross section is curved surface.The size and shape of flow cross section varies along the direction of fluid flow The mean velocity is variable along the direction of fluid flow大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.5 Some fundamental conception for fluid flow Gradually varied flow:i s one in which the curvature radius of streamline is large.Since the streamlines is almost parallel, the angle between the streamlines is small. With small remove acceleration and the inertia force can be neglected.大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.5 Some fundamental conception for fluid flow Rapidly varied flowThe angle between the streamlines is large.With larger curvature radius With larger remove acceleration and the inertia force can not be neglected.大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.6 Flow rate and mean velocityFlow rate: the quantity of fluid flowing per unit time across any section.Volume flow rate (discharge) : SI unit, cubic meters per second (m 3/s)Mass flow rate: SI unit, kilogram per second (kg/s) Weight flow rate: SI unit, kilonewtons per second (kN/s)The volume flow rate passing through the element of area dA is Element Mean velocity ()cos (cos )'dQ u dA u dA u dA udA θθ==== i dA’is projection of dA on the plane normalto the direction of u. 大连理工大学Dalian University of Technology Fluid mechanics Chapter 3 Basics of Fluid Flow3.6 Flow rate and mean velocityMass flow rate and the weight flow rateThe flow rate in a real fluidmQ ρ= G Q γ=A A Q dQ udA AV===∫∫A A m dQ udA AV Q ρρρρ====∫∫ AG gmudA AV Q γγγ====∫ u : is the time mean velocity throughan infinitesimal area dA.V: is mean velocity over the entire sectional area A大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.7 Equation of continuityFluid system and control volumeFluid system: a continuous mass of fluid that always contains the same fluid particle.¾The mass of a system is constant¾The shape of the system, and so the boundaries, may change with time.¾The size and shape of system is entirely optional.大连理工大学Dalian University of TechnologyCV character of this term大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowFluid flow from the fire extinguisher tank. Discuss the differences between dB sys /dt and dB cv /dt if B represent mass.Example 3.4Solution:0sys sys sys d dV dB m dt dt dtρ⎛⎞⎜⎟⎜⎟∂⎝⎠===∫0CVCV CV d dV dB m dt dt dtρ⎛⎞⎜⎟∂⎝⎠==<∫大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.7 Equation of continuityConsider a steam tube shown in figureNo fluid can leave or enter the stream tube except at the ends.The fixed volume between the two end sections is a control volume, of volume V.out in CV cv c s v ys B B DB B t t t Dt ∂∂∂=+−∂∂∂CV CV CV dm d V V t dt t ρρ∂==∂∂222222out cvdB A V dt A V dt dt ρρ==111111in cv dB AV dt AV dt dt ρρ==111222CV V AV A V tρρρ∂=−∂111222111222AV A V m AV A V gm G ρργγ===== For steady flowThe mass flow rate in isSo the mass is accumulating in the tank atthe rate of 14.5 kg/s大连理工大学Dalian University of Technology Fluid mechanics Chapter 3 Basics of Fluid FlowA 10-cm jet of water issues from a 1-m diameter tank, as shown. Assume that the velocity in the jet is (2gh)1/2m/s. How long it take for the water surface in the tank to drop from h 0=2m to h f =0.5m?Example 3.6Solution:We will let the control surfacesurround the volume of liquidwithin the tank at all times, so thatthe control volume will decrease insize as time passes.大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.8 Energy equation for steady flow ofincompressible fluids along a streamlineConsider a stream tube, two cross sectional areas d A 1,d A 2at right angles to the streamline, elevation of d A 1,d A 2are Z 1and Z 2, Velocity of the fluid are u 1, u 2in section 1 and section 2,respectively. And the pressure is p 1 and p 2Assumption:The flow is steady;The fluid is isothermal,incompressibleand inviscid.Apply work energy theoremto the fluid system within thestream tube between the twoends.大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.8 Energy equation for steady flow ofincompressible fluids along a streamlineIncrease of mechanical energyThe increase of mechanical energy can be obtained by comparing the spaces that the fluid system occupy before and after dt.Before dt, the space occupied by fluid is 1-1’+1’-2After dt, the space occupied by fluid is 1’-2+2-2’ the volume 1’-2 is the same before and after dt , so thepotential energy and the kinetic energy is invariable.Hence, The increase of the mechanicalenergy of the fluid system is onlyassociated with the increase due tothe new volume occupied 2-2’anddecrease duo to the volume 1-1’left inthe fluid system.大连理工大学Dalian University of Technology Fluid mechanics Chapter 3 Basics of Fluid Flow3.8 Energy equation for steady flow ofincompressible fluids along a streamlineThe volume of 1-1’,2-2’is dQdtMass is Increase of kinetic energy:Increase of potential energy Applying work energy theoremdQdt dQdt gγρ=22222212112222u u u u dQdt mu dQdt g g g γγ⎛⎞⎛⎞−==−⎜⎟⎜⎟⎝⎠⎝⎠()21dQdt Z Z γ−()()2221122122u u p p dQdt dQdt dQdt Z Z g g γγ⎛⎞−=−+−⎜⎟⎝⎠2211221222p u p u Z Z g gγγ++=++Bernoulli equation大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowPitot TubeStatic pressureIn a flowing fluid, we call the fluid pressure p the static pressure because it is the pressure that an instrument would measure if it were static with respect to the fluid, i.e., moving with the fluid. We measure it with piezometer tubes and other devices that attempt to minimize disturbance to the flow. To measure the static pressure in a flow field, we use a static tube. in this device the pressure is transmitted to a gage or manometer through piezometric holes that are evenly space around the circumference of the tube.Holes大连理工大学Dalian University of Technologyobtainable along a given streamline.大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowPitot TubeStatic headTotal head Small holes on bothsides of outer tube Stagnation point Writing Bernoulli equation alongthe streamline ab22a b p p u g γγ=+2a b p p u g γ−=a b v p p h γ−=2vu gh ϕ=Coefficient of instrument: because rarely are the piezometer holes located in precisely the correct position toindicate the true value of p /γ大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.9 Pressure in fluid flowFor the uniform flow, the inertial force disappears, now let us consider how pressure varies over a cross section of flow in a uniform conduit. The figure shows a small prism of the flowing fluid.Forces parallel to the direction of motion, namely the pressure and friction forces and the weight component, must balance out if the flow is steady and parallel.N N The projection of friction forces tothe axis N-N is zero, so the forcesalong N-N, namely pressure andweight component, must balance.12cos 0p A Ay p A γα+−=1212p p Z Z γγ+=+大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.9 Pressure in fluid flowThe pressure variation over a cross section perpendicular to the streamline show that in any plane perpendicular to the direction of parallel and steady flow the pressure varies according to thehydrostatic law. The average pressure is then the pressure at the centroid of such an area.In other words, on a horizontal axis through the conduit andperpendicular to its centerline the pressure is everywhere the same. Since the velocity is higher near the center than near the walls, it follows that the local energy head is also near the center.The height of liquid column are the sameThe streamline is almost parallel forthe gradually varied flow, so it can bedealt with as uniform flow大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowExample 3.7Fluid (water) )flowing in a inclined pipe, the pressure of point A measured by U-tube manometer using mercury is shown in figure. Determine the pressure of point ASolution:Since the point A and point B locate in the same cross section,the hydrostatic law can be satisfied in the cross section.'0.60.3A p γγ+=20.3980713.60.6980734.23/A p kN m =××−×=Note that although point E , D and A locateon the same horizontal plane, the pressureof point E and D are not equal to point A.1Ap ⎜⎝∫A ∫2A大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.10 Energy equation for steady flow of incompressible(b) Kinetic energy2323322222Q A A Au u V dQ dA u dA V dA Q g g g g g γγαγγαγ====∫∫∫∫3333A A A u dA u dA V AV dAα==∫∫∫Kinetic energycorrection factor V: mean velocity in the cross section23311111222A A u dA V V Q g g dA g αγγαγ==∫∫23322222222A A u dA V V Qg g dA g αγγαγ==∫∫大连理工大学Dalian University of Technology Fluid mechanics Chapter 3 Basics of Fluid Flow3.10 Energy equation for steady flow of incompressible(c) Energy loss'1212l l Qh dQ h dQγγ−−=∫Represents the negative work done by viscousfriction per unit time when the fluid across thesection flows from section 1 to section 222111222121222l p V p V Z Z h g g ααγγ−⎛⎞⎛⎞++=+++⎜⎟⎜⎟⎝⎠⎝⎠p 1, Z 1: pressure and elevation for the same point in cross section 1p 2, Z 2: pressure and elevation for the same point in cross section 2Both are absoluteor gage pressure2g大连理工大学Dalian University of TechnologyMass conservation123Q Q Q =+22111222121222l p V p V Z Z h ggααγγ−++=+++22333111131322l p V p V Z Z h ggααγγ−++=+++Generally we can write an energy equation that will fulfill conditions 4and 5. if there are two unknowns in the equation then we must also use the continuity equation.Example 3.8Solution:(1)Choose section 1-1 and 2-2 as flow cross section=2g大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowExample 3.8Z 1=4m, Z 2=0, p 1/γ=0, p 2/γ=021102V gα≈222222V V ggαα=21232l V h g−=2240000322V V g gα++=+++2 4.43/V g m s==()233.140.14.430.0348/4Q VA m s×==×=Similarly: p M =4.904kN/m 2大连理工大学Dalian University of Technology大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowVenturi meter1122(1)Write the Bernoulli equationbetween section (1) and (2), we have2211220022p V p V g gγγ++=++22122122p p V V h g gγγ−=−=∆(2) According to the continuity equation, we have22112V d V d ⎛⎞=⎜⎟⎝⎠422111222d V V h d g g⎛⎞−=∆⎜⎟⎝⎠141221g h V d d ∆=⎛⎞−⎜⎟⎝⎠22111412112441g h Q V d d d d ππ∆==⎛⎞−⎜⎟⎝⎠Which can be measured by experimental method大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.12 hydraulic grade line and energy lineDefinitionHydraulic grade line: if we connected a series of piezometers all along the pipe, the liquid would rise in them to various levels along what is called the hydraulic grade line (HGL) (piezometric line). 22p V H Z gγ=++Elevation headvelocity headPiezometric headTotal engy headStatic pressure headThe z portion of the piezometric head represents the elevation of point A. the vertical distance from point A to the corresponding point on the HGL represent p/γin the flow at point A 大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.12 hydraulic grade line and energy lineEnergy line: is above the HGL by a distance V 2/2g. That is the linedrawn through the pitot-tube liquid surfaces.For the flow of an ideal fluid, the energy line is horizontal. For a real fluid, the energy line must slope downward in the direction of flow because of head loss due to fluid friction大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.12 hydraulic grade line and energy lineHow to draw hydraulic grade lines and energy lines(1) By definition, the EGL is positioned above the HGL by an amount v 2/2g. Thus if the velocity is zero, as in a lake or reservoir , the HGL and EGL will coincide.(2)Head loss for flow in a pipe or channel always means that the EGL will slope downward in the direction of flow, the only exception to this rule occurs when a pump supplies energy to the flow, then an abrupt rise in the EGL (and the HGL) occurs from the upstream side to the downstream side of the pump.Energy addeda大连理工大学Dalian University of Technologygradual expansion such as at the outlet.Energy removed Gradual expansion大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.12 hydraulic grade line and energy lineHow to draw hydraulic grade lines and energy lines(4) if the outlet to a reservoir is an abrupt expansion, all the kinetic energy is lost. Thus the EGL drops an amount v 2/2g at the outlet. (5) If a flow passagechanges diameter,such as in a nozzle or by means of a change in pipe size, the velocity therein will also change, hence, the distance between the EGLand HGL will change, and the slope on the EGL will change.大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.12 hydraulic grade line and energy lineHow to draw hydraulic grade lines and energy lines(6) For steady flow in a pipe that has uniform physicalcharacteristics (diameter, roughness, shape, and so on) along its length, the head loss per unit length will be constant. thus the slope of the EGL and HGL will be constant along the length of pipe.(7)If the HGL fall below the pipe, then p/γis negative, indicating subatmospheric pressure.And so on, energy line:1-a-b-b0-c Hydraulic grade line: 1-a’-b’-bo’-c’大连理工大学Dalian University of Technology11221222l p Z p Z p γγ−++=+++But for the gases flow, we must consider the difference ofatmospheric pressure when the specific weight of gases is not equal to that of atmosphere, specially, in the case which the elevation difference is very large.大连理工大学Dalian University of Technology'11a p p p =+()'2221a a p p p Z Z γ=−+−Pressure difference221211221212()22a a a l V V p p Z p p Z Z Z p ρργγγ−+++=+−−+++γa : the specific weight of atmosphere2212121212()()22a l V V p Z Z p p ρργγ−++−−=++Static pressure Kinetic pressure Elevation pressure21()()s a p p Z Z γγ=+−−22q V p p ρ=+221()()2z a Vp p Z Z ργγ=++−−Potential pressure Stagnation pressure Total pressure大连理工大学Dalian University of Technology(2)if the density of the gas ρ=0.8kg/m . (ρa =1.3kg/m )大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowExample 3.10solution(1): writing energy equationbetween the section A and C, Because the density of gas ρ=ρa =1.2kg/m 3, thus22C A lA C V p p ρ−=+22129.8 1.29 1.222C C V V ×=×+××2117.6/12 4.43/C V m s=×=2314.430.0348/4Q d m sπ=×××=The pressure of point B: Writing energy equation between the section B and C2222B lB CV V p p ρρ−+=+22219 1.221.2 1.2222B V V V p ××××=×++224.5 1.252.92/2B V p N m =××=大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowExample 3.10(2): if the density of the gas ρ=0.8kg/m 3, writing energyequation between the section A and C,2()()2C A a A C lA C V p Z Z p ργγ−+−−=+22129.8(1.20.8)9.8400.890.822C C V V ×+−××=×+××8.28/B V m s=30.065/Q m s=Τhe pressure of point B22190.8(1.20.8)9.82045/22B B V p N m =×××−−××=z p ρ=−Zero pressure lineD Unsteady flow∑The rate of change oraccumulation of momentum within the fixed control volumeThe rates at which momentum leaves the control volumeThe resultant force acting on a fluid mass is equal to the rate of change of momentum of the fluid mass大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.15 The momentum principleIn the case of steady flow, conditions withinthe control volume do not change, soIf we select a control volume so that the control surface is normal to the velocity where it cuts the flow, and lets us specify that the velocity is constant where it cuts across the control surface.()()out in cvcvd d d mV mV F tdt=−∑()11111d d m dt dtmVm V V == ()22222d d m dt dt mVm V V ==Steady flow2211222111F V m V Q V V mQ ρρ=−=−∑大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid Flow3.15 The momentum principleSince the flow is steady, from continuity, we have121122mm m Q Q ρρ==== According to the vector relation21out inV V V V V ∆=−=−()()()21F V V V V mQ Q ρρ=∆=∆=−∑ The direction of must be the same as that of the velocity change Represents the vectorial summation of all forces acting on the fluid mass in the control volume, including:•Gravity, shear forces•Pressure forces including those exerted by fluid surrounding the fluid mass under consideration as well as the pressure forces exerted by the solid boundaries in contact with the fluid massF ∑F ∑ρAV(2(2V Qβyx大连理工大学Dalian University of TechnologyFluid mechanics Chapter 3 Basics of Fluid FlowExample 3.12Energy equation: in free-surface flow such as this where the streamlines are parallel, the water surface is coincident with the hydraulic grade line.221122121222l p V p V Z Z hg g γγ−++=+++22122129.8129.81V V +=+××Continuity equation:122313V V ×=×1 2.56/V m s=2 5.11/V m s=2112215.34/Q AV A V m s===4) Free-body diagram of the fluid within the control volume5) Applying momentum equation()1221x F F F Q V V ρ−−=−4.91x F kN =。

力学双语

3-2 Newtonian Mechanics
★ The relationship between a force and the
acceleration it causes was first understood by Isaac Newton
Newton published his book 《The Mathematical. Principles of Natural Philosophy》in 1687. ★ The study of that relation is called Newtonian Mechanics
3-4 Force
★ Define the unit of force in terms of the
acceleration that a force gives to a standard reference body (a mass of 1 kg). ★ A force (vector) mass acceleration force is measured by 1kg 1 m/s2 1N acceleration it 1kg 2 m/s2 2N produces.
magnitude; direction
1kg
a m/s2
aN
★Principle of superposition for forces
When two or more forces act on a body, a net force or resultant force can be found. The net force has the same effect on the body as all the individual forces together.

弹性力学第三章

• Select satisfying the compatibility equation
设定，并满足相容方程 4 =0 (2.12.11)
• find the stress components by 由下式求出应力分量
x=2/y2-Xx y= 2/x2-Yy xy=-2/xy
(2.12.10)
compression (c<0) of a rectangular plate in x
direction. P41 Fig.3.1.1(c)
弹性力学第三章
8
C. =cy2 ,
• 满足相容方程 4 =0
X=0, Y=0
• 由下式求出应力分量 x=2/y2= 2c y= 2/x2=0 xy=-2/xy=0
the coordinate axes, find the surface force
components by
(lx+m yx)s=X
(my+lxy)s =Y
• the stress function =cy2 can solve the problem
of uniform tension (c>0) or uniform
x=2/y2=0 y= 2/x2=2a xy=-2/xy=0
• 对于具有平行于坐标轴的边缘的矩形板，求出
其表面力分量
(lx+m yx)s=X
(my+lxy)s =Y
• 对和坐标轴平行的矩形板求出面力分量知
=ax2 能解决矩形板y向受均匀拉力(a>0)或均
匀压力(a<0)的问题。P41 Fig.3.1.1(a)
of uniform tension (a>0) or uniform

弹性力学翻译

弹性力学 p180—181 土木0903 潘雨婷The stress components and their differential increments are shown in the figure,. The bodyforces component in radial direction is denoted by k r and that in z direction is still denoted by Z .Of course, they are functions of r and z only .Summing up all the forces in the r direction at the center of the element, we have theequilibrium equation,Performing the multiplication, dividing through by drdz rd θ,and then neglecting the infinitesimal terms, we obtain0=+-+∂∂+∂∂r e r zr r K rz r σστσ ( Similarly,we have the equilibrium equation in z direction asFor which we obtain0=++∂∂+∂∂Z rr z rz rz z ττσ ( Equations ( are the differential equations of equilibrium for a spatialaxisymmetric problem in cylindrical coordinates.Besides the normal strain components θεε,r 和z ε there is only one shearing straincomponent zr γ,since ez γγand re banish because of symmetry .The displacement component in rdirection is denoted by u ，and the one in z direction is still denoted by w .we have .0=θuReferring to Eqs （（ and （ can write the geometrical equations for a spatial axisymmetric problemasrw z u z w r u r u r zr z r r r ∂∂+∂∂=∂∂==∂∂=γεεεθ,,, （ Similarly ,referring to Eqs （ we can write the physical equations as:()[]()[]()[]()⎪⎪⎪⎪⎭⎪⎪⎪⎪⎬⎫+==+-=+-=+-=.121,1,1,1zr zr zr r z z r r Z R r E G EE E τμτγσσμσεσσμσεσσμσεθθθθ （ Adding up the first three of Eqs （,we obtain,21θμEe -=（ ,zw r u r u e r r z r ∂∂++∂∂=++=εεεμ （ .z r σσσθθ++= （ Besides , referring to Eqs （ can express the stress components in terms of strain components as⎪⎪⎪⎪⎪⎭⎪⎪⎪⎪⎪⎬⎫+=⎪⎪⎭⎫ ⎝⎛+-+=⎪⎪⎭⎫ ⎝⎛+-+=⎪⎪⎭⎫ ⎝⎛+-+=.21,211,211,211zr zr z z r r E e E e E e E γμτεμμμσεμμμσεμμμσθθ （ When the geometrical shape of the body concerned,the condition of constraint and the externalloads ate all symmetrical with respect to any plane passing through a certain point, the body is saidto be in a condition of point symmetry or spherical symmetry.In this case,the stresses, strains anddisplacements will be functions of a single variable R, the distance from the point of symmetry.Evidently such a condition exists only in solid or hollow spheres.p180—181 土木0903 潘雨婷弹性力学径向方向的体力组件用Kr 表示在z 方向仍然用Z 表示。

力学名词中英对照

[推荐][名词委审定]汉英力学名词(1993)[翻译与翻译辅助工具] [回复] [引用回复] [表格型] [跟帖] [转发到Blog] [关闭] [浏览930 次] 用户名: westbankBZ反应||Belousov-Zhabotinski reaction, BZ reactionFPU问题||Fermi-Pasta-Ulam problem, FPU problemKBM方法||KBM method, Krylov-Bogoliubov-Mitropolskii methodKS[动态]熵||Kolmogorov-Sinai entropy, KS entropyKdV 方程||KdV equationU形管||U-tubeWKB方法||WKB method, Wentzel-Kramers-Brillouin method[彻]体力||body force[单]元||element[第二类]拉格朗日方程||Lagrange equation [of the second kind][叠栅]云纹||moiréfringe; 物理学称“叠栅条纹”。

[叠栅]云纹法||moirémethod[抗]剪切角||angle of shear resistance[可]变形体||deformable body[钱]币状裂纹||penny-shape crack[映]象||image[圆]筒||cylinder[圆]柱壳||cylindrical shell[转]轴||shaft[转动]瞬心||instantaneous center [of rotation][转动]瞬轴||instantaneous axis [of rotation][状]态变量||state variable[状]态空间||state space[自]适应网格||[self-]adaptive meshＣ0连续问题||C0-continuous problemＣ1连续问题||C1-continuous problemＣＦＬ条件||Courant-Friedrichs-Lewy condition, CFL conditionＨＲＲ场||Hutchinson-Rice-Rosengren fieldＪ积分||J-integralＪ阻力曲线||J-resistance curveＫＡＭ定理||Kolgomorov-Arnol'd-Moser theorem, KAM theoremＫＡＭ环面||KAM torusｈ收敛||h-convergenceｐ收敛||p-convergenceπ定理||Buckingham theorem, pi theorem阿尔曼西应变||Almansis strain阿尔文波||Alfven wave阿基米德原理||Archimedes principle阿诺德舌[头]||Arnol'd tongue阿佩尔方程||Appel equation阿特伍德机||Atwood machine埃克曼边界层||Ekman boundary layer埃克曼流||Ekman flow埃克曼数||Ekman number埃克特数||Eckert number埃农吸引子||Henon attractor艾里应力函数||Airy stress function鞍点||saddle [point]鞍结分岔||saddle-node bifurcation安定[性]理论||shake-down theory安全寿命||safe life安全系数||safety factor安全裕度||safety margin暗条纹||dark fringe奥尔-索末菲方程||Orr-Sommerfeld equation奥辛流||Oseen flow奥伊洛特模型||Oldroyd model八面体剪应变||octohedral shear strain八面体剪应力||octohedral shear stress八面体剪应力理论||octohedral shear stress theory巴塞特力||Basset force白光散斑法||white-light speckle method摆||pendulum摆振||shimmy板||plate板块法||panel method板元||plate element半导体应变计||semiconductor strain gage半峰宽度||half-peak width半解析法||semi-analytical method半逆解法||semi-inverse method半频进动||half frequency precession半向同性张量||hemitropic tensor半隐格式||semi-implicit scheme薄壁杆||thin-walled bar薄壁梁||thin-walled beam薄壁筒||thin-walled cylinder薄膜比拟||membrane analogy薄翼理论||thin-airfoil theory保单调差分格式||monotonicity preserving difference scheme 保守力||conservative force保守系||conservative system爆发||blow up爆高||height of burst爆轰||detonation; 又称“爆震”。

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.
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elastic region
yield strength 屈服应力屈服强度
plastic region
ultimate tensile strength 抗拉强度

材料力学双语教学学习资料(英汉对照)

材料力学双语教学学习资料第一章绪论Chapter 1 Introduction§1-1 材料力学的任务The Tasks of Mechanics of Materials1＊. 材料力学: Mechanics of Materials2. 构件: Structural Members3. 变形: Deformation4＊. 强度: Strength5＊. 刚度: Rigidity6＊. 稳定性: Stability§1-2 变形固体的基本假设Fundamental Assumptions of SolidDeformation Bodies1. 连续性假设: Continuity2. 均匀性假设: Homogeneity3. 各向同性假设: Isotropy§1.3 外力及其分类External Forces and Classification1. 分布力: Distributed Force2. 集中力: Point Force3. 静载荷: Static Load4. 动载荷: Dynamic Load§1.4 内力、截面法和应力的概念Concepts of Internal Forces，Method ofSection and Stress1＊. 内力: Internal Force2＊. 截面法: Method of Section3. 截面法的三个步骤：截开，代替，平衡Three steps of method of section: cut off, substitute , and equilibrium.4＊. 应力: Stress5. 平均应力：Average stress6. 应力（全应力）：Whole stress（sum stress）7＊. 正应力: Normal Stress8＊. 剪应力(切应力)：Shearing Stress§1.5 变形与应变Deformation and Strain1．线应变: Strain2．剪应变: Shearing Strain§1.6 杆件变形的基本形式Basic Types of Deformations of Rods1＊. 拉伸或压缩: Tension or Compression2＊. 剪切: Shear3＊. 扭转: Torsion4＊. 弯曲: Bending第二章拉伸、压缩与剪切Chapter 2 Tension，Compression andShear§2.1 轴向拉伸与压缩的概念和实例The Concept and Examples of AxialTension and Compression1. 拉杆: Tensile Rod2. 压杆: Compressive Rod3. 受力特点：外力合力的作用线与杆轴线重合Characteristic of the External Forces: The acting line of the resultant of external forces is coincided with the axis of the rod.4. 变形特点：杆沿轴向伸长或缩短Characteristic of Deformation: Rod will elongate or contract along the axis of the rod.§2.2 轴向拉伸或压缩时横截面上的内力和应力Internal Force and Stress of Axial Tension or Compression on the Cross Section1＊. 横截面: Cross Section2＊. 轴力: Normal Force3＊. 轴力图: Diagram of Normal Force§2.3 直杆轴向拉伸或压缩时斜截面上的应力Stress of Axial Tension or Compressionon the Skew Section1. 斜截面: Skew Section2.ασσα2cos = αστα2s i n 2=§2.4 材料在拉伸时的力学性能Mechanical Properties of Materialswith Tensile Load1. 标准试件: Specimen2. 低碳钢(C ≤0.3%): Low Carbon Steel3. 弹性阶段:Elastic Region4. 屈服阶段:Yielding Stage5. 强化阶段:Hardening Stage6. 颈缩阶段: Necking Stage 7＊.σp ----比例极限: Proportional Limit 8＊.σe ----弹性极限: Elastic Limit 9＊.σs ----屈服极限: Yielding Stress 10＊.σb ----强度极限: Ultimate Stress 11. 延伸率: Percent Elongation12. 断面收缩率: Percent Reduction of Area 13. 塑性材料: Ductile Materials 14. 脆性材料: Brittle Materials 15. 铸铁:Cast iron§2.7 失效、安全系数和强度计算 Failure, Safety factor and Strengthcalculation1＊. 许用应力: Allowable Stress 2. 安全系数: Safety Factor 3＊. 强度条件: Strength Condition][max σσ≤=AF N4＊. 强度校核: Check strength][max σσ≤5＊. 截面设计: Section design][σNF A ≥6＊. 确定许可载荷:Determine allowable load][σA F N ≤§2.8 轴向拉伸或压缩时的变形 Deformation in Axial Tension orCompression1. 弹性变形: Elastic Deformation2. 塑性变形: Plastic Deformation3. 纵向应变: Longitudinal Strainll l l l -=∆=1ε 4. 横向应变: Lateral Straindd d d d -=∆=''ε5．线弹性变形:Linear Elastic Deformation6.泊松比:Poisson’s ratioεεμ'=7＊.弹性模量-E ：表示材料抵抗拉压变形的能力 E - modulus of elasticity ：Indicates the capability of materials for resisting tension or compression 8＊.抗拉刚度-EA :表示构件抵抗拉压变形的能力EA -the axial rigidity: Indicates the capability of constructive members for resisting tension or compression 9＊. 胡克定律（Hooke’s Law ）:当应力不超过材料的比例极限时，应力与应变成正比.The stress is proportional to the strain within the elastic region.εσE =§2.12 应力集中的概念The Concept of Stress Concentration 1.由于截面尺寸的突然变化，使截面上的应力分布不再均匀，在某些部位出现远大于平均值的应力，称应力集中。

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3

(a)
= ay 3 能解决矩形梁受纯弯曲的问题.如图结论:应力函数
M
+
h
M
2 2
σx 图
σx
y
y
l
图3-2
h
x
h
1
10
Specification as following: In fig3-2,considering the unit width beam ,named the moment of double force on per unit width M .The order of here is[force][length]/[length],the result is [force] M . On the left or right,the two-dimensional force should be combined to a double force,as the moment of double force is M ,this request that:
o
2a
b
x
o
b y (b)
图3-1
b x 2c
o
2c
x
y (a)
y (c)
2.对应于 = bxy ,应力分量 σ x = 0, σ y = 0,τ xy = τ yx = b
.
结论:应力函数 = bxy 能解决矩形板受均布剪力问题.如图3-1(b).
8
3.The stress function = cy can be used to solute the problem of uniformly distributed tensile(if c < 0 ) or compressive(if c > 0 ) stresses on -axis of rectangular plate.(Fig3-1c)

弹性力学课件Chapter3

y 1
2 zy
1 2

xz

1 2

yz

z

且 (ij ) 为一二阶对称张量。
（3-2）
5
应用弹塑性力学
APPLIED ELASTO-PLASTICITY OF SOLIDS
3-3、应变分量与位移分量之间的微分关系—几何方程:
应变是与位移有关的。物体中各质点相对位置的改变，则产生变形。因此要分析物体的变形，就要研究各点的位置的变化。
v
xy

yx

v x

u y
x （3-5）
v(x, y) b
d
dy
yo
p
x
a
dx
p yx
a
v v(x dx, y)
u
dx u u
z u(x, y)
dx u
11
应用弹塑性力学
APPLIED ELASTO-PLASTICITY OF SOLIDS
x
y
z
v' v( x, y, z) v dx v dy v dz
x
y
z
w' w( x, y, z) w dx w dy w dz
x
y
z
14
应用弹塑性力学
APPLIED ELASTO-PLASTICITY OF SOLIDS
为了表示成应变分量的关系，对 u, v, w 作如下改写：
x
v v(x, y, z) v' v(x dx, y dy, z dz)
位移分量是坐标的函数 w w(x, y, z) w' w(x dx, y dy, z dz)

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2
σx 图
σx
y
y
l
h
x
1
h
Fig.3-2
9
2 3.应力函数 = cy 能解决矩形板在 x 方向受均布拉力 (设 c > 0)或均布压力(设 c < 0 )的问题.如图3-1(c).
三,应力函数取三次式对应的应力分量: 3-2所示的矩形梁.
= ay 3 σ x = 6ay, σ y = 0, τ xy = τ yx = 0
εx =
σx =
M y, σ y = 0, τ xy = τ yx = 0 I
1 (σ x σ y ) E 1 ε y = (σ y σ x ) E 2(1 + ) γ xy = τ xy E
15
§3 - 2
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. 一,平面应力的情况将应力分量 σ x =
7
σ x = 0, σ y = 0,τ xy = τ yx = b
= bxy
b y (b) Fig.3-1 ,stress components
y (c)
= ax 2 能解决矩形板在 y 方向受均布拉力结论:应力函数
2a b
(设 a > 0)或均布压力(设 a < 0 )的问题.如图3-1(a).
M y, σ y = 0, τ xy = τ yx = 0 代入物理方程 I
1 ε x = (σ x σ y ) E 1 ε y = (σ y σ x ) E 2(1 + ) γ xy = τ xy E
16
Then the distortion components are:
M M εx = y, γ xy = 0 y, ε y = EI EI
Then put (a) into the geometric equation:
(a)
so: Integrate the two equation above:
u M = y, = y, + =0 x EI y EI x y
2
3.The Stress Function in the form of a Polynomial of the Third Degree The Corresponding Stress Components
= ay 3
σ x = 6ay, σ y = 0, τ xy = τ yx = 0
(a)
5
= ax 2 + bxy + cy 2
§3 - 1
一,应力函数取一次多项式
多项式解答
= a + bx + cy
应力分量: 应力边界条件:
σ x = 0, σ y = 0,τ xy = τ yx = 0
X =Y =0
结论:(1)线性应力函数对应于无面力,无应力的状态. (2)把任何平面问题的应力函数加上一个线性函数,并不影响应力. 二,应力函数取二次多项式
M σx = y, σ y = 0, τ xy = τ yx = 0 I
The result is same with corresponding part in material mechanics Note: : The result above is useful to the beam which the length l is greatly more than the depth h ; to the beam which the length l is equal to the depth h , this result is useless.
Elasticity
1
2
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 §3-4 Loading of a Wedge by Gravity and Hydraulic Pressure §3-5 Solution by Series §3-6 Bending of a Simply Supported Beam by Arbitrary Lateral Load Exercises
2a
b
o
2a
b
x
o
b x 2c
o
2c
x
y (a)
2.Corresponding to
Conclusion: The stress function = bxy can used to solute the problem of uniformly distributed shearing stresses rectangular plate.(Fig3-1b)
o
2a
b
x
o
b y (b)
图3-1
b x 2c
o
2c
x
y (a)
y (c)
2.对应于 = bxy ,应力分量 σ x = 0, σ y = 0,τ xy = τ yx = b
.
结论:应力函数 = bxy 能解决矩形板受均布剪力问题.如图3-1(b).
8
3.The stress function = cy can be used to solute the problem of uniformly distributed tensile(if c < 0 ) or compressive(if c > 0 ) stresses on -axis of rectangular plate.(Fig3-1c)
u ε x = x v εy = y v u + γ xy = x y v M v u
(b)
M M 2 u= xy + f1 ( y ), v = y + f 2 ( x) EI 2 EI
(c)
f1 and f 2 Is the arbitrary function.put(c)into the third equation of(b)
2.The Stress Function in the form of a Polynomial of the Second Degree 1.Corresponding to = ax 2,the stress components s x = 0, s y = 2 a ,t xy =t yx = 0.
= a + bx + cy
The Stress Components: The Stress Boundary Condition:
σ x = 0, σ y = 0,τ xy = τ yx = 0
X =Y =0 Conclusion:(1)The linear stress function is corresponding to the state of no surface force and no stress.(2)There's no effect to the stress to add a linear function to any stress function of two-dimensional problem.
13
1× h 3 因为梁截面的惯矩是 I = ,所以上式可改写为: 12 M σx = y, σ y = 0, τ xy = τ yx = 0 I
结果与材料力学中完全相同. 注意: 注意: 对于长度 l 远大于深度 h 的梁,上面答案是有实用价值的;对于长度 l 与深度 h 同等大小的所谓深梁,这个解答是没有什么实用意义的.
Conclusion:The stress function(a) can be used to solute the problem of pure bending of rectangular beam. The rectangular beam is shown in Fig3-2.
M
+
h
M
2
6a ∫ ydy = 0,6a ∫ y 2 dy = M
Put in x σ equation(a)into the formula above,then:
h 2 h 2 h 2 h 2
h 2 h 2
h 2 h 2
∫
σ x dy = 0, ∫ σ x ydy = M
The first one always can meet ,and the second one request that : 2M a= h3 Put into formula(a),then:
(a)
= ay 3 能解决矩形梁受纯弯曲的问题.如图结论:应力函数
M
+
h
M
2 2
σx 图
σx
y
y
l
图3-2hxh Nhomakorabea1
10
Specification as following: In fig3-2,considering the unit width beam ,named the moment of double force on per unit width M .The order of here is[force][length]/[length],the result is [force] M . On the left or right,the two-dimensional force should be combined to a double force,as the moment of double force is M ,this request that:

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