Motion estimation of elastic articulated objects from image contours

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弹性模量与硬度关系

1.5
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Fig. 1. Calculated elastic modulus as a function of the reduced modulus for a diamond indenter (Ei = 1141 GPa, vi = 0.07), varying with the PoissonÕs ratio.
Keywords: Nano-indentation; Er–H relationship; Recovery resistance; Energy dissipation
1. Introduction
Elastic modulus E and hardness H are two essential parameters of structural materials, and the relationship between them is of keen interest to material scientists. From statistical trend, elastic modulus is usually considered to be an increasing function of hardness [1], but this rule neither has analytical support nor is generally obeyed. For example, layered ternary ceramics that have low hardness and high modulus are exceptions to this rule. Another E–H relation, often used in evaluating the elastic modulus of coatings, involves the compressive

商务英语高级试题及答案

商务英语高级试题及答案一、词汇题（每题1分，共10分）1. The company is looking for a _______ to expand its market share.A) strategyB) tacticC) policyD) procedure2. The _______ of the new product launch was a success.A) initiationB) inceptionC) commencementD) implementation3. The _______ of the project was delayed due to unforeseen circumstances.A) completionB) executionC) initiationD) termination4. The _______ of the company's financial report is scheduled for next week.A) releaseB) publicationC) issuanceD) distribution5. The _______ of the company's profits has been a concern for the shareholders.A) fluctuationB) stabilityC) consistencyD) stagnation6. The _______ of the company's assets is a crucial part of the audit process.A) valuationB) assessmentC) evaluationD) estimation7. The _______ of the merger was approved by the board of directors.A) proposalB) suggestionC) recommendationD) initiative8. The _______ of the contract is expected to be completed within a month.A) negotiationB) discussionC) deliberationD) consultation9. The _______ of the market has led to a decrease in sales.A) saturationB) expansionC) contractionD) diversification10. The _______ of the company's products has been a keyfactor in its success.A) innovationB) imitationC) replicationD) standardization答案：1-5 A B A A A6-10 A C A A A二、阅读理解（每题2分，共20分）阅读以下商务文章，回答下列问题。

弹性模量与硬度关系

H ¼ ð2=3Þ½1 þ lnðE cos h=3ryÞry:
ð1Þ
Since its theoretical basis is not clear, the range of applicability of Eq. (1) might be limited. A simple examination was made in the case of Ti3SiC2 whose hardness (4 GPa), compressive yield strength (1 GPa) and modulus (310 GPa) were known [4]. By Eq. (1), a modulus value as high as 1188 GPa was obtained, which was much higher than the measured value of 310 GPa. The unsatisfactory prediction of elastic modulus from hardness leads to two essential questions: (a) Does there exist a theoretical and generally valid relationship between elastic modulus and hardness? (b) If there is an inherent E–H relationship for solid materials, what is it?
1359-6454/$30.00 Ó 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.08.002

CALPHAD软件介绍

Abstract
The phase-ﬁeld method has become an important and extremely versatile technique for simulating microstructure evolution at the mesoscale. Thanks to the diffuse-interface approach, it allows us to study the evolution of arbitrary complex grain morphologies without any presumption on their shape or mutual distribution. It is also straightforward to account for different thermodynamic driving forces for microstructure evolution, such as bulk and interfacial energy, elastic energy and electric or magnetic energy, and the effect of different transport processes, such as mass diffusion, heat conduction and convection. The purpose of the paper is to give an introduction to the phase-ﬁeld modeling technique. The concept of diffuse interfaces, the phase-ﬁeld variables, the thermodynamic driving force for microstructure evolution and the kinetic phase-ﬁeld equations are introduced. Furthermore, common techniques for parameter determination and numerical solution of the equations are discussed. To show the variety in phase-ﬁeld models, different model formulations are exploited, depending on which is most common or most illustrative. c 2007 Elsevier Ltd. All rights reserved.

JournalofHarbinInstituteofTechnology》（NewSeries）

《Journal of Harbin Institute of Technology》(New Series)V ol.15, No.3June 2008ContentsTowards structural web services discoveryCHEN Jiang feng297A control model for hysteresis based on microscopic polarization mechanisms in piezoelectric actuatorRU Chang hai, SUN Li ning, RONG Wei bin302Activity based resource capability modeling307Similarity theory based method for MEMS dynamics analysisLI Gui xian, PENG Y un feng, ZHANG Xin312Anti impact and energy absorption of metal and compound thin wall cylindrical tubes CHEN Y ong tao, SHEN Zhi chun, ZHENG Gang tie317Hydrogen producting characteristics by a novel strain of bacteria ethanoligenens sp. B49XU Li ying, REN Nan qi, WANG Xing zu, ZHANG Ying, XU Hui, CHEN Guan xiong, JIA Y ong feng321Motion estimation of elastic articulated objects from image contoursPAN Hai lang, DAI Y ue wei, SHI Lei326Impact of artificial waterfall using reclaimed water to VOCs and its health risk assessmentMA Jin jun, ZHU Hong liang, ZHAO San ping, W ANG Y ong jie, ZHU Y ong bing 331Gene control of acupuncture and moxibustion preconditioning on apoptosis in ischemic cardiac muscle of rats with re perfusionSUN Zhong ren, LI Xiao ning, ZHAO Y u hui, TIAN Y an yan, XU Li 341 Analysis on testing and operational reliability of softwareZHAO Jing，LIU Hong wei，CUI Gang，W ANG Hui qiang345Nonlinear dynamic characteristics model of labyrinth seal based on Muszynska modelYE Jian huai, LIU Zhan sheng, ZHANG Guang hui351Modified rubberized stone matrix asphalt for Nineveh roadsAl Hadidy AI, TAN Yi qiu356A real time fault tolerant scheduling algorithm with low dependability cost in on board computer systemWANG Pei dong, WEI Zhen hua361Test case generation based on orthogonal table for software black box testingLIU Jiu fu,Y ANG Zhong,Y ANG Zhen xing,SUN Lin365Supplier pricing based on threshold cointegration in agri supply chainLENG Zhi jie, TANG Huan wen 369Correlation of the positive stress ratio effects on fatigue crack propagation rate of aluminium alloys based on a new parameter da／dSLU Xia mei, MA Y un fei, ZHANG Jia zhen374Experimental study on tensile failure process of double K fracture parameters in rollercompacted concrete layerHUANG Zhi qiang, SONG Y u pu,WANG Xue zhi378Julia sets of semi conjugated transcendental entire functionsWANG Xiao ling, SUN Lang wei, Y ANG De gui, BAO Y uan sheng383 Application of fuzzy logic in content based image retrievalWANG Xiao ling, XIE Kang lin386V ertical dynamic response characteristics of single pile in non homogeneous soil layers KONG De sen, LUAN Mao tian, LING Xian zhang393Experimental study of a simple pressure loss coefficient model for multi hole orificeZHAO Tian yi, ZHANG Ji li399Optimization of S surface controller for autonomous underwater vehicle with immune genetic algorithmLI Y e, ZHANG Lei, WAN Lei, LIANG Xiao404Three controllable factors of steady operation of EGSB reactorLI Hui li, LU Bing nan, LI Fang 411Fault tolerant design for joint of HIT／DLR space robot armNI Feng lei, JIN Ming he, SHI Shi cai, LIU Hong415Radius model of convex vertical curve of freeway based on attachment coefficientLI Song ling, PEI Y u long 422Surface flow constructed wetland with composite plant bed for pretreatment of micro polluted Y ellow River raw water in ChinaY ANG Xu, YU Shui li, Y AN Xiao ju, ZHAO Y an,XIU Chun hai, ZHANG Hong yang426Information loss recovery for JPEG2000 image transmission in an error prone environment LIU Jie yu, ZHANG De yun430Synthesis and electrochemical characterization of LiNi0 78Co0 2Al0 02O2 cathode materials in a novel co precipitation methodGU Da ming, TIAN Qi you436Transport and transformation of nitrobenzene in Songhua River and calculation of flux and remnant based on mathematical quantification analysisGAO Fei, HAN Hong jun, MA Wen cheng, W ANG Wei439。

用转子动力学及有限元建模分析大型工业涡轮压缩机

用转子动力学及有限元建模分析大型工业涡轮压缩机J. Jeffrey Moore Giuseppe Vannini Massimo Camatti Paolo Bianchi 用转子动力学分析一个大型工业压缩机箱体和转子—轴承支撑系统。

建立复杂箱体及支撑结构的三维有限元模型。

在这里介绍了两种方法，包括箱体与基础间的传递函数法以及转子—箱体—基础的完全联接模型。

获得了箱体模型对轴承支承及转子的影响。

第一种方法获得了有限元模型中轴承支撑位置的频响函数。

用该频响函数产生一维曲线。

然后将这些传递函数纳入转子动力学模型中。

第二种方法解决了完全联接的转子及箱体模型。

用一个不平衡响应计算进行了在这两种情况下的转子临界转速和箱体模型响应。

压缩机及支撑的影响导致第二临界转速的下降至工作速度，不符合美国石油协会(API)第6177版要求。

结合转子轴颈轴承，箱体,支撑修改得出了一个满意的API兼容的解决方案。

结果验证了完全联接模型传递函数的方法。

DOI: 10.1115/1.2938272介绍：在典型的大型涡轮机械中，基础和箱体对转子响应及临界转速有显著影响。

箱体还在其他应用场合包括液体火箭发动机和重要垂直泵浦用于海上钻井作业有影响.Darlow et al[1]包括箱体影响的一个长的垂直泵。

Corbo et al.[2]也提出了建立垂直泵工作箱体影响。

Childs et al.[3] 显示火箭发动机涡轮泵的一项分析,包括弹性箱体模式。

Kubany et al[4] 用三维有限元法模拟了10MV的电动马达并展示了这种联接方法记录所有的基础的模式在操作速度范围内的重要的意义。

多数现代有限元程序允许为有转子陀螺效应的元素包括梁用3 D建模。

轴承可以被精确地模拟出等效刚度和阻尼系数类似转子动力学参数。

这些轴承可以被纳入一个三维有限元模型,以代表复杂几何实体单元的箱体和基础。

虽然这种方法捕捉真实的动态互动的转子和外壳,有限元模型不允许使用依赖速度系数轴承,这需要大量人工操作来产生不平衡响应的情节。

尸体肛温与死亡时间推断

死后间隔时间又称死亡时间（postmortem interval ，PMI ），是指死亡发生距检验尸体的间隔时间。

死亡时间推断是法医病理学的基本任务之一，在法医学实践中具有举足轻重的作用，主要体现在印证证人陈述基金项目：法医病理学公安部重点实验室开放课题资助项目（GABFYBL201808）作者简介：杨安顺（1984—），男，硕士研究生，主检法医师，主要从事法医临床学及法医病理学鉴定及研究；E-mail ：15863735@ 通信作者：吴锡福，副主任法医师，主要从事法医病理学和法医临床学鉴定；E-mail ：719394670@ 通信作者：罗斌，博士，主任法医师，博士研究生导师，主要从事法医病理学和法医临床学科研及鉴定；E-mail ：luobin@·综述·尸体肛温与死亡时间推断杨安顺1，2，权国林1，高云贵1，汪君1，隋鹏1，黎光锋1，龙定峰1，林少磊1，吴锡福1，罗斌2（1.广州市公安局海珠区分局，广东广州510290；2.中山大学中山医学院法医学系，广东广州510080）摘要：测量尸温主要用于早期死亡时间推断，肛温因其测量简便、快捷及无创常被作为尸体核心温度的代表用于实际检案。

目前，HENSSGE 列线图法是被普遍接受并广泛运用的肛温推断死亡时间法，国内很多学者也通过大量案例数据推导出各自的回归方程。

肛温推断死亡时间还有很多未知领域有待探索，列线图法也有待优化及扩展，其对影响因素的量化有待更科学地处理。

平台期的发生概率及持续时长尚缺乏统一认识，各种原因导致初始温度改变的发生率及程度亦无明确认识。

新的方法及思路丰富了方法学研究，但尚缺乏系统性及实用性。

本文对肛温推断死亡时间的研究进行综述，旨在总结当前研究的现状并寻求突破点。

由于尸温的下降易受体内外诸多因素的影响，不同地区的影响因素差异较大，地区化研究及应用也许是提高死亡时间推断精度的实用性探索。

关键词：法医病理学；温度；尸体；直肠；死亡时间推断；综述中图分类号：DF795.1文献标志码：Adoi ：10.12116/j.issn.1004-5619.2019.06.015文章编号：1004-5619（2019）06-0726-07Rectal Temperature of Corpse and Estimation of Postmortem IntervalYANG An-shun 1,2,QUAN Guo-lin 1,GAO Yun-gui 1,WANG Jun 1,SUI Peng 1,LI Guang-feng 1,LONG Ding-feng 1,LIN Shao-lei 1,WU Xi-fu 1,LUO Bin 2（1.Haizhu Branch of Guangzhou Public Security Bureau,Guangzhou 510290,China;2.Department of Fo⁃rensic Medicine,Zhongshan School of Medicine,Sun Yat-sen University,Guangzhou 510080,China ）Abstract ：Measurement of corpse temperature is mainly used for estimation of early postmortem inter-val,and rectal temperature is often used as a representative of body ’s core temperature in actual work because it is simple,quick and non -invasive.At present,the rectal temperature postmortem inter-val estimation method internationally accepted and widely used is HENSSGE ’s nomogram method,while many domestic scholars also deduced their own regression equations through a large number of case data.Estimation of postmortem interval based on rectal temperature still needs further study.The nomogram method needs to be optimized and extended,and quantification of its influencing factors needs to be dealt with more scientifically.There is still a lack of consensus on the probability and du-ration of the temperature plateau.There is no clear understanding of the probability and extent of the change in initial temperature caused by various causes.New methods and ideas enrich methodological research,but it still lacks systemicity and practicality.This article reviews the researches on estimation of postmortem interval based on rectal temperature in order to summarize the current situation of pre-vious researches and seek new breakthrough points.Because the decline of body temperature can be easily influenced by many factors in vitro and vivo ,and the influencing factors in different regions vary greatly,regionalization research and application may be a practical exploration to improve the ac-curacy of postmortem interval determination.Keywords ：forensic pathology;temperature;cadaver;rectum;estimation of postmortem interval;review及嫌疑人供述、划定侦查范围、争取破案时间、推断受伤距死亡的时间、分析案件性质以及现场重建等方面[1-2]。

Motion Estimation

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2 Introduction to Digital Video 2.1 Deﬁnitions and terminology . . . . . 2.1.1 Images . . . . . . . . . . . . . 2.1.2 Video sequences . . . . . . . 2.1.3 Video interlacing . . . . . . . 2.1.4 Contrast . . . . . . . . . . . . 2.1.5 Spatial frequency . . . . . . . 2.2 Digital image processing . . . . . . . 2.2.1 Fourier transform . . . . . . . 2.2.2 Convolution . . . . . . . . . . 2.2.3 Digital ﬁlters . . . . . . . . . 2.2.4 Correlation . . . . . . . . . . 2.3 MPEG-2 video compression . . . . . 2.3.1 The discrete cosine transform 2.3.2 Quantization . . . . . . . . . 2.3.3 Motion compensation . . . . 2.3.4 Eﬃcient representation . . .
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c Philips Electronics N.V. 2001
no classiﬁcation

弹性力学英语

弹性力学elasticity弹性理论theory of elasticity均匀应力状态homogeneous state of stress应力不变量stress invariant应变不变量strain invariant应变椭球strain ellipsoid均匀应变状态homogeneous state ofstrain应变协调方程equation of strain compatibility拉梅常量Lame constants各向同性弹性isotropic elasticity旋转圆盘rotating circular disk楔wedge开尔文问题Kelvin problem布西内斯克问题Boussinesq problem艾里应力函数Airy stress function克罗索夫--穆斯赫利什维利法Kolosoff-Muskhelishvili method基尔霍夫假设Kirchhoff hypothesis板Plate矩形板Rectangular plate圆板Circular plate环板Annular plate波纹板Corrugated plate加劲板Stiffened plate,reinforced Plate中厚板Plate of moderate thickness 弯[曲]应力函数Stress function of bending 壳Shell扁壳Shallow shell旋转壳Revolutionary shell球壳Spherical shell[圆]柱壳Cylindrical shell锥壳Conical shell环壳Toroidal shell封闭壳Closed shell波纹壳Corrugated shell扭[转]应力函数Stress function of torsion翘曲函数Warping function半逆解法semi-inverse method瑞利--里茨法Rayleigh-Ritz method松弛法Relaxation method莱维法Levy method松弛Relaxation量纲分析Dimensional analysis自相似[性]self-similarity影响面Influence surface接触应力Contact stress赫兹理论Hertz theory协调接触Conforming contact滑动接触Sliding contact滚动接触Rolling contact压入Indentation各向异性弹性Anisotropic elasticity颗粒材料Granular material散体力学Mechanics of granular media热弹性Thermoelasticity超弹性Hyperelasticity粘弹性Viscoelasticity对应原理Correspondence principle 褶皱Wrinkle塑性全量理论Total theory of plasticity 滑动Sliding微滑Microslip粗糙度Roughness非线性弹性Nonlinear elasticity大挠度Large deflection突弹跳变snap-through有限变形Finite deformation格林应变Green strain阿尔曼西应变Almansi strain弹性动力学Dynamic elasticity运动方程Equation of motion准静态的Quasi-static气动弹性Aeroelasticity水弹性Hydroelasticity颤振Flutter弹性波Elastic wave简单波Simple wave柱面波Cylindrical wave水平剪切波Horizontal shear wave 竖直剪切波Vertical shear wave 体波body wave无旋波Ir rotational wave畸变波Distortion wave膨胀波Dilatation wave瑞利波Rayleigh wave等容波Equivoluminal wave 勒夫波Love wave界面波Interfacial wave边缘效应edge effect塑性力学Plasticity可成形性Formability金属成形Metal forming耐撞性Crashworthiness结构抗撞毁性Structural crashworthiness拉拔Drawing破坏机构Collapse mechanism回弹Springback挤压Extrusion冲压Stamping穿透Perforation层裂Spalling塑性理论Theory of plasticity安定[性]理论Shake-down theory运动安定定理kinematic shake-down theorem 静力安定定理Static shake-down theorem率相关理论rate dependent theorem载荷因子load factor加载准则Loading criterion加载函数Loading function加载面Loading surface塑性加载Plastic loading塑性加载波Plastic loading wave简单加载Simple loading比例加载Proportional loading卸载Unloading卸载波Unloading wave冲击载荷Impulsive load阶跃载荷step load脉冲载荷pulse load极限载荷limit load中性变载nentral loading拉抻失稳instability in tension加速度波acceleration wave本构方程constitutive equation 完全解complete solution名义应力nominal stress过应力over-stress真应力true stress等效应力equivalent stress流动应力flow stress应力间断stress discontinuity应力空间stress space主应力空间principal stress space静水应力状态hydrostatic state of stress 对数应变logarithmic strain工程应变engineering strain等效应变equivalent strain应变局部化strain localization应变率strain rate应变率敏感性strain rate sensitivity应变空间strain space有限应变finite strain塑性应变增量plastic strain increment 累积塑性应变accumulated plastic strain 永久变形permanent deformation 内变量internal variable应变软化strain-softening理想刚塑性材料rigid-perfectly plastic Material刚塑性材料rigid-plastic material理想塑性材料perfectl plastic material 材料稳定性stability of material应变偏张量deviatoric tensor of strain 应力偏张量deviatori tensor of stress 应变球张量spherical tensor of strain 应力球张量spherical tensor of stress 路径相关性path-dependency线性强化linear strain-hardening应变强化strain-hardening随动强化kinematic hardening各向同性强化isotropic hardening强化模量strain-hardening modulus 幂强化power hardening塑性极限弯矩plastic limit bending Moment塑性极限扭矩plastic limit torque弹塑性弯曲elastic-plastic bending弹塑性交界面elastic-plastic interface弹塑性扭转elastic-plastic torsion粘塑性Viscoplasticity非弹性Inelasticity理想弹塑性材料elastic-perfectly plastic Material极限分析limit analysis极限设计limit design极限面limit surface上限定理upper bound theorem上屈服点upper yield point下限定理lower bound theorem下屈服点lower yield point界限定理bound theorem初始屈服面initial yield surface后继屈服面subsequent yield surface屈服面[的]外凸性convexity of yield surface 截面形状因子shape factor of cross-section 沙堆比拟sand heap analogy屈服Yield屈服条件yield condition屈服准则yield criterion屈服函数yield function屈服面yield surface塑性势plastic potential能量吸收装置energy absorbing device能量耗散率energy absorbing device塑性动力学dynamic plasticity塑性动力屈曲dynamic plastic buckling塑性动力响应dynamic plastic response塑性波plastic wave运动容许场kinematically admissible Field静力容许场statically admissible Field流动法则flow rule速度间断velocity discontinuity滑移线slip-lines滑移线场slip-lines field移行塑性铰travelling plastic hinge塑性增量理论incremental theory 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-Westergaardstress space洛德应变参数Lode strain parameter德鲁克公设Drucker postulate盖林格速度方程Geiringer velocity Equation结构力学structural mechanics结构分析structural analysis结构动力学structural dynamics拱Arch三铰拱three-hinged arch抛物线拱parabolic arch圆拱circular arch穹顶Dome空间结构space structure空间桁架space truss雪载[荷]snow load风载[荷]wind load土压力earth pressure地震载荷earthquake loading弹簧支座spring support支座位移support displacement支座沉降support settlement超静定次数degree of indeterminacy 机动分析kinematic analysis结点法method of joints截面法method of sections结点力joint forces共轭位移conjugate displacement影响线influence line三弯矩方程three-moment equation单位虚力unit virtual force刚度系数stiffness coefficient柔度系数flexibility coefficient力矩分配moment distribution力矩分配法moment distribution method 力矩再分配moment redistribution分配系数distribution factor矩阵位移法matri displacement method 单元刚度矩阵element stiffness matrix单元应变矩阵element strain matrix总体坐标global coordinates贝蒂定理Betti theorem高斯--若尔当消去法Gauss-Jordan elimination Method屈曲模态buckling mode复合材料力学mechanics of composites复合材料composite material纤维复合材料fibrous composite单向复合材料unidirectional composite 泡沫复合材料foamed composite颗粒复合材料particulate composite层板Laminate夹层板sandwich panel正交层板cross-ply laminate斜交层板angle-ply laminate层片Ply多胞固体cellular solid膨胀Expansion压实Debulk劣化Degradation脱层Delamination脱粘Debond纤维应力fiber stress层应力ply stress层应变ply strain层间应力interlaminar stress比强度specific strength强度折减系数strength reduction factor强度应力比strength -stress ratio横向剪切模量transverse shear modulus横观各向同性transverse isotropy正交各向异Orthotropy剪滞分析shear lag analysis短纤维chopped fiber长纤维continuous fiber纤维方向fiber direction纤维断裂fiber break纤维拔脱fiber pull-out纤维增强fiber reinforcement致密化Densification最小重量设计optimum weight design 网格分析法netting analysis混合律rule of mixture失效准则failure criterion蔡--吴失效准则Tsai-W u failure criterion达格代尔模型Dugdale model断裂力学fracture mechanics概率断裂力学probabilistic fracture Mechanics格里菲思理论Griffith theory线弹性断裂力学linear elastic fracture mechanics, LEFM弹塑性断裂力学elastic-plastic fracture mecha-nics, EPFM断裂Fracture脆性断裂brittle fracture解理断裂cleavage fracture蠕变断裂creep fracture延性断裂ductile fracture晶间断裂inter-granular fracture 准解理断裂quasi-cleavage fracture 穿晶断裂trans-granular fracture 裂纹Crack裂缝Flaw缺陷Defect割缝Slit微裂纹Microcrack折裂Kink椭圆裂纹elliptical crack深埋裂纹embedded crack币状裂纹penny-shape crack预制裂纹Precrack短裂纹short crack表面裂纹surface crack裂纹钝化crack blunting裂纹分叉crack branching裂纹闭合crack closure裂纹前缘crack front裂纹嘴crack mouth裂纹张开角crack opening angle,COA 裂纹张开位移crack opening displacement, COD裂纹阻力crack resistance裂纹面crack surface裂纹尖端crack tip裂尖张角crack tip opening angle, CTOA裂尖张开位移crack tip opening displacement, CTOD裂尖奇异场crack tip singularity Field裂纹扩展速率crack growth rate稳定裂纹扩展stable crack growth定常裂纹扩展steady crack growth亚临界裂纹扩展subcritical crack growth 裂纹[扩展]减速crack retardation止裂crack arrest止裂韧度arrest toughness断裂类型fracture mode滑开型sliding mode张开型opening mode撕开型tearing mode复合型mixed mode撕裂Tearing撕裂模量tearing modulus断裂准则fracture criterionJ积分J-integralJ阻力曲线J-resistance curve断裂韧度fracture toughness应力强度因子stress intensity factorHRR场Hutchinson-Rice-Rosengren Field守恒积分conservation integral有效应力张量effective stress tensor应变能密度strain energy density能量释放率energy release rate内聚区cohesive zone塑性区plastic zone张拉区stretched zone热影响区heat affected zone, HAZ延脆转变温度brittle-ductile 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 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 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 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 interfero - metry网格法grid method全息光弹性法holo-photoelasticity全息图Hologram全息照相Holograph全息干涉法holographic interferometry 全息云纹法holographic moire technique 全息术Holography全场分析法whole-field analysis散斑干涉法speckle interferometry散斑Speckle错位散斑干涉法speckle-shearing interferometry, shearography 散斑图Specklegram白光散斑法white-light speckle method 云纹干涉法moire interferometry[叠栅]云纹moire fringe[叠栅]云纹法moire method云纹图moire pattern离面云纹法off-plane moire method参考栅reference grating试件栅specimen grating分析栅analyzer grating面内云纹法in-plane moire method脆性涂层法brittle-coating method条带法strip coating method坐标变换transformation of Coordinates计算结构力学computational structural mecha-nics加权残量法weighted residual method 有限差分法finite difference method 有限[单]元法finite element method配点法point collocation里茨法Ritz method广义变分原理generalized variational Principle最小二乘法least square method胡[海昌]一鹫津原理Hu-Washizu principle赫林格-赖斯纳原理Hellinger-Reissner Principle修正变分原理modified variational Principle约束变分原理constrained variational Principle混合法mixed method杂交法hybrid method边界解法boundary solution method 有限条法finite strip method半解析法semi-analytical method协调元conforming element非协调元non-conforming element 混合元mixed element杂交元hybrid element边界元boundary element强迫边界条件forced boundary condition 自然边界条件natural boundary condition 离散化Discretization离散系统discrete system连续问题continuous problem广义位移generalized displacement 广义载荷generalized load广义应变generalized strain广义应力generalized stress界面变量interface variable节点node, nodal point[单]元Element角节点corner node边节点mid-side node内节点internal node无节点变量nodeless variable杆元bar element桁架杆元truss element梁元beam element二维元two-dimensional element 一维元one-dimensional element 三维元three-dimensional element 轴对称元axisymmetric element板元plate element壳元shell element厚板元thick plate element三角形元triangular element四边形元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。

MOTION ESTIMATION SYSTEM AND METHOD

专利名称：MOTION ESTIMATION SYSTEM ANDMETHOD发明人：RODRIGUEZ, Arturo, A.,SIMERLY, Timothy, W.,PATEL, Neilesh R.申请号：EP99918599.4申请日：19990416公开号：EP1072017B1公开日：20040922专利内容由知识产权出版社提供摘要：Techniques for doing motion estimation in video encoding. A predictor block which is a best match for a current block is located by comparing the current block of the picture currently being encoded with candidate blocks that are located using the motion vectors of blocks that are either spatially or temporally proximate to the current block. If a given proximate block does not have a usable motion vector, another proximate block is used. The temporally proximate blocks are blocks in the last picture to be encoded prior to the current picture. The candidate blocks are further used to define a minimized portion of the search space which will fit inside the local RAM of the processor used to compare the current block with the candidates. The minimized search space is used in a two-phase method which begins with the candidates located using the proximate blocks and continues with a diamond-shaped search space centered on the best candidate located using the proximate blocks. The duration of the search method is controlled by three thresholds. Each succeeding one of the thresholds requires a closer match for the predictor than the previous threshold. The size and shape of the diamond-shaped search space may vary according to the motion vectors of previous predictorsand according to the number of processor cycles that are available to perform the search. Similarly, the number and locations of the proximate blocks may vary according to the motion vectors of previous predictors and the number of processor cycles available.申请人：SCIENTIFIC ATLANTA地址：US国籍：US代理机构：Kügele, Bernhard更多信息请下载全文后查看。

基于元结构的螺杆转子磨床床身动静态特性分析与优化

摘要：螺杆转子磨床床身是关键的承载大件，其动静态性能的好坏将直接影响整机的加工精度和稳定性。为实
现床身的快速动态优化设计，首先基于元结构理论，使用ＡＳＳ软件仿真分析了床身筋格元结构各主要参数对其动态特ＮＹ性的影响。在此基础上，以提高床身低阶模态固有频率和降低床身重量为目标，对床身的结构参数进行优化，同时通过静
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第３第ｌ１卷６期
动与冲Fra bibliotek击ＪＯＵＲＮＡＬＯＦＶＩＢＲＡＴＯＮＩＡＮＤＨＯＣＳＫ
基于元结构的螺杆转子磨床床身动静态特性分析与优化
王禹林，孙文钊，冯虎田
（京理工大学机械工程学院机械电子工程系，南南京２０９）１０４
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力分析验证了优化方案的可行性。优化后，床身低阶固有频率得到了较大幅度的提高，中一阶固有频率提高了２．％，其２３床身的重量下降了８３％，．９同时静刚度也有明显提高，改善了床身的动静态特性，节约了制造成本。该方法对其他类似关键零部件的动态优化设计具有一定的借鉴意义。关键词：元结构；身；床动静态特性；参数优化

基于机器学习的钛合金弹性模量预测方法研究

第16卷第1期精密成形工程2024年1月JOURNAL OF NETSHAPE FORMING ENGINEERING33基于机器学习的钛合金弹性模量预测方法研究王园园，武川*，彭志伟，时文才（天津职业技术师范大学汽车模具智能制造技术国家地方联合工程实验室，天津 300222）摘要：目的探索一种高效可行的预测方法以提高钛合金弹性模量的预测精度，采用第一性原理计算方法与机器学习相结合的方式建立高精度的预测模型。

方法通过数据挖掘获取材料数据库中钛合金的力学性质微观结构参数，结合第一性原理计算方法构建初始数据集，并对其进行预处理，包括噪音消除、归一化及标准化，以得到高质量的数据集。

同时，采用随机森林特征重要性分析法对输入参数进行筛选，去除弱相关变量以降低预测模型的复杂度。

在此基础上，构建随机森林模型、支持向量机模型、BP神经网络模型及优化后的GA-BP神经网络模型，综合对比各模型的回归能力，分析误差后选出最优的算法模型。

结果最终建立了钛合金弹性模量预测模型，其中随机森林模型、支持向量机模型、BP神经网络模型、GA-BP神经网络模型的预测相关系数R分别为0.836、0.943、0.917、0.986。

结论 GA-BP模型对弹性模量的预测误差基本保持在5%~7%。

遗传算法可以优化BP神经网络的权值和阈值，使预测精度大幅提升。

说明通过该方法可以实现钛合金弹性模量的预测，大大节省研发和实验成本，加快高性能材料的筛选。

关键词：钛合金；第一性原理；机器学习；遗传算法；力学性能DOI：10.3969/j.issn.1674-6457.2024.01.004中图分类号：TG135+.1 文献标志码：A 文章编号：1674-6457(2024)01-0033-10Prediction Method of Elastic Modulus of Titanium Alloy Based on Machine LearningWANG Yuanyuan, WU Chuan*, PENG Zhiwei, SHI Wencai(National-local Joint Engineering Laboratory of Intelligent Manufacturing Oriented Automobile Die & Mould,Tianjin University of Technology and Education, Tianjin 300222, China)ABSTRACT: The work aims to improve the prediction accuracy of elastic modulus of titanium alloy through an efficient and feasible prediction method, and establish a high-precision prediction model which combines first-principle calculation and ma-chine learning. Through data mining, the microstructure parameters of mechanical properties of titanium alloy in the material database were obtained, and the initial data set was calculated and constructed based on the first principle, which was pretreated, including noise elimination, normalization and standardization, so as to obtain a high-quality data set. At the same time, the random forest characteristic importance analysis method was used to screen the input parameters and remove the weakly corre-收稿日期：2023-09-06Received：2023-09-06基金项目：国家自然科学基金（52075386）；天津市自然科学基金多投入重点项目（22JCZDJC00650）；中国博士后科学基金第67项研究基金（2020M672309）；陕西省高性能精密成形技术与装备重点实验室项目（PETE2019KF02）Fund：National Natural Science Foundation of China (52075386); China-Multi-input Key Project of Tianjin Natural Science Foundation (22JCZDJC00650); Research Fund 67 of China Postdoctoral Science Foundation (2020M672309); Shaanxi Key Laboratory of High-performance Precision Forming Technology and Equipment (PETE2019KF02)引文格式：王园园, 武川, 彭志伟, 等. 基于机器学习的钛合金弹性模量预测方法研究[J]. 精密成形工程, 2024, 16(1): 33-42. WANG Yuanyuan, WU Chuan, PENG Zhiwei, et al. Prediction Method of Elastic Modulus of Titanium Alloy Based on Machine Learning[J]. Journal of Netshape Forming Engineering, 2024, 16(1): 33-42.*通信作者（Corresponding author）34精密成形工程 2024年1月lated variables to reduce the complexity of the prediction model. On this basis, a random forest model, a support vector machine model, a BP neural network model and an optimized GA-BP neural network model were constructed, and the optimal algorithm model was selected after comprehensive comparison of regression capacity of each model and error rate analysis. Finally, a pre-diction model for elastic modulus of titanium alloy was established, in which the correlation coefficient R of the random forest model, the support vector machine model, the BP neural network model and the optimized GA-BP neural network model was0.836, 0.943, 0.917, and 0.986. Through comparative analysis, the prediction error of elastic modulus of GA-BP models is basi-cally kept at 5%-7%, showing high prediction accuracy. It is found that genetic algorithm can optimize the weight and threshold of the BP neural network, so as to give higher prediction accuracy. This method can realize the prediction of elastic modulus of titanium alloy, greatly save the research and development and experimental costs, and is applicable to the selection of high-performance materials.KEY WORDS: titanium alloy; first principles; machine learning; genetic algorithm; mechanical property目前，我国正在积极推动高端装备领域的结构材料向高强度、轻量化、高可靠性和可持续性等方向发展。

normalheatconduc...

a r X i v :1107.3306v 3 [c o n d -m a t .s t a t -m e c h ] 2 J u l 2012Normal heat conduction in one-dimensional momentum conserving lattices withasymmetric interactionsYi Zhong,Yong Zhang,Jiao Wang,∗and Hong Zhao †Department of Physics and Institute of Theoretical Physics and Astrophysics,Xiamen University,Xiamen 361005,Fujian,China.(Dated:December 31,2013)We study heat conduction behavior of one-dimensional lattices with asymmetric,momentum con-serving interparticle interactions.We ﬁnd that with a certain degree of interaction asymmetry,the heat conductivity measured in nonequilibrium stationary states converges in the thermodynamical limit.Our analysis suggests that the mass gradient resulting from asymmetric interactions may provide a phonon scattering mechanism in addition to that caused by nonlinear interactions.PACS numbers:05.60.Cd,44.10.+i,63.20.-e,66.70.-fThe heat transport properties of low-dimensional sys-tems have attracted intensive studies for decades [1–20](see also Refs.[21–23]for reviews and references therein).A challenge is to relate the heat conduction behavior of a system to its microscopic ingredients.In 1984Casati et al.investigated the role chaos may play [2],and since then their seminal work has trigged numerous eﬀorts for identifying the microscopic mechanism(s)of the Fourier law.In a one-dimensional (1D)case,the Fourier law statesJ =−κ∂T∂xis the spatial tem-perature gradient,and κis a ﬁnite constant termed as “thermal conductivity.”The heat conduction behavior is also known as ”normal heat conduction”if it follows the Fourier law or “abnormal heat conduction”otherwise.Now it has been clariﬁed that chaos is neither suﬃcient nor necessary to the Fourier law [5–7].For 1D lattices,another signiﬁcant step was made in 1998by Hu et al.,who pointed out that,besides the dynamical properties,whether or not the system has a conserved total momentum is another key ingredient [9,10];i.e.,lattices with (without)a momentum conser-vation property should disobey (obey)the Fourier law.In 2000Prosen and Campbell went a step further;they proved that for 1D momentum conserving lattices with non-vanishing internal pressure the heat conductivity di-verges in the thermodynamical limit [8].Though for lattices with a vanishing internal pressure their proof is not applicable,many numerical studies support the same conclusion.In addition,in their later study Prosen and Campbell also showed that momentum conserving is not a necessary condition for abnormal heat conduc-tion [7].More recent progress was made by employing the renormalization group analysis for hydrodynamical models [16,17]and the mode coupling theory [18–21].3or1FIG.1:(Color online)The schematic plot of the potential function V(x)given by Eq.(3)for r>0,r=0,and r<0, respectively.for short.)We shall present our simulation resultsﬁrst, then discuss their relation to existing theoretical and nu-merical studies.We consider homogeneous lattices with nearest neigh-boring coupling,whose Hamiltonian isH= i p2i2(x+r)2+e−rx.(3)Here r is a controlling parameter that governs the de-gree of the interaction asymmetry;by increasing|r|from zero where the potential is harmonic and symmetric,one gets increasingly stronger asymmetry.Fixing the system size to be that at zero temperature with a free boundary condition,the potential asymmetry implies a nonzero in-ternal pressure at aﬁnite temperature:While for r>0 the internal pressure is positive and the system is ther-mally expansive,for r<0it is negative and the system is of negative thermal expansion.Note that x=0is the equilibrium point of the potential,and V(x)for r and−r is symmetric with respect to x=0.The schematic plots of the potential function are presented in Fig.1.To measure the heat conductivity of our system,two Nose-Hoover heat baths[25]at temperatures T L and T R are coupled to the left-and rightmost N0particles,whosemotions follow˙x i=p i∂x i −ς±p i,and˙ς±=FIG.2:(Color online)The heat conductivityκvs the num-ber of particles N in our lattice model for various values ofthe interaction asymmetry parameter r.The size and tem-peratures of the two heat baths coupled to the system areN0=12,T L=3,and T R=2,respectively.The error bars(not shown)are much smaller than the symbols.The dashedline indicates∼N.p2iµand˙p i=−∂H2(T L+T R).Then the system is evolved for a long enough time(>108for all the cases investigated)to ensure that it has relaxedto the stationary state.After that the next evolution oftime∼109is performed to obtain the time average of thefollowing quantities:(i)local temperatures T i≡ p2i∂x ias adopted convention-ally[9,17];and(iii)heat conductivityκbased onκ≈JNaFIG.3:(Color online)The temperature proﬁles for r=1.5. The size and temperatures of the two heat baths coupled to the system are N0=12,T L=3,and T R=2,respectively.that the Fourier law holds.This is opposite to the the-oretical[7,8,16–21]and simulation[14,15,20]results that in1D momentum conserving lattices the Fourier law does not hold.To give further support for the converging heat conductivity observed for|r|≥1,we plot in Fig.3 the temperature proﬁles for r=1.5.It shows that for N>104the temperature proﬁles can be well rescaled by x i2x2+14x4as was considered in Ref.[15]is much weaker than the case of|r|=1in our model. On the other hand,the existing theoretical predictions may not be applicable to the LWAII.It should be noticed that in these theoretical treatments,the system is usu-ally assumed to be at an equilibrium state with a uniformtemperature,and thus a homogeneous mass distribution. But,however,in the LWAII there is an important dif-ference between nonequilibrium stationary states(with a temperature gradient)and equilibrium states:In the former the thermal expansion eﬀect may simultaneously give rise to a mass gradient across the system.This is essentially diﬀerent from lattices with symmetric interac-tions where a mass gradient is not expected in either the equilibrium or the nonequilibrium cases.In Fig.4the mass density functionρfor our model is compared withthat of the FPU-βmodel with Vβ(x)=14x4.Itshows clearly that,when being coupled to two heat baths at diﬀerent temperatures,a mass gradient is eventually established in our system for r=0when the stationary state is approached.It has been known that in systems with symmetric interactions,a nonlinearity of interac-tions may result in scattering to the heat current that is strong enough to establish the temperature gradient but not strong enough to lead to normal heat conduction[5,9].Therefore in systems with asymmetric interac-tions,the resultant mass gradient may provide an addi-tional scattering mechanism to the heat current.We con-jecture that this is the reason why normal heat conduc-tion can then be observed.According to theﬂuctuation-dissipation theorem,such a macroscopic,nonequilibrium eﬀect must have its microscopic,equilibrium counterpart, but the latter may have not been the object of the exist-ing theoretical studies.As one more evidence for our conjecture–that the mass gradient may provide an additional scattering mechanism to the heat current–it is worthwhile to notice that in a very recent study[13],a diﬀerent1D momentum conserv-ing system having aﬁnite thermal conductivity has also been reported.The system is a momentum conserving variant of the“ding-a-ling”model[2]:The even num-bered particles are bound to the adjacent even numbered particles by harmonic springs,and are subject to the elastic collisions with their neighboring odd numbered particles.The odd numbered particles are free except for elastic collisions with their even numbered neighbors. Signiﬁcantly,the interactions are asymmetric due to the elastic collisions,and as a result the system is thermally expansive.In Fig.4the mass density of the system in a nonequilibrium state is compared with our system;it can be seen that its asymmetry degree of the interactions is even stronger than our system with|r|=1.5.This ex-plains why the saturating regime of the heat conductivity can be numerically accessed in this system[13],provided that our conjecture is correct.Finally,we would like to emphasize that,not only in 1D LWAII but also in1D gases,the mass gradient in nonequilibrium stationary state may have signiﬁcant ef-fects on heat conduction.This has been shown in a1D hard-core gas with alternative molecule masses[26]and a variant1D hard-core gas model where two neighboring molecules are bound by a massless string[27].The inter-particle interactions in both of them are asymmetric.In the former it has been shown both analytically and nu-merically that,when the system is exposed to two heat baths of diﬀerent temperatures,the temperature gradi-ent across the system is maintained by the mass density gradient.In the latter the heat conduction behavior has been found to dramatically depend on whether or not the system has a nonzero external pressure(equivalently,a non-zero internal pressure due to the force balance).In addition,as was stressed in Ref.[27],the heat transport properties measured in equilibrium and nonequilibrium states could be qualitatively diﬀerent.However,it should be noticed that in these two studies the heat conductivity has been shown to diverge in the thermodynamical limit, which implies that,lacking a phonon scattering mecha-nism in gases,the mass gradient cannot guarantee the Fourier law exclusively.To summarize,we have performed a numerical investi-gation for several1D momentum conserving LWAII and observed normal heat conduction paring ourﬁnding in1D LWAII and the heat conduction charac-teristics of1D lattices with symmetric interactions such as the FPU-βmodel,we conjecture that the mass gra-dient may provide a phonon scattering mechanism in addition to that which is caused by nonlinear interac-tions,which jointly leads to the observed normal heat conduction behavior in1D LWAII.Based on our under-standing,we conjecture the same mechanism also works in the two-dimensional(2D)case.Indeed,normal heat conduction has been observed in both our ongoing study of2D momentum conserving LWAII[28]and a recent numerical study of thermal conductivity in empty and water-ﬁlled carbon nanotubes[29].As thermal expan-sion is ubiquitous among real lattice systems,suggesting their interparticle interactions are generally asymmetric, we expect that the Fourier law generally holds in real low-dimensional systems.In this regard experimental in-vestigations of carbon nanotubes and grapheneﬂakes of large sizes are very desirable.This work is supported by the NNSF(Grants No. 10805036,No.10975115,and No.10925525)and SRFDP (Grant No.20100121110021)of China.[1]Z.Rieder,J.L.Lebowitz,and E.Lieb,J.Math.Phys.8,1073(1967).[2]G.Casati,J.Ford,F.Vivaldi and W.M.Visscher,Phys.Rev.Lett.52,1861(1984).[3]T.Prosen,M.Robnik,J.Phys.A25,3449(1992).[4]T.Hatano,Phys.Rev.E59,1(R)(1999).[5]S.Lepri,R.Livi,and A.Politi,Phys.Rev.Lett.78,1896(1997).[6]B.Li,G.Casati,J.Wang,and T.Prosen,Phys.Rev.Lett.92,254301(2004).[7]T.Prosen and D.K.Campbell,Chaos15,015117(2005).[8]T.Prosen and D.K.Campbell,Phys.Rev.Lett.84,2857(2000).[9]B.Hu,B.Li,and H.Zhao,Phys.Rev.E57,2992(1998).[10]B.Hu,B.Li,and H.Zhao,Phys.Rev.E61,3828(2000).[11]C.Giardin`a,R.Livi,A.Politi,and M.Vassalli,Phys.Rev.Lett.84,2144(2000);O.V.Gendelman and A.V.Savin,ibid,84,2381(2000).[12]C.Giardin`a and J.Kurchan,J.Stat.Mech.2005,P05009.[13]G.R.Lee-Dadswell,E.Turner,J.Ettinger,and M.Moy,Phys.Rev.E82,061118(2010).[14]T.Mai,A.Dhar,and O.Narayan,Phys.Rev.Lett.98,184301(2007).[15]L.Wang and T.Wang,Europhys.Lett.93,54002(2011).[16]O.Narayan and S.Ramaswamy,Phys.Rev.Lett.89,200601(2002).[17]T.Mai and O.Narayan,Phys.Rev.E73,061202(2006).[18]G.R.Lee-Dadswell,B.G.Nickel,and C.G.Gray,Phys.Rev.E72,031202(2005);J.Stat.Phys.132,1(2008).[19]L.Delﬁni,S.Lepri,R.Livi,and A.Politi,Phys.Rev.E73,060201(R)(2006);J.Stat.Mech.2007,P02007. [20]J.S.Wang,B.Li,Phys.Rev.Lett.92,074302(2004);Phys.Rev.E70,021204(2004).[21]S.Lepri,R.Livi, A.Politi,Physics Reports377,1(2003).[22]A.Dhar,Adv.Phys.57,457(2008);F.Bonetto,J.L.Lebowitz,and L.Rey-Bellet,in Mathematical Physics 2000,edited by A.S.Fokas,A.Grigoryan,T.Kibble,andB.Zegarlinski(Imperial College Press,London,2000),pp.128-150[23]R.Klages,Microscopic Chaos,Fractals and Transport inNonequilibrium Statistical Mechanics(World Scientiﬁc, Singapore,2007),p.337.[24]C.Kittel,Introduction to Solid State Physics,7th ed.(Wiley,New York,1996),p.130.[25]S.Nose,J.Chem.Phys.81,511(1984);W.G.Hoover,Phys.Rev.A31,1695(1985).[26]S.Chen,Y.Zhang,J.Wang,and H.Zhao,arXiv:1106.2896.[27]A.Politi,J.Stat.Mech.2011,P03028.[28]Y.Zhong,Y.Zhang,J.Wang,and H.Zhao(unpub-lished).[29]J.A.Thomas,R.M.Iutzi,and A.J.H.McGaughey,Phys.Rev.B81,045413(2010).。

人体行走过程中上肢运动仿真及生物力学特征分析

第43卷第8期 2009年8月上海交通大学学报JOU RN AL O F SH AN G HA I JIA OT O N G U N IV ERSIT YVol.43No.8 Aug.2009收稿日期:2008 09 02基金项目:国家自然科学基金重点项目资助(30530230,30470455);上海市体育局科研攻关与科技服务项目资助(07J T018)作者简介:王洪生(1986 ),男,江西上饶人,硕士生.主要研究方向为人体生物力学、人体运动学.王成焘(联系人),男,教授,博士生导师,电话(T el.):021 ********;E m ail:trib@s .文章编号:1006 2467(2009)08 1302 05人体行走过程中上肢运动仿真及生物力学特征分析王洪生, 白雪岭, 张希安, 张琳琳, 王成焘(上海交通大学机械与动力工程学院,上海200240)摘要:为了分析人体行走过程中上肢运动状态的影响因素,对正常步态下人体上肢运动仿真模型与理想单摆模型进行了对比分析.以7名(4男,3女)步态无异常的志愿者为研究对象,采集人体测量学参数,建立上肢理想单摆模型.采用运动捕捉系统及肌电测量系统,对志愿者常速(1.2m/s)步行下的上肢运动以及肩关节周围6组肌肉的肌电信号进行同步测量,并基于所测运动学参数对人体行走中上肢运动进行仿真,计算实际肩关节角位移和角速度,分析相关肌肉的肌电信号特征.理想模型与实际测量结果比较表明,不同志愿者在同速行走过程中上肢的摆动周期相近,各相关肌肉肌电信号随摆臂而周期性变化,上肢实际最大摆动角速度均大于理想单摆角速度.证明摆臂过程中肩关节周围相关肌群驱动力大于肩关节阻尼.关键词:上肢;肌电信号;步态;运动捕捉中图分类号:R 318.01 文献标识码:AKinematics Simulation and Biomechanics Characteristic Analysis of U pper Extremity during Human WalkingWA N G H ong sheng , BA I X ue ling , ZH A N G X i an, ZH AN G L in lin, WAN G Cheng tao (School of M echanical Eng ineer ing ,Shanghai Jiaotong U niv er sity,Shanghai 200240,China)Abstract:In order to investig ate the factors that influence the mo vem ent condition o f upper extremity dur ing hum an walking,a co mparative study betw een the ex perimental conditio n and the ideal pendulum mo del condition w as co nducted.Firstly,sev en health participants (4males and 3females)w ere inv olved in the ex periment and the pendulum m odels w ere built according to their anthro pom etric parameters.Secondly,the markers coordinatio n and the EM G of related m uscles w ere simultaneously m easured w hen the partici pant w as w alking on a tr eadm ill w ith a daily v elo city of 1.2m/s.Based on the captured signals,the angle and angular velocity of the sho ulder joint w as calculated and the actual angular velocity w as co mpared w ith the v elo city of the upper extremity pendulum mo del.Also an analy sis w as undertaken for the recorded EM G.The study sho ws that the actual maxim um angular velocity of shoulder joint ex ceeds those of the virtual pendulum s and the EM G of the related m uscles w as cycling according to the periods of sw ing.The ex periment also indicates that the actual periods o f upper limb swing represent a level of similarity amo ng different participants;the related muscular forces contribute larg er motivity than the damp of the shoulder joint during human w alking in a no rmal speed.Key words:upper ex trem ity ;electro myo graphy (EM G)sig nals;g ait;mo tion capture正常人体步行过程中,上肢伴随下肢的运动而做周期摆动.Wagenaar等[1]认为,人体在低速运动过程中上肢的习惯摆动周期与上肢的固有频率(质量与质心到肩关节的长度的函数)有关;而在高速过程中上肢摆动频率主要与下肢的频率有关.Webb 等[2]在对人体上肢运动特性的研究中引入了虚拟单摆理论,分析了步频与人体上肢单摆频率的关系,并认为单摆假设将在上肢运动研究中扮演重要角色. Bertram等[3]对人体上肢单摆模型进行了进一步研究,并从能量角度对模型仿真性能加以探讨.而基于上肢单摆模型的研究表明[4],人体肌肉能量消耗主要用来改变人体的质心位置.Neptune等[5]提出肌肉的能量输出不仅用于双脚支撑阶段时人体质心位置的改变,还用于单脚支撑阶段质心位置抬高. Gutnik等[6]把步态过程中人体上肢运动与虚拟单摆运动进行了比较,认为肌肉对上肢运动具有一定的影响.然而,以上研究没有在人体步态测量过程中同步进行主要肌肉群的肌电信号测量.本文在步态试验中对肌电信号进行同步测量,与理想单摆模型进行对比,分析上肢肌肉群对人体行走过程中上肢摆臂运动的影响.1 试验方法1.1 试验对象在上海交通大学机械与动力工程学院师生中挑选7名身体健康并步态无异常的志愿者(4男3女)作为研究对象(试验之前他们均不知道本试验的直接目的).测量志愿者的人体测量学参数(见表1),包括:身高、体重、前臂长度、上臂长度以及手长;前臂长度为桡骨茎突到外上髁距离、上臂为肩峰到外上髁,手为桡骨茎突到中指指尖距离,臂长取为肩峰到桡骨茎突.表1 志愿者人体测量学基本参数Tab.1 Anthropom etric parameters of participants试验对象(编号)身高/m体重/kg上臂长/m前臂长/m手长/m#1 1.76363.20.3150.2450.195男性#2 1.63350.20.3000.2180.177#3 1.73563.50.3120.2550.190#4 1.81780.10.3250.2620.200#5 1.65455.20.2820.2250.178女性#6 1.58746.50.2850.2100.175 #7 1.72153.40.3170.2450.1801.2 试验设备及方案本试验采用Optotrak Certus运动捕捉系统对人体行走过程中上肢运动进行运动捕捉.如图1所示,2个Marker刚体(每个刚体至少由3个Marker 点组成)通过自黏性纱布分别固结在前臂、上臂的外侧,另一个刚体贴附于胸骨,以参考计算上臂摆动角度.由于手腕关节在行走过程中运动幅度微小,故可把手与前臂视为同一个刚体.对于不易采集的各关键解剖特性点,采用Optotrak Certus运动捕捉系统的虚拟工具进行虚拟M arker设置(虚拟M arker所对应刚体的位置不变),分别对上肢运动相关的6个解剖特征点(肩峰、外上髁、内上髁、桡骨茎突、尺骨茎突、中节指关节)设置虚拟Marker点,并测量贴附于试验对象上肢主动发光Marker点的三维运动轨迹.上肢的运动的捕捉频率为30H z,测量误差在0.1m m以内.图1 前臂/上臂刚体及创建的虚拟M arker(白色的亮点示意)F ig.1 T he attached M arker cluster s of for earm/upper arm&the anat omical land mar ker s(w hite highlig hts)采用8 通道肌电测试系统对摆臂过程中肩关节周围6块主要肌肉(三角肌前部、胸大肌锁骨部、肱二头肌、背阔肌、大圆肌、三角肌后部)的肌电信号进行同步测量,试验过程详见文献[7].1.3 试验过程首先对试验对象进行人体学参数测量,然后按以上制定的M ar ker点和肌电电极方案依次对其进行贴附.志愿者上身穿短T恤或背心.在捕捉试验开始之前调节跑步机速度至1.2m/s,每位试验者都将进行至少4次适应性练习,以适应试验室的光线、温度、跑步机及其他仪器设备.要求试验者以自然放松的状态走,然后开始捕捉测量;每位试验者同样动作循环20次.2 结果及数据分析2.1 上肢单摆模型的运动分析上肢运动过程中单摆的质量为上肢的总质量,1303第8期王洪生,等:人体行走过程中上肢运动仿真及生物力学特征分析单摆长度为上肢质心到肩关节距离.如图2所示,前屈/后伸过程中质心落在上肢体以外,具体位置确定如下[8]:x = (m ix i )m iy = (mi y i )mil =(x 2+y 2)(1)式中:m i 为各部位的质量;x i 为m i 质心到支点(肩关节)的水平距离;y i 为m i 质心到支点(肩关节)的垂直距离;l 为单摆的长度.得到最大前屈位置或最大后伸位置的等效单摆的质量与长度,则在最低点的转速:I max =m l 2maxE potential =mg (L -l max )max =2E potential /I max(2)式中:l max 为平衡位置单摆最大臂长;L 为平衡位置单摆臂长;E potential 为上臂最高点(最大前屈)势能,g 为重力加速度;I max 为平衡位置转动惯量; max 为单摆最大角速度.根据人体惯性参数的国际标准[9],把已测得的人体参数代入如下的二元回归方程:y =B 0+B 1X 1+B 2X 2(3)图2 上肢摆动前屈/后伸过程F ig.2 T he fo rw ard flex io n/backwar d ex tensiono f upper limb式中:X 1、X 2分别为试验对象的体重与身高;B 0、B 1、B 2为方程系数(与性别有关).由式(3)计算出试验者上肢各部位的质量、质心位置.将上肢各部位的质量、质心位置代入式(1)可得各位试验者上肢的l max 、L 和I max (见表2).最大前屈/后伸垂直位置可由三维捕捉系统(NDI)测量得到;理想单摆模型的最大前屈势能全部转化为摆动最低点的动能,把所得数据分别代入式(2)可得单摆平均最大角速度 max ,结果如表2所示.表中质心测量起点为:上臂,即桡骨点;前臂,即桡骨茎突点;手,即中指指尖点.表2 志愿者上肢基本惯性参数及计算所得单摆模型参数Tab.2 The inertial parameters of upper limb and the calculated parameters of virtual pendulum试验对象(编号)质心位置(m)/质量(k g)上臂前臂手l ma x /m I ma x /(k g !m 2) max /(rad !s -1)#10.167/1.750.137/0.910.116/0.470.2810.2477 1.024男性#20.154/1.350.124/0.690.110/0.380.2470.1995 1.457#30.164/1.760.135/0.910.116/0.460.2750.2454 1.214#40.174/2.260.147/1.200.122/0.540.3020.2832 1.078#50.158/1.450.122/0.650.116/0.270.2540.2024 1.201女性#60.150/1.190.116/0.520.112/0.250.2420.1878 1.054#70.161/1.310.123/0.630.116/0.280.2650.21841.1652.2 实际运动测量数据分析利用NDI 将测得的各解剖特性点的运动学参数以及肌电测量仪(Bo rtec)同步采集的目标肌肉的肌电信号保存为*.c3d 格式的文件.然后,将该文件导入Visual3D 中建立对象的三维骨架模型,并进行运动计算,计算正常行走过程中上肢摆动的角位移、角速度.其中,典型运动阶段如图3所示.图4所示为正常行走过程中上肢摆动状态下的肩关节角位移和角速度曲线.其中,#1为所测4名男性试验者运动学参数平均值,#2为3名女性试图3 V isual3D 上肢模型摆动的典型阶段F ig.3 T he mo del of ty pical perio ds dur ing upperlimb swing1304上海交通大学学报第43卷(a)#1试验者步行时手部解剖特性点垂直位置变化(b)#2试验者步行时手部解剖特性点垂直位置变化(c)#1试验者步行时肩关节矢状面角度(d)#2试验者步行时肩关节矢状面角度(e)#1试验者步行时肩关节矢状面角速度(f)#2试验者步行时肩关节矢状面角速度图4 试验对象的中节指关节点垂直位移、肩关节角位移与角速度曲线F ig.4 T he vert ical displacement o f PM,ang ular displacement and velocity of shoulder joint fo r participants验者的平均值,采样频率为30H z.可见:正常速度(1.2m/s)下不同对象同速步行时,摆臂周期具有一定统一性[(1.1∀0.08)s],但摆臂幅度以及角速度有较大差异.#1步行过程中肩关节最大转角为(0.17∀0.01)rad与(-0.12∀0.01)rad(后伸);最大角速度为(0.64∀0.11)rad/s与(-0.88∀0.07)rad/s(后伸).#2肩关节最大转角为(0.20∀0.02)rad与(-0.13∀0.01)rad(后伸);最大角速度为(0.84∀0.12)rad/s与(1.00∀0.05)rad/s(后伸).将实测结果与理想单摆模型计算结果进行比较发现,人体上肢理想单摆模型计算得到的矢状面上肢运动学参数与实际结果偏差较大.2.3 肌电信号分析本文对志愿者正常行走过程中上肢主要肌肉的肌电信号进行了同步采集,采集频率为900H z.结果表明,在步态过程中,肌电信号呈现出周期性变化特征.图5所示为一个步态周期下,志愿者正常行走过程中肩关节主要肌肉的肌电信号,其中,高频信号已经过整流与低通滤波处理.由图可见,1个周期内各肌电信号的变化趋势:前屈阶段(0~0.75s)三角肌前头、三角肌后头受到较大刺激,肌电信号分别从0.02mV增至(0.103∀0.007)mV(三角肌前头)、(0.081∀0.006)mV(三角肌后头);大圆肌有平均1305 第8期王洪生,等:人体行走过程中上肢运动仿真及生物力学特征分析0.37mV 的肌电信号;后伸阶段(0.75~1.17s)大圆肌肌电信号从0.037m V 增大到0.105mV,三角肌前/后头也分别受到0.03mV 水平的肌电刺激;在整个周期中,背阔肌、肱二头肌及胸大肌的肌电信号较小.图5 上肢摆动中肩关节主要肌肉的肌电信号Fig.5 EM G o f the main muscles related to upperlimb s movement3 讨论男性试验者上肢单摆模型的平均最大角速度为0.51rad/s,而实际所测最大前屈角速度为(0.64∀0.11)r ad/s;女性试验者上肢单摆模型最大角速度为0.73rad/s,而实际所测最大前屈角速度为(0.84∀0.12)r ad/s.比较上述数据,即人体实际最大摆臂速度大于无阻尼下的单摆速度.所测肌电信号反映了上肢肌肉对摆臂的作用情况,即前屈阶段三角肌前/后头发出较大的肌肉力、而后伸阶段大圆肌对上肢施加了较大的驱动力.肱二头肌肌电信号较小,说明在摆臂过程中肘关节屈伸幅度较小;胸大肌肌电信号较小,说明摆臂过程中上肢外展、外旋(即冠状面、横截面运动)幅度较小.背阔肌对上臂的作用主要为使臂内收、内旋和后伸,其信号微弱,说明摆臂过程中内收、内旋的阻力较小.同时,由于前屈时较大的势能转化为后伸的动能,使得在正常行走中需要背阔肌作为后伸原动力较小.上肢摆动状态受重力、相关肌肉力和肩关节关节阻尼的综合影响,由实际与理想模型的比较结果可知,肌肉力驱动作用大于关节阻尼,则实际速度大于理想模型速度.4 结语本文基于运动捕捉系统和肌电测量系统,以7名无步态异常的高校师生为试验对象,对其进行了正常步态过程中上肢运动的运动学测量,并同步测量了相关肌肉的肌电信号,避免了运动与肌电分开测量时所带来的误差.将实际运动与上肢理想单摆模型运动进行比较,得出正常步态(1.2m/s)三角肌、大圆肌对肩关节驱动力作用大于关节阻尼,且实际摆臂角速度大于无阻尼状态的理想单摆模型角速度.文中建立的一整套试验方案对以后人体上肢运动测量试验有一定的指导作用,对人体上肢运动状态的深入研究、人体运动机制研究、脑偏瘫诊断、康复治疗等领域具有深远意义.参考文献:[1] Wag enaar R C,v an Emmer ik R E.R eso nant fr equencies of arms and legs identify different w alking patterns [J].Journal of Biomechanical ,2000,33(7):853 861.[2] Webb D,T uttle R H,Baksh M .Pendular activ ity o fhuman upper limbs during slo w and no rmal w alking [J].American Journal of Physical Anthropology ,1994,93(4):477 489.[3] Bert ram J E,Chang Y H.M echanical energ y oscillations o f tw o brachiatio n g aits:M easurement and simu latio n [J].Am erican Journal of Physical Anthropology ,2001,115(4):319 326.[4] Kuo A D.Ener getics o f actively pow ered lo co motionusing the simplest w alking mo del [J].Journal of Bio mechanical Engineering ,2002,124(2):113 120.[5] Neptune R R,Zajac F E,Kautz S A.M uscle mechanical w or k r equir ements during no rmal w alking :T he en er getic cost of r aising the bo dy s center of mass is sig nificant [J].Journal of Biomechanics ,2004,37(6):817 825.[6] Gutnik B,M ackie H ,H udson G,et al .H ow clo se toa pendulum is human upper limb mov ement during walking ?[J].Journal of Comparative Human Biology ,2005,56(1):35 49.[7] Luttg ens K ,Hamilto n N.Kinesio lo gy :Scientif ic basisof human motio n [M ].Bosto n:W CB M cGr aw H ill,1997.[8] T imo shenko S,Y oung D H.Eng ineer ing mechanics[M ].4th edition .N ew Y or k:M cGr aw H ill,1956.[9] 刘静民.GB/T 17245 2004成年人人体惯性参数[M ].北京:中国标准出版社,2004.1306上海交通大学学报第43卷。

空气弹簧力学性态的非线性有限元模拟仿真_兰艳

空气弹簧力学性态的非线性有限元模拟仿真兰　艳1,2, 蔡海涛1, 王成国2, 刘金朝2 江　军3(1.中南大学应用数学系,长沙410083;2.铁道科学院机车车辆研究所,北京1000083.湘潭大学数学与计算科学学院,湖南湘潭411105)[摘要]　利用非线性有限元方法,在国内第一次给出了提速客车上空气弹簧的全实体单元模拟仿真方法.运用ABAQU S软件,给出了详细的力学性态分析过程与结果,通过与实验结果的比较,改进了提速客车空气弹簧设计的方法,并提供了重要的理论依据.关　键　词:空气弹簧;非线性;有限元;模拟仿真;全实体单元;ABAQUS中图分类号:O245;O246;TP319 文献标识码:A 文章编号:10005900(2005)01009004The Nonlinear Finite Element Imitatingof Airspring Mechanics QualityLAN Yan 1,2, CAI Hai tao 1, WANG Chen guo 2, LIU Jin chao 2, JIANG Jun3(1.Mathematics Department of Central South University ,Changs ha 410083China ;2.Ins titute of Equipment ,Chines e Academy of R ail way Seieuces ,Beijing 100008China ;3.Mathematics Department of Xiangtan University ,Xiangtan 411105China )【A bstract 】　We analyze the non -linear character of the air -spring by using the non -linear FE M ,and give an simu -lation method with whole substance unit first in China .In computation ,we get the detail mechanical property analyzingprocess and result by ABAQUS soft ware .After comparing with the experiment result ,author also improves the designmethod of the air -spring .Key words :　air -spring ;non -linear ;FEM ;Simulate ;whole substance unit ;AB AQUS空气弹簧的性能对车辆运行的稳定性有重要的影响.新型空气弹簧的研制对改善和提高列车、高速列车和城市轨道车辆的运行品质,延长零部件的使用寿命都具有极其重要的意义,并对其他相关行业的发展也起着重要作用.从早期的主要依靠试验和实际运用中得到的数据来改进研制,到现在欧美、日本及我国的研究部门运用计算机模拟仿真设计的方法来研制开发空气弹簧,在空气弹簧的有限元计算和控制理论方面已经有了一些成果[4,5,6,9],不过,国际上的空气弹簧模拟仿真设计因其强非线性性,目前还没有找到解决空气弹簧的非线性性理论问题的办法.本文所做的工作是在文献[3,10,7]的基础上,对空气弹簧的非线性性给以一定说明,并第一次通过有限元软件AB AQUS [1]将空气弹簧的模拟仿真设计,用实体单元给出其相关的力学性态分析.通过与实验结果的比较,改进了提速客车空气弹簧设计的方法,并提供了重要的理论依据.1　空气弹簧模拟仿真中的非线性问题空气弹簧的性能分析过程中,包含有几何非线性、材料非线性、边界非线性三大非线性问题,即为一三重耦合的强非线性问题.空气弹簧的胶囊和橡胶堆的材料是典型的超弹性材料———橡胶,其计算就牵涉到了材料的非线性,本文中空气弹簧的材料模型是依Moongy -Rovlin 模型[8]:W =C 1(I 1-3)+C 2(I 2-3)给出,其中C 1,C 2的取值依赖于实验数据而得.对此模型,既可运用大变形非线性弹性有限元法中的全拉格朗日模式来求解,也可用更新拉格朗日模式来求解.胶囊和橡胶堆在模拟的过程中变形是很大的,传统有限元计算的小变形情况的理论就不再适用了,因而必须考虑有限元计算中的几何非线性问题.而收稿日期:20031115 基金项目:湖南省教育厅基金资助项目(02C571) 作者简介:蔡海涛(1935-)男,湖南南县人,教授,博士生导师,E -mail :l anyan @rongyuan .cn ;第27卷第1期2005年3月湘　潭　大　学　自　然　科　学　学　报Natural Science Journal of Xiangtan University Vol .27No .1Mar .2005空气弹簧的接触非线性问题则是由上下盖板与胶囊相接触引起的,当胶囊与盖板相接触,它们相互之间会产生法向压力和摩擦剪切力,因胶囊及与胶囊相接触的盖板材料均为橡胶,硬度较大,在模拟过程中设其接触条件为接触体之间无相对滑动,对于无相对滑动接触,在接触有限元法中可用罚单元法来求解.本文主要的分析目的就是确定空气弹簧对应的载荷-位移响应,然后通过此响应来综合分析空气弹簧的力学性能,故本文要求解的方程组属求解非线性结构的响应类型.一般地应用于非线性有限元方程的非线性结构问题可表示为[8]图1　空气弹簧结构示意图图2　空气弹簧CAD 建模示意图K (q )q =g其中q 是未知位移的适量,g 是施加的结点载荷矢量,三大非线性因素则隐含于内力K (q )q 中,而内力由内应力σ的空间积分得到K (q )q =∫v B Tσd V 其中是结构刚度矩阵.一般的几何非线性有限元法中的应变与位移的非线性关系,材料非线性有限元法中的应力与应变的非线性关系,接触非线性问题中因载荷与节点位移有关,最后均会导致整体刚度方程为非线性方程.求解非线性方程一般都采用线性化方法,即把非线性线性问题转化为一序列线性问题求解.如何转化为线性问题,其作法是多种多样的.在AB AQUS 中对本文的非线性问题就是用基于Newton -Raphson [2]的增量法来求解的,当运用Newton -Raphson 来求解时,求解过程中的Jacobi [8]矩阵即为切线刚度矩阵.本文分析过程中是通过逐步施加给定的位移,以增量形式趋于最终解而得到结果,因此AB AQUS 将模拟计算分为许多位移增量步,并在每个位移增量步结束时确定近似的平衡,所有增量响应的和就是非线性分析的近似解:首先求出线性解(最好,求出“分界点”处所相应的解)[8]:d (0)=K -1P其中K 为整体结构刚度矩阵,P =P (0)为常量载荷;其次,按下列步骤进行迭代计算.第一步:三种方法均取d (0)作为第一次逼近值.第二步:计算不平衡力,由应变-位移和应力应变关系分别计算ε(0)和σ(0)并依据线性有限元原理,可知给出内力并求得不平衡力.第三步:计算移步方向.第四步:计算下一次的逼近值.第五步:循环计算与收敛检查.空气弹簧的有限元模型是以空气弹簧整体来进行模拟,空气弹簧的模型分为四部分:胶囊部分,橡胶堆部分,流体部分,上下盖板部分,其中在上盖板处还加了一附加空气室.2　空气弹簧的模拟仿真及分析结果2.1　有限元网格划分有限元网格的划分对这几部分纬线方向上都采取相同的划分,将其等分为四十份,每一单元对应轴心的转角为9°.实际的模型生成时,只需要作出边界轮廓线上的节点,将这些节点绕对称轴每次旋转9°,重复40次,然后作出相应的单元,再同样将这些单元绕对称轴每次旋转9°,重复40次就得到如图2的91第1期兰　艳等空气弹簧力学性态的非线性有限元模拟仿真整体模型,此为包含了附加空气室的模型.图2　空气弹簧有限元网格划分　2.2　边界条件为了与实验一致,将橡胶堆下平面所有节点在对称面上施加对称约束,初始时,由于模型是空气弹簧在工作高度基本不变下的模型,所以先将刚体上盖板的参考点作固定约束处理,约束其三个自由度.然后在上盖板的垂向和横向施加试验位移,再通过求解垂向和横向反力获得的刚度来研究空气弹簧的力学特性.如图3所示.2.3　接触条件实际的D 550空气弹簧上盖板的内侧与下盖板均为硬度较高的橡胶材料,故在选取单元时以三维实体杂交单元为主,因而盖板和胶囊的接触定义为三维实体杂交单元与三维实体杂交单元间的接触.当盖板与胶囊接触时摩擦很大,所以假设胶囊和盖板之间的接触是无相对滑移的.在本算例中,一共有两对这样的接触,分别为上盖板和胶囊、下盖板和胶囊,由这两对接触确定了模拟分析中的两对接触面.图3　空气弹簧有限元模型的边界位移约束2.4　单元选择针对空气弹簧的三重非线性性,分析过程整体主要采用三维块状(六面体)杂交实体单元(ABAQUS 中定义为C3D8H [1]),因上盖板内侧几何形状限制,还采用了极少数三维楔形杂交实体单元,但对求解没有很大的影响,对定义胶囊内决定其品质的帘线夹层,ABAQUS 提供了相关功能,其中一些必要参数是从试验中得到的.空气弹簧内部流体部分的定义在本文的计算中,用到了AB AQUS 提供的两种流体单元:三维三节点(AB AQUS 定义为F3D3[1])和三维四节点(ABAQUS 定义为F3D4[1])流体单元(节点的个数不包括参考节点).在本文的模型中,一共定义了12762个节点,8280个三维八节点实体单元(C3D8H ),80个三维六节点单元,3800个三维四节点(F3D4)和120个三维三节点(F3D3)流体单元.2.5　结　果图4　400kPa 大气压下空气弹簧的垂向与横向刚度曲线计算和试验比较92 湘　潭　大　学　自　然　科　学　学　报 2005年通过分析本文选取在400kPa 大气压下空气弹簧的垂向与横向刚度曲线计算和试验比较结果见图.图5　500kPa 大气压下空气弹簧的垂向与横向刚度曲线计算和试验比较从图可以看出,垂向与横向的分析结果和试验结果两者相比具有较好的一致性,而且在计算过程中收敛性很稳定,计算速度提高了.3　结　语从以上分析中可以看出,针对空气弹簧的三重非线性,采用ABAQUS 软件,选取实体单元对空气弹簧进行力学性态分析的方法,是切实可行的,计算过程的收敛性得到了保证,运算速度加快,它对空气弹簧的设计有现实的指导意义,减少了试验次数,降低了研制成本,缩短了产品投向市场所需的时间.为非线性有限元模拟仿真提供了极佳的应用前景.参　考　文　献[1]　ABAQU S /Standard Us er 's Manual 6.1-1[M ].HKS Co L td ,1990-1997.[2]　王勖成,邵敏.有限单元法基本原理和数值方法(第二版)[M ].北京:清华大学出版社,1999.Wang Maocheng ,Shao ming .Concepts and Applications of Finite Element Anal ysis (secondl y edition )[M ].Beijing :Publishing company of QingHua universit y .1999.[3]　赵洪伦.运用Marc 软件进行高速客车空气弹簧非线性横向刚度分析[A ].MSC 用户年会文集[C ],北京:2000.Zhao Hongl un .Anal ysis of Nonlinear Landscape Orientation Stiffness on Airs pring of Bullet Train by using MSC [A ].Aannual meeting corpus of MSC us er [C ],Beij ing ,2000.[4]　Alf Homeyer .采用现代方法设计空气弹簧系统[J ].郭荣生译,国外铁道车辆,1999,3.Alf Homeyer .Introduce of Modern Times Technique D es ign of Airspring Sys tem ,translate by R ongs heng Guo [J ].National Equipment ,1999,3.[5]　Jacek Grajnert ,Piotr Wolko .Library of Components of Pneumatic Suspension Sys tem Modeled in MA TL AB /SIMULINK and poss ibilities of its Appli -cation in ADA MS /Rail [A ].5th ADA MS /R ail Users 'Conference [C ].Harrle m :the Netherlands ,2000.[6]　Fursdon P M T ,Modelling a Cord Reinforced Component with ABA QU S [A ].6th UK ABAQU S User Group Conference Proceedings [C ],1990.[7]　方凯,王成国.高速客车空气弹簧力学参数的非性有限元分析[J ].铁道机车车辆,2001,8:30-32.Fang Kai ,Wang Chengguo .The Nonlinear FEM Analys is of Air Spring Mechanics Parameter of High -Speed Train [J ].R ail way Rolling -Stock .2001,8:30-32.[8]　卡德斯图赛H .有限元法手册[M ].北京:科学出版社,1996.Kads tusai H .FEM Manual [M ].Beijing :Science publ is hing house ,1996.[9]　郭荣生.空气弹簧悬挂的震动特性和参数计算(上)[J ].铁道车辆,1992,5:18-20.Guo R ongsheng .Impendent Shake Speciality and Para meter Account of Airs pring [J ].Vehicle of rail way ,1992,5:18-20.[10]　程慧萍.准高速客车空气弹簧力学性能的有限元分析[J ].吉林大学,2002,1:30-32.Cheng Huiping .Finite Ele ment Analys is of Airspring Mechanics Capability of Standard Bullet Train [J ].Jilin university ,2002,1:30-32.93第1期兰　艳等空气弹簧力学性态的非线性有限元模拟仿真。

中英文力学对准

一般力学类：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 methodWKB方法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固体力学类：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,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 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 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 fracturemechanics, 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 openingdisplacement, 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 transitiontemperature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 tension specimen, 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, crack Propagation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-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 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 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 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 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 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流体动力学类：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-Zhoukowskicondition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滞后lag相似性解 similar solution局域相似 local similarity气体润滑 gas lubrication液体动力润滑 hydrodynamic lubrication 浆体 slurry泰勒数 Taylor number纳维-斯托克斯方程 Navier-Stokes equation 牛顿流体 Newtonian fluid边界层理论boundary later theory边界层方程boundary layer equation边界层 boundary layer附面层 boundary layer层流边界层laminar boundary layer湍流边界层turbulent boundary layer温度边界层thermal boundary layer边界层转捩boundary layer transition边界层分离boundary layer separation边界层厚度boundary layer thickness位移厚度 displacement thickness动量厚度 momentum thickness能量厚度 energy thickness焓厚度 enthalpy thickness注入 injection吸出suction泰勒涡 Taylor vortex速度亏损律 velocity defect law形状因子 shape factor测速法 anemometry粘度测定法 visco[si] metry流动显示 flow visualization油烟显示 oil smoke visualization孔板流量计 orifice meter频率响应 frequency response油膜显示oil film visualization阴影法 shadow method纹影法 schlieren method烟丝法smoke wire method丝线法 tuft method。

结构设计常用专业英语词汇汇编

accidental combination偶然组合accidental load偶然荷载action作用apartment公寓arched roof拱形屋面area projected on a horizontal plane水平投影面ash load积灰荷载attic阁楼balcony阳台ballroom/ dance hall舞厅basic load combination基本荷载组合basic variable基本变量basic wind speed基本风速boundary condition边界条件boundary layer边界层cab驾驶室（吊车）canopy雨棚cantilever member悬挑构件cantilever slab悬臂板case工况catwalk马道characteristic value标准值nominal value标准值standard value标准值characteristic/nominal combination标准组合cladding system围护系统coefficient of thermal expansion温度膨胀系数column effective length柱有效长度combination value组合值comply with requirement of Chinese code满足中国规范要求concentrated load集中荷载concentration of plastic deformation塑性变形集中construction and maintenance load施工和检修荷载construction load施工荷载construction sequence施工顺序control room控制室corner转角，角部corridor走廊crane load吊车荷载crane wheel load吊车轮压dead load恒载dead-load-resisting moment恒载产生的弯矩deformed position变形后位置degree of reliability可靠度density密度design reference period设计基准期design situation设计状况design value设计值design value of a load荷载设计值design working life设计使用年限determinate structure静定结构diaphragm stiffness楼板刚度differential settlement不均匀沉降distribution factor of snow pressure屋面积雪分布系数double span double pitched roof双跨双坡屋面during service life使用期间dynamic analysis动力分析dynamic coefficient动力系数earthquake action地震作用eave屋檐/挑檐edge beam边梁edge column边柱elasticity modulus弹性模量electric hoist电动葫芦element check构件校核enclosed structure封闭式结构energy能量equibrium equation平衡方程equivalent uniform live load等效均布活荷载expansion膨胀exposure category地面粗糙度类别（美）exposure factor for wind pressure风压高度变化系数（美）field experiment现场试验fire escape防火楼梯first mode第一振型fixed seats固定座位flat roof平屋顶flexible lifting hook软钩吊车floor live load楼面活荷载fluid pressure流体压力fractile分位值frequent combinations频遇组合frequent value频遇值fundamental combination基本组合gable山墙garage车库geometrical parameter几何参数gradient height梯度风高度gust阵风gust factor coefficient阵风系数gymnasium健身房hand-geared bridge crane手动吊车handrail栏杆，扶手hard lifting hook硬钩吊车height variation factor of wind pressure风压高度变化系数height-to-width ratio高宽比heliport直升飞机平台horizontal component水平分量horizontal load水平荷载horizontal load on railing栏杆水平荷载hydrostatic uplift load水浮力impact factor冲击系数impact load冲击荷载importance factor重要性系数indeterminate structure超静定结构interpolation内插值法laboratory实验室large(long)-span structure大跨结构lateral force on crane runaway beam吊车横向水平荷载lateral load侧向力leeward背风面lifted load吊重limit state极限状态live load活荷载load code for the design of building structures建筑结构荷载规范load combination荷载组合load combination coefficient荷载组合系数load effect荷载效应lobby大厅local area局部部位local load局部荷载longitudinal force on crane runaway beam吊车纵向水平荷载long-term deflection长期变形magnification factor of wind fluctuation脉动增大系数manned roof上人屋面mass质量material property材料性能maximum wheel load最大轮压mean roof height平均屋面高度minimum potential energy principle最小势能原理mode superposition振型叠加法mountainous region山区movable seats活动座位multi degree-of-freedom system多自由度体系multi-defense system多道设防体系occupancy category房屋类别office building办公楼on adjacent span相邻跨on alternate span隔跨on the entire span满跨on the half span半跨open-frame tower敞开式塔架operating load操作荷载operating room手术室overturning倾覆overturning moment倾覆弯矩parapet wall女儿墙partial safety factor for loads荷载分项系数partially enclosed structure半敞开式结构partition load隔墙荷载passenger vehicle客车patient room病房performance function功能函数period for no.1第一周期period reduction factor周期折减系数permanent action（load）永久作用（荷载）permanent load永久荷载permanent partition固定隔墙pitched roof坡屋顶，斜屋面place of public assembly人口密集处plant厂房platform看台Poisson's ratio泊松比pond load积水荷载portable partition可移动隔墙primary load-resisting system主要承重体系probability distribution概率分布probability of failure失效概率purlin檩条quasi-permanent combinations准永久组合quasi-permanent value准永久值rated capacity额定起重量（吊车）reading room阅览室recurrence interval重现期reducing coefficient of live load活荷载折减系数reduction of live load活荷载折减reference snow pressure基本雪压reference wind pressure基本风压reliability可靠性reliability index可靠指标repeated service load反复荷载representative value代表值representative value of a load荷载代表值representative value of gravity load重力荷载代表值residential住宅resistance抗力ridge屋脊roof garden屋顶花园roof live load屋面活荷载roof slope屋面坡度safety category安全等级saw-toothed roof锯齿形屋面scaffolding脚手架self-straining force自应力荷载serviceablility limit state正常使用极限状态shape factor of wind load风荷载体形系数shear modulus剪切模量single degree-of-freedom system单自由度体系single span monopitched roof单跨单坡屋面skylight天窗sliding滑移snow load雪荷载soil pressure土压力stack room书库stage舞台stair楼梯stair tread踏步板statistical data统计资料statistical parameter统计参数steel rail钢轨，轨道stiffness刚度stiffness enlargement factor for middle-span beam中梁刚度放大系数stiffness restraint of backfill soil to basement回填土对地下室约束的相对刚度storey drift层间位移strain energy应变能stress-strain relationship应力－应变关系strong shear – weak bending强剪弱弯suburban area城市郊区take-off weight起飞重量temporary partition临时隔墙terrain roughness地面粗糙度the most critical combination最不利组合the most critical effect最不利效应the worst case最不利情况theatre剧院time history analysis时程分析transverse traveling load横向行驶的荷载（吊车）tributary area从属面积trolley小车（吊车）tunnel test风洞试验ultimate limit state承载能力极限状态unbalanced accumulation不均匀堆积unenclosed structure敞开式结构unmanned roof不上人屋面urban area城市市区variable action（load）可变作用（荷载）variational principal变分原理vertical component竖向分量vertical element竖向构件vertical load竖向荷载virtual work虚功wind fluctuation factor脉动影响系数wind fluttering factor风振系数wind load风荷载wind shield挡风板wind-excited oscillation风致振动windward迎风面work功working grade工作级别（吊车）accidental eccentricity偶然偏心additional bending moment附加弯矩additional damping附加阻尼additional seismic action factors at top of the building顶部附加地震作用系数allowable value of drift angle层间位移角限值amplifying factor for elaso-plastic story drift弹塑性层间位移放大系数artificial acceleration time-history curve人工模拟加速度时程曲线avalanche崩塌axial-force-ratio轴压比backing bar垫板base shear force底部剪力base shear method基底剪力法bearing wall承重墙boundary of slope边坡边缘brittle mode of failure脆性破坏buried depth埋置深度cast-in-situ concrete floor现浇混凝土楼板center of mass质量中心center of rigidity刚度中心circular natural frequency自振圆频率code for seismic design of buildings建筑抗震设计规范compaction method加密法composite floor with fluted plate压型钢板钢筋混凝土组合楼板compound hoop复合箍筋compound or continuous compound rectangular复合或连续复合矩形螺旋箍 spiral hoopconcentrically braced frame中心支撑框架confining boundary element约束边缘构件core column芯柱corner column角柱coupled torsion method扭转藕联方法coupling beam连梁critical damping临界阻尼crosswise brace交叉支撑damped free vibration有阻尼自由振动damping ratio阻尼比deformations predominantly due to shear剪切变形为主design basic acceleration of ground motion设计基本地震加速度design characteristic period of ground motion设计特征周期design earthquake groups设计地震分组design parameters of ground motion设计地震动参数detail of seismic design抗震构造措施diaphragm discontinuity楼面不连续discontinuity in bearing capacity承载力突变discontinuity in vertical anti-lateral-force members竖向抗侧力构件不连续displacement-relevant type位移相关型dog-bone connection狗骨节点double plate贴板double-limb coupling wall双肢抗震墙ductility延性dynamic characteristics动力特性earthquake action地震作用eccentrically braced frame偏心支撑框架elasto-plastic deformation analysis弹塑性变形分析elato-plasic time-history analyzing method弹塑性时程分析end-column端柱energy-dissipating beam segment耗能梁段energy-dissipating component耗能构件equivalent static lateral force等效侧向静力荷载equivalent viscous damping ratio等效粘滞阻尼比expansion joint/contraction joint伸缩缝favorable有利fixing location嵌固部位frame structure框架结构frame-brace框架-支撑frame-core-tube structure框架-核心筒结构framed tube框架-筒体frame-support wall structure部分框支抗震墙结构frame-wall structure框架-抗震墙结构frequently earthquake多遇地震full penetration butt welds完全熔透坡口焊geotechnical stability岩土地震的稳定性grade 1/2/3 framed structure1/2/3级框架grade 1/2/3 wall1/2/3级抗震墙grade of liquefaction液化等级gravity additional bending moment重力附加弯矩great frame巨型框架ground subsidence震陷height-width ratio高宽比hidden column暗柱hidden-beam暗梁horizontal brace水平支撑horizontal seismic influence coefficient水平地震影响系数horizontal transmission member水平转换构件inverted-v shape brace人字支撑isolation joint抗震缝joint-panel shear deformation节点域剪切变形k-shape brace K型支撑landslide滑坡lateral braced point侧向支承点lateral displacement(sway) stiffness侧移刚度lateral-force-resisting system抗侧力体系limit value of elaso-plastic story drift rotation弹塑性层间位移角限值limit value of elastic story drift rotation弹性层间位移角限值linear static/dynamic analyzing method线性静/动力分析方法liquefaction液化liquefaction index液化指数liquefaction mitigation measure抗液化措施liquefaction subsoil液化地基lonely tall hill高耸孤立的山丘long-cantilevered structure长悬臂结构longitudinal wall纵墙lumped mass集中质量major earthquake大震maximum pressure on foundation bottom基底最大压力maximum ratio of total height to total width最大高宽比mean pressure on foundation bottom基底平均压力mechanic model力学模型mode振型、模态mode participation factor振型参与系数moment resisting frame框架non-liquefaction不液化non-rocky steep slope非岩石的陡坡oblique direction lateral-force-resisting member斜交抗侧力构件ordinary boundary element构造边缘构件ordinary braced frame普通支撑框架ordinary hoop普通箍筋overlaying depth覆盖层厚度parapet without anchorage无锚固女儿墙partial factor for horizontal seismic action水平地震作用分项系数partial factor for vertical seismic action竖向地震作用分项系数peak ground acceleration地面加速度峰值plastic hinge塑性铰polar moment of inertial极惯性矩pre-cast floor/roof装配式楼盖/屋面prefabricated concrete roof/floor预制楼盖/屋盖probability of exceedence超越概率rarely earthquake罕遇地震recurrence interval重现周期reduction factor for the liquefaction effect of soil layer土层液化影响折减系数reentrance corners irregularity凹凸不规则reentrant corner凹角regular seismic building规则抗震建筑reinforced concrete spandrel girder钢筋混凝土托墙梁reinforced concrete wall plane with hidden steel brace 内藏钢支撑钢筋混凝土墙板reinforced concrete wall plane with vertical separators 带竖缝钢筋混凝土墙板representative value of gravity重力荷载代表值response spectrum反应谱response spectrum method for modal analysis振型分解反应谱法restoring-force characteristic model恢复力模型retaining wall抗撞墙rigid base刚性地基rigid/semi-rigid/flexible diaphragm刚性/半刚性/柔性隔板river bank河岸rubber isolator unit橡胶隔震单元saturated sand饱和砂土saturated silt饱和粘土secant stiffness割线刚度secondary effect of gravitation重力二阶效应seismic adjusting factor for loading capacity承载力抗震调整系数seismic capacity for the nodes of frame框架节点核心区地震承载力seismic concept design of buildings建筑抗震概念设计seismic detail requirement抗震构造要求seismic fortification category抗震设防类别seismic fortification criterion抗震设防标准seismic fortification intensity抗震设防烈度seismic fortification measures抗震措施seismic multiple-defense lines多道抗震防线seismic overturning moment地震倾覆弯矩seismic shear factor value of floor level楼层地震剪力系数seismic shear force地震剪力seismic soil bearing capacity地基抗震承载力seismically isolated隔震的settlement caused by liquefaction液化沉陷settlement joint沉降缝shear-wave velocity of soil剪切波速single diagonal brace单斜杆支撑site场地site-classes场地类别slab-column-structural wall structure板柱-抗震墙结构soft subsoil软土地基special concentrically braced frame特殊中心支撑框架speed linear relevant type速度线性相关型speed non-linear relevant type速度非线性相关型spiral hoop螺旋箍stiffness irregularity侧向刚度不规则story displacement楼层位移story strengthening with outrigger member加强层story yield strength coefficient楼层屈服强度系数strength reducing factor under cycling load受循环荷载时强度降低系数stress concentration应力集中strip-protruding spur条状突出的山嘴strong-column/weak-beam强柱弱梁supporting-column框支柱the adjusting factor of slope for the linear decreasesection直线下降段的下降斜率调整系数the damping adjustment factor阻尼调整系数the horizontal dynamic stiffness水平动刚度the minimum hoop characteristic最小配箍率特征值the natural vibration period自振周期the power index of the curvilinear decrease section曲线下降段的衰减指数the spacing of hoops箍筋间距the ultimate shear capacity of a bolt一个螺栓的极限受剪承载力the yield capacity for the joint-panel of beam and column 梁柱节点区域屈服承载力tie column构造柱torsion effect扭转效应torsional irregularity扭转不规则transference story转换层transverse wall横墙truss tube桁架-筒体tube in tube structure筒中筒结构tubes束筒vertical and lateral distribution web reinforcement竖向和横向分布钢筋(抗震墙) vertical seismic action竖向地震作用vertical seismic influence coefficient竖向地震影响系数volumetric ratio of hoop reinforcement体积配箍率wall structure抗震墙结构weak region of seismic building抗震建筑薄弱部位weak story薄弱层a under-reamed cast-in-situ pile扩底灌注桩a weak underlying stratum软弱下卧层active earth pressure主动土压力adjacent excavation相邻基坑adjacent pile相邻桩allowable differential settlements容许差异沉降allowable subsoil deformation地基变形允许值allowable value允许值anchor depth锚固深度anchor force锚固力anchor pile锚桩anchor plate锚垫板anchor rod锚杆anchored retaining wall锚杆挡墙angle of inclination倾角angle of internal friction of the soil土的内摩擦角angular gravel角砾arc sliding surface method圆弧滑动面法average additional pressure平均附加压力average pressure平均压力base failure地基破坏base plate of mat foundation筏基底板beams on elastic foundation弹性地基梁block stone块石bored pile钻孔桩boring钻孔boulders漂石box foundation箱型基础braced excavation支撑开挖brick foundation砖基础broken stone/crushed stone碎石cantilever sheet pile wall悬臂式板桩墙casing套管casing filled with concrete套管内灌混凝土cast-in-situ concrete pile foundation混凝土灌注桩基础center pile中心桩changing of ground water level地下水位变化characteristic value特征值check on compression抗压验算check on shear strength抗剪验算clay粘土clearance space净空coarse sand粗纱cobble卵石coefficient of additional stress附加应力系数coefficient of compressibility压缩系数coefficient of consolidation固结系数coefficient of permeability渗透系数cohesion force粘聚力cohesive soil粘性土combined foundation联合基础compaction piles压实桩compensated foundation补偿基础composite subgrade /composite foundation复合地基concrete against infiltration抗渗混凝土concrete foundation混凝土基础cone foundation锥形基础cone penetration test圆锥灌入试验connection beam联系梁consolidation固结consolidation curve固结曲线consolidation test固结试验consolidation theory固结理论constant head常水头contents of grains颗粒含量corner pile角桩corner point method角点法correction factor for depth深度修正系数counter-fort walls扶壁式挡土墙cushion course垫层deep basement深层地下室deep excavation深开挖deep-mixing pile深层搅拌桩deformation compatibility变形协调degree of saturation饱和度depth of excavation开挖深度design of wall against sliding挡土墙抗滑设计diaphragm walls地下连续墙difference in settlements沉降差direct shear test直剪试验drainage layer排水层drainage of footing基础排水drainage of wall挡墙的排水driven cast-in-place pile沉管灌注桩driven pile打入桩driving打桩driving shoe桩头/桩靴drop hammer落锤dry density干密度dry unit weight干容重dynamic pile capacity桩的动承载力earth works土方工程eccentric load偏心荷载eccentrically loaded foundation偏心受荷基础effective gravitational density浮重度embedment depth埋深end bearing piles端承桩end resistance of a pile桩端承载力excavation开挖基坑excavation support structure基坑维护结构excess pore water pressure超空隙水压力external ground level室外地面标高field vane test现场十字板试验filled and leveled area填方整平地区filled ground level填土面标高filled soil人工填土final settlement最终沉降量fine sand细纱flange of varying thickness变厚度翼缘floating foundation浮筏基础foundation基础foundation base基础底面foundation top基础顶面foundation types基础类型fraction粒组含量friction piles / floating piles摩擦桩general shear failure整体剪切破坏geological conditions地质条件gravitational density重度gravity density重力密度gravity retaining walls重力式挡土墙ground anchor土锚/地锚ground beams地梁ground surface室外地面ground treatment地基处理high socket foundation高杯口基础high-rise pile cap高桩承台H-pile H 型桩hydraulic gradient水力梯度inclined anchor斜锚杆inclined wall倾斜式挡土墙initial ground water level初始地下水位insertion depth插入深度in-situ static loading test of a single pile单桩静载荷试验internal ground level室内地面标高jacked-down piles静压桩laboratory vane test室内十字板试验large diameter pile大直径桩large displacement pile大量挤土桩large-area storage loading大面积堆载lateral earth pressure侧向土压力lateral earth pressure at rest侧向静止土压力laterite /red clay红粘土layered soil成层土lifting of piles桩上拔lime concrete foundation三合土基础lime-soil foundation灰土基础liquid limit液限liquidity index液性指数loaded pile受荷桩local shear failure局部剪切破坏low pile cap低桩承台main load-bearing layer主要受力层mat slab筏板medium sand中砂method of beams and slabs on elastic foundation弹性地基梁板法modulusof compressibility压缩模量Mohr's stress circle摩尔应力圆moisture content of soil土的含水量muck淤泥mucky soil淤泥质土multi-layer summation method分层总和法natural subsoil天然地基negative skin friction负摩阻力net pressure净压力net water pressure净水压力non-displacement pile非挤土桩non-reinforced spread foundation无筋扩展基础non-uniform soils不均匀地基normally consolidated正常固结offshore foundation海岸基础optimum water content最佳含水量order of driving打桩顺序overburden pressure超载压力over-consolidated超固结overturning of retaining wall挡土墙的倾覆pad foundation beneath columns柱下独立基础partial tilting局部倾斜particle shape颗粒形状particle size粒径passive earth pressure被动土压力penetration depth灌入深度penetration-resistant grade抗渗等级per liner meter每延米pile cap承台pile defect桩的缺陷pile failure桩破坏pile failure mode桩的破坏模式pile foundation桩基础pile group群桩pile point桩尖pile shaft桩身pile shaft strength桩身强度pile space桩距pile type桩型plastic limit塑限plasticity index塑性指数plate load test平板载荷试验pore pressure空隙压力pore water pressure空隙水压力porosity空隙率pre-cast concrete pile foundation混凝土预制桩基础preloaded foundation soils预压地基primary consolidation主固结primary settlement初始沉降pull out resistance of footing at depth深基础的抗拔力pull out resistance of shallow footing浅基础的抗拔力punching冲切punching failure冲切破坏punching failure cone冲切破坏锥体racked piles斜桩raft foundation筏基redriving of piles桩复打reinforced earth加劲土reinforced earth wall加劲土墙retaining walls挡土墙retraining structure支挡结构rigid foundation刚性基础risen pile上抬的桩rock岩石rock anchor岩锚rock discontinuity structure plan岩体结构面rock-inlaid cast-in-situ pile嵌岩灌注桩rounded gravel圆砾rubble concrete foundation毛石混凝土基础rubble foundation毛石基础sample disturbance土样扰动screw piles螺旋桩secondary consolidation次固结settlement沉降，沉降量settlement observation沉降观测settlement rate沉降速率shallow foundation浅基础shear key in sliding wall抗滑墙上的剪力键side of pile group群桩的周边silky clay粉质粘土silky sand粉沙silky soil粉土single-story bent structures单层排架结构skin friction of a pile桩侧摩阻力skin area of piles桩周面积slab foundation平板式筏基sliding moment滑动力矩sliding-resistant moment抗滑力矩slip surface滑动面slope边坡slope angle边坡坡角slope stability边坡稳定性slurry excavation泥浆开挖slurry trench pile泥浆护壁类桩型slurry walls泥浆连续墙small displacement pile少量挤土桩socket base杯底socket foundation杯口基础socket wall杯臂soft cohesive soil软弱粘土soil aggregate gravelly soil碎石土soil classification土的分类soil of high compressibility高压缩性土soil of low compressibility低压缩性土soil of medium compressibility中压缩性土soil-compacting effectsqueezing effect挤土效应soil-rock composite subgrade土岩组合地基solidier pile直桩spread foundation扩展基础stability of foundation地基稳定性standard frost penetration标准冻深standard penetration test标准灌入试验static water pressures静止水压力steel sheet piles钢板桩stepped foundation阶梯型基础stiffened slab foundation梁板式筏基stress increase应力增量stress release应力释放strip foundation beneath columns柱下条形基础strip foundation beneath walls墙下条形基础strip foundation with cross beams交叉条形基础strip load条形荷载struts critical depth支撑临界深度subgrade地基subgrade bearing capacity地基承载力substratum下卧层superstructure上部结构surface-empty phenomena脱空现象the bearing stratum持力层depth of foundation for settlement calculation地基沉降计算深度the medium weathered rock中风化岩石the minimum reinforcement ratio最小配筋率the peripheral length of the pile shaft桩身周长the principle of stress superposition应力叠加原理the report of engineering geological survey工程地质勘查报告the slightly weathered rock微风化岩石the Winkler foundation model文可勒地基模型three-pile cap三桩承台thrust due to land slide滑坡推力tilting倾斜toe of retaining wall挡土墙趾triaxial test三轴试验ultimate load of pile group群桩极限荷载unconfined compression test无侧限压缩试验undrained shear strength不排水抗剪强度uniaxial compression单轴压缩unit weight of soil土的容重vertical bearing capacity of a pile单桩竖向承载力void ratio/ porosity ratio空隙比water saturation水饱和weighted average gravitational density加权平均重度width-height ratio of step台阶高宽比abamurus挡土墙，扶壁abutment wall/flange wall翼墙accelerant/accelerated agent促凝剂accelerated cement快凝水泥acceptance specification验收规范acid and alkali-resistant grout耐酸碱水泥浆acid and alkali-resistant mortar耐酸碱水泥砂浆addition agent添加剂adhesive胶粘剂adhesive attraction附着力adhesive bitumen primer冷底子油aeroconcrete加气混凝土age龄期aggregate骨料allowable stress design容许应力设计axial compression轴压axial compressive load轴心压力axial tension轴拉be bent cold冷弯beam depth梁高beam-to-column connections梁柱节点bent-up bar弯起钢筋bottom reinforcement底筋boundary elements边缘构件bundle绑轧buttress扶壁柱cantilever beam悬臂梁cast-in-place concrete现浇混凝土centroidal axis中心轴clear cover保护层clear spacing净距clear span净跨coarse aggregate粗骨料collar tie beam/ring-beam圈梁column柱column-to-footing connection柱脚节点compression reinforcement受压钢筋compression-controlled section受压控制截面compressive strength抗压强度concrete structures混凝土结构construction joints施工缝continuing bar连续钢筋continuous连续continuous beams连续梁continuous slabs连续板corrosion protection防腐crack开裂，裂缝cracking moment开裂弯矩creep徐变cross section横截面cross section截面cure养护deep beam深梁deformed/spiral reinforcement螺纹钢筋depth of slab板厚depth-span ratio高跨比design load combinations设计荷载组合development length/lap length搭接长度ducts for grouted灌浆管durability耐久性dynamic amplification factor动力放大系数effective compressive flange有效受压翼缘effective cross-sectional area有效截面effective depth of section截面有效高度effective prestress有效预应力elastic deflection弹性变形embedment length锚固长度equivalent rectangular column正方形截面柱expansive cement膨胀水泥exterior basement wall地下室外墙factored load乘以分项系数的荷载fine aggregate细骨料fire protection防火fixed固定flange翼板flexural and compression members压弯构件footings of buildings建筑物底部form模板formulas公式frame structure with special-shaped columns异型柱框架结构frame-truss structure with special-shaped columns异型柱框架－桁架结构grade等级grade 60 concrete C60混凝土grade beam地基梁gross section全截面grout水泥浆grouting灌浆high-early-strength cement早强水泥high-strength steel bar高强钢筋hollow-core slab空心楼板hydraulic cement水泥inclined beam斜梁inclined stirrup斜向箍筋in-plane force面内荷载isolation joint分隔缝joint节点lap splices搭接large volumes of concrete大体积混凝土lateral force-resisting systems抗侧体系layer层length over梁、柱全长lift-slab construction升板施工lightweight aggregate轻骨料lightweight concrete轻质混凝土loaded area荷载面积longitudinal reinforcement纵筋long-time deflection永久变形loss of prestress预应力损失materials for grout灌浆料mechanical anchorage机械锚固mechanical connections机械连接midspan跨中minimum slab thickness最小板厚mix搅拌mix proportions配比moment magnification factor弯矩放大系数moment of inertia惯性矩moment-resisting frames刚架negative moment负弯矩negative moment reinforcement梁上部纵筋neutral axis中和轴nominal diameter of bar钢筋直径nominal strength强度标准值non pre-stressed reinforcement非预应力钢筋nonbearing wall非承重墙non－potable water非饮用水nonstructural members非结构构件nonsway column非摇摆柱nonsway frame无侧移框架one-way slabs单向板opening开洞overall thickness总厚overstressed超应力pedestal基座pilaster壁柱plain concrete素混凝土plain reinforcement光面钢筋plastic hinge region塑性铰区Portland cement波特兰水泥positive moment正弯矩positive moment reinforcement梁下部纵筋post-tension后张拉pre-cast concrete预制混凝土prestress losses预应力损失pre-stressed concrete预应力混凝土pre-stressing tendons预应力钢筋pretension先张法rectangular beam矩形梁reduction factors折减系数reinforced concrete钢筋混凝土reinforced gypsum concrete钢筋石膏混凝土reinforcement around structural steel core钢骨外包混凝土reinforcement ratio配筋率relaxation of tendon stress钢筋预应力松弛residual deflection/deformation残余变形rib肋seismic hook箍筋抗震钩seismic zones地震区settlement of supports支座沉降seven-day strength7天强度shear bar抗剪钢筋shear key抗剪键shear reinforcement梁箍筋shear walls剪力墙shore支撑架short-limb shear wall短肢剪力墙short-limb shear wall structure with special-shaped异型柱－短肢剪力墙结构columnsshrinkage/contraction收缩shrinkage-compensating concrete无收缩混凝土side face reinforcement梁腰筋simply supported beams简支梁simply supported solid slabs简支板six-bar-diameter六倍钢筋直径slab楼板slab without beams.无梁楼盖slag矿渣slag cement火山灰水泥span length跨度special-shaped column异形柱spiral reinforcement柱箍筋splitting tensile strength拉裂强度standard deviation标准差steam curing蒸汽养护steel-encased concrete core钢包核心混凝土stiffness reduction factor刚度折减系数stirrup箍筋strength强度strength design强度设计strength-reduction factor强度折减系数stripping拆模strong column/weak beam强柱弱梁strong connection强节点structural diaphragm结构隔板structural members结构构件structural system with special-shaped columns异型柱结构体系structural trusses结构桁架strut支柱support支座support reaction支座反力tensile strain拉应变tensile strength抗拉强度tension and shear act simultaneously拉力与剪力同时作用tension reinforcement受拉钢筋tension-controlled section受拉控制截面tolerance公差top reinforcement顶筋torsion reinforcement抗扭钢筋transverse reinforcement横向钢筋two-way slab双向板volumetric ratio体积比wall pier短肢墙water-cement ratio水灰比water-cement ratio by weight重量水灰比web腹板welded splices焊接white Portland cement白水泥a rigid beam-to-column connection梁柱刚性连接accuracy of construction(fabrication)安装精度acid-pickle酸洗additional tests附加检验additional tests on steels钢材附加检验alignment对准allowable slenderness ratio容许长细比allowable stress range容许应力幅angle of stress dispersal应力扩散角automatic welding自动焊automatic or semi-automatic process全自动或半自动方式backing plate衬板，垫板battened members缀板柱battens，batten plate缀板beam-columns压弯构件bearing connection承压连接bearing stength承压强度bearing stiffener支承加劲肋bend test弯曲试验blast-clean磨砂bolt tightening螺栓拧紧bolted connections螺栓连接bolting螺栓branch member支管brittle fracture脆断butt welds对头焊接camber起拱carbon content碳含量carbon structural steels碳素结构钢cast steel铸钢Charpy V-notch impact test v形坡口冲击试验chord member弦杆cladding涂层closed section闭口截面coefficient of linear expansion线膨胀系数cold-formed steel structural member冷弯型钢构件compact section厚实截面component stability单肢稳定condition of bolts螺栓状态condition of steel钢材状况constant amplitude fatigue常幅疲劳couposite rubber and steel support橡胶支座crane girder吊车梁crane truss吊车桁架cross diagonals交叉斜杆cutting切割defect acceptance criteria缺陷可接受准则design value of strength of steel钢材强度设计值diagonal stiffeners斜加劲肋dimensions and tolerances尺寸和允许误差direct dynamic loading/直接动力荷载distortion/deformation变形double-stepped column双阶柱doubly symmetric section双轴对称截面edge distance边距effective length计算长度，有效长度effective length factor计算长度系数effective length for torsional bucking扭转屈曲计算长度effective thickness of fillet welds角焊缝有效厚度effective width有效宽度effective width factor有效宽度系数end bearing端面承压end moment端弯矩equal leg angles等边角钢equivalent slenderness ratio换算长细比erection安装erection drawing安装图evaluation of welding techniques焊接工艺评定excessive deformation过度变形eyebar眼杆factor of equivalent moment等效弯矩系数fatigue failure疲劳破坏faying surfaces for hsfg fasteners高强摩擦连接的构件表面field /site welding现场焊接field connection现场接头fillers填板fillet welds角焊缝finish/surface layer面层first order elastic analysis一阶弹性分析flame-cut edge焰切边flange凸缘flexural buckling弯曲失稳flexural-torsional buckling弯扭屈曲forged steel connection node pieces节点锻造钢构件forming成孔frame braced with strong bracing system强支撑纯框架frame braced with weak bracing system弱支撑纯框架frequency of weld examination焊接检验次数。

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。

表示有人认为的英文高级短语四级作文

表示有人认为的英文高级短语四级作文全文共6篇示例，供读者参考篇1It's Believed That the Earth is RoundPeople say that the Earth is round, like a big ball. I'm not totally sure if that's true or not, but a lot of grown-ups seem to think it is. My teacher Mrs. Johnson told our class that it's a proven fact that the Earth is spherical in shape. She said scientists have pictures from space showing the round Earth. I guess those scientists must really know what they're talking about!Some kids make fun of me for believing the Earth is round. They say "Don't be stupid, if the Earth was round we'd all fall off!" But I don't think that makes sense. I've seen a globe at school that shows what the round Earth looks like. There's land and oceans all over it, but nowhere does it show people just floating off into space. It's hypothesized that gravity is what keeps people stuck to the Earth's surface, no matter where you are on the globe.My friend Michael remains unconvinced that the Earth is spherical. He theorizes that it must be flat, like a big frisbeefloating in space. When I asked him about that, he claimed that sailboat captains have sailed all the way to the edge and nearly fallen off! I'm pretty skeptical of that explanation though. My dad, who is a ship captain himself, has assured me there are no edges - you can just keep sailing around and around the curved surface. He subscribes to the widely-held view of a spherical world.It's my perception that most educated people accept the notion of a globally round Earth these days. Though I can't claim to fully comprehend it myself, the prevailing wisdom propagated by teachers and scientists seems to be that the Earth is not flat, but rather a sort of rolling ball soaring through the cosmos. Admittedly, it's a difficult concept for a kid like me to grasp!There are still some grownups who appear to harbor doubts about the spherical model. My crazy Uncle Mike contends that the whole idea of a globular planet is an unsubstantiated myth made up by the government. He purports that NASA's pictures from space are just animations cooked up on a computer. Uncle Mike is convinced that in reality, our world is a vast, unbounded plain - essentially one humungous sidewalk that goes on forever. To me, that just sounds silly. But Uncle Mike firmly holds to his personal conviction about the true nature of Earth's form.Overall, while I'm still a little uncertain myself, the widespread consensus from most authoritative sources I've encountered is that the Earth is round, approximating the shape of a spherical globe. That seems to be the prevalent theory that most people put credence in these days. Or at least, that's the common assumption that the grown-ups are promulgating. Whether it's an absolute fact or not, I can't say for sure. But it's what my teachers have indicated is the accepted truth about our planetary home. I guess I'll just have to take their word for it!篇2Some People Reckon...Some people reckon that school is a drag and a total waste of time. In their considered opinion, we would be better off just playing video games all day or watching TV shows until our eyes glazed over. I beg to differ with that notion, as misguided as it may be.There are those who opine that learning stuff like math, science, and reading is utterly pointless. They would have you believe that memorizing multiplication tables and mastering long division is an exercise in futility. To that contention, I can only shake my head in vehement disagreement.It is the conviction of certain individuals that history class is an utter snoozefest. They would have us buying into the fallacy that understanding events of the past holds no significance in our technologically advanced modern era. How wrongheaded can you get?There are those who labor under the delusion that spending hours poring over books is tantamount to cruel and unusual punishment. To hear them spiel, you would think that expanding one's vocabulary and honing reading comprehension skills is akin to being locked in the dungeons of an ancient castle.According to the line of thought propagated by many a kid, art class is an absolute bore. They would have it that smearing tempera paint onto construction paper or shaping lumps of clay is a cosmic waste of everyone's precious time. How tragically misguided is that perspective!It is widely believed in certain juvenile circles that music education is superfluous at best. To listen to their diatribes against having to learn about rhythm, melody, and harmony would leave one with the impression that mastering musical notation is more painful than a root canal.There are those who have deluded themselves into believing that physical education is nothing more than sadistic torturesanctioned by the Board of Education. By their reckoning, having to run laps and stretch muscles is debilitating both physically and mentally. What abject poppycock!Some people advance the seriously flawed notion that acquiring knowledge about civics, economics, and geography will bear no relevance to our future lives. They would have us swallow the preposterous falsehood that understanding how government works or being able to locate countries on a map is useless trivia. How misinformed can an opinion possibly be?At the end of the day, I cannot comprehend the mindset that views education as a colossal waste of time and energy. In my humble yet astute estimation, the acquisition of knowledge and development of skills is the key to unlocking a world of opportunities. Let the naysayers gripe and grouse all they want - this student is eager to learn!篇3My Grandma is Utterly Perplexing but I Love Her NotwithstandingDespite the fact that my grandma embodies numerous idiosyncratic predilections and mannerisms, I must concede that she is a truly unique individual who constantly piques myinsatiable curiosity. Albeit her ways may appear utterly perplexing and cryptic to the untrained observer, I have developed a profound appreciation and ardent fondness for her capricious nature over the years.To elucidate, my grandma adamantly adheres to the paradigm that one should perpetually maintain an immaculate domicile. In her unwavering pursuit of this ideology, she will instantaneously cease any endeavor she is engaged in if a mere speck of dirt is detected. Regardless of the amplitude of the task at hand or the pressing temporal constraints, she deems it an inviolable priority to attend to even the most infinitesimal areas that require meticulous cleaning and tidying. This steadfast fixation is the impetus for her oft-repeated mantra: "Cleanliness is indeed next to godliness."Moreover, my grandma exhibits an unyielding proclivity to economize in virtually every facet of her life. A quintessential illustration of this frugal modus operandi manifests when she perpetually reiterates that I should consume all thenutrition-replete comestibles on my plate, as she emphatically elucidates the superfluous expenditure and egregious wastefulness inherent in discarding even morsels of sustenance.Consequently, I must invariably exhibit judicious self-restraint when indulging my culinary cravings in her formidable presence.Additionally, despite her relatively diminutive stature, my grandma possesses a propensity to adopt an excessively vociferous decibel level while articulating, irrespective of spatial proximity. This proclivity frequently elicits surreptitious gestures and furtive grimaces from strangers in our vicinity, who are seemingly disconcerted by her resounding enunciations. Nonetheless, I have become adeptly accustomed to this quirk and perceive it as an endearing idiosyncrasy that renders her wholly unique.My grandma's predilection for dispensing draconian admonitions also warrants elucidation. If I exhibit even the most infinitesimal transgression or perceived misconduct, she does not hesitate to articulate an interminable litany of prolix homilies regarding morality, ethics and propriety. These protracted diatribes are invariably replete with archaic colloquialisms and idiomatic vernacular that I find perplexingly arcane, yet curiously fascinating.Furthermore, my grandma's sartorial choices are indubitably eccentric and idiosyncratic. She seems to cultivate an unequivocal affinity for garments that could be characterized asaesthetically incongruous - such as chromatic combinations and prints that would likely be perceived as diametrically opposed to contemporary modish sensibilities. Yet, she exudes an aura of ebullient self-assurance and an utter disregard for conventional sartorial norms that I find incredibly empowering.Ergo, in summation, despite the myriad aforementioned idiosyncrasies that render my grandma a veritably perplexing and bemusing individual, I am suffused with an inextinguishable feeling of profound adulation for her singularity. Her multifarious quirks and eccentricities amalgamate to formulate an authentically unique personage whom I perceive as intrinsically endearing. Ultimately, my grandma's sui generis nature is an intricate component of her irrefutable charm and the indubitable impetus for my ardent adoration. Notwithstanding her mercurial predilections, I am unequivocally enamored of this remarkable woman.篇4Certainly! Here's an essay with a length of around 2000 words, written in the voice of an elementary school student, using advanced English expressions to convey others' perspectives. Please note that the language and vocabulary usedmay not be entirely age-appropriate for a typical elementary school student.Title: What People Say About Our ClassHi there! My name is Emily, and I'm here to tell you all about what people think of our class. You see, we're not just any ordinary bunch of kids – we're a special group, or at least that's what they say.According to my mom, our class is a "melting pot of diverse cultures and backgrounds." She says that having friends from different parts of the world is such a valuable experience because it exposes us to new perspectives and teaches us to appreciate different traditions. Isn't that neat?My dad, on the other hand, claims that we're a "breeding ground for future leaders." He always brags about how we're encouraged to speak up, share our ideas, and take on responsibilities. Apparently, that's supposed to help us develop essential skills like confidence, critical thinking, andproblem-solving. Grown-ups sure love using fancy words, don't they?But wait, there's more! My teacher, Mrs. Johnson, often remarks that our class is a "vibrant community of curious minds."She says we're constantly asking questions, exploring new concepts, and challenging each other to think outside the box. Sounds like we're a bunch of little geniuses, huh?Now, let me tell you about what the principal thinks. Mr. Thompson calls us a "shining example of inclusivity and acceptance." According to him, our class is a safe space where everyone feels valued and respected, regardless of their differences. He's always going on about how we embrace each other's unique qualities and support one another's growth. It's like we're one big happy family or something.Oh, and you should hear what my best friend Lily's grandpa says! He refers to our class as a "nurturing environment that fosters creativity and self-expression." Apparently, we're encouraged to let our imaginations run wild and express ourselves through various artistic mediums, like painting, music, and storytelling. Who knew we were such talented little artists?But you know what's really funny? My neighbor, Mr. Wilson, calls our class a "rambunctious bunch of mischief-makers." He's always complaining about how loud we are during recess and how we leave toys scattered all over the playground. I guess some people just don't appreciate our youthful energy and enthusiasm.Anyway, those are just a few examples of what people say about our class. Some think we're super special, while others find us a bit overwhelming. But you know what? At the end of the day, we're just a group of kids trying to learn, grow, and have fun along the way. And that's what really matters, right?So, there you have it – a glimpse into the world of our classroom through the eyes of others. Whether you think we're a "melting pot," a "breeding ground for leaders," or a "rambunctious bunch," one thing's for sure: we're a class like no other!篇5My Big Sis Thinks...You know what my big sis thinks? She's like, super smart and stuff. She always uses these crazy long words that make my head spin! Like the other day, she was telling me about this "quintessential" book she read. I was like "Quinten-what now?" She just giggled and said it means something is the perfect example of its kind. Ohhh, got it! Why didn't she just say that in the first place?Anyway, my sis thinks I should "cultivate" a love for reading too. Cultivate...isn't that what farmers do with their crops? Shesays it means to nurture and develop something over time. I mean, I like reading comics and stuff, but those giant novels she loves are just way too "intricate" for me. Yep, that's another one of her words - it means something is very complex with lots of little details. No thanks, sis!She's always going on about how books can be so "riveting" and "mesmerizing." I know those words mean really interesting and absorbing. But half the time, I can barely stay "engrossed" (her word, not mine) in the simple books I have to read for school! My sis just shakes her head and calls me "lackadaisical" about my studies. Yeah, that means someone is lazy and doesn't try hard enough. Harsh, sis!But you know what I think is really "perplexing?" (I'm using her lingo now, you like that?) How she can spend hours with her nose stuck in those brick-thick books instead of playing outside with me. Don't get me wrong, reading is great and all. But there's so much other "exhilarating" stuff to do! (That means really exciting and thrilling, if you didn't know.)Speaking of exhilarating, we went to this "recreational" water park last weekend for my birthday. Recreational is just a fancy way of saying it's for fun, not serious exercise or whatever. Anyway, I was freaking out because they had these "mammoth"water slides that seemed incredibly tall and scary. Mammoth means gigantic, in case you can't figure that one out.After a lot of "cajoling" from my parents (nagging and pestering, basically), I finally went on one of those monster slides.I was "trepidatious" at first, which is just a posh way to say I was nervous and hesitant. But you know what? Once I took that initial plunge, it was such an "euphoric" experience! My sis helped me out with that vocab word - it means something that gives you an amazing, indescribable feeling of joy and happiness.So yeah, my big sis thinks she's like, a vocabulary "connoisseur" or something with all her fancy 10 words. But I'm slowly catching on to her lingo. You've got to "assimilate" it bit by bit, you know? Assimilate means to gradually absorb and incorporate something. Just like my sis hopes I'll "assimilate" my love for reading someday!I'll get there, sis. But for now, you can keep your riveting books. I'll be out back playing "invigorating" games that pump me up with energy. Oh, and invigorating? Yeah, you know exactly what that means by now, don't you smartypants?篇6People Say the Darndest ThingsFolks at school have been saying some pretty wild stuff lately. My buddy Timmy reckons recess is too short. Can you believe that? Recess is like the best part of the day! Who in their right mind would want it to be longer? I hypothesize that Timmy just doesn't like learning much.Then there's Jenny. Word on the playground is that she maintains her mom makes the nastiest lunches. Personally, I've always thought Mrs. Baker's sandwiches looked delicious. Loaded up with fresh veggies and hearty meats between those soft, fluffy slices of bread? Yes please! I'd swap lunches with Jenny any day. Nevertheless, she persists in her conviction that her mom's cooking is absolutely revolting.My teacher Miss Martin has been spreading the peculiar notion that homework is "good for us." As if! From my keen observations, it's evident that homework only serves to dampen our youthful spirits after an arduous day at school. By her rationale, I posit that going to the dentist must be tremendously "good" as well, since it's even more unpleasant than homework. No thank you, ma'am!According to my intellectual rival Nigel, academic success in the present day is practically preordained to yield a prosperous professional life. While I acknowledge the general importance ofworking diligently, I have my doubts that excelling at long division will directly determine one's career trajectory. Nigel has put forth the hypothesis that our math grades will be critical factors in our hireability for high-powered corporate roles later in life. From my vantage point, it seems his theory is predicated on a erroneous overvaluation of fractions and decimals in the employment landscape.Conventional wisdom from school staff suggests that eating all your veggies is beneficial for health and growth. I happen to subscribe to the iconoclastic idea that vegetables are decidedly unnecessary. Has anyone pored over the comprehensive empirical data arising from veggie consumption? The purported advantages appear rather overstated to me. I venture to postulate that a diet comprised purely of chicken nuggets and pizza would fare just swimmingly for a strapping young lad like myself.My crackpot buddy Zach has been espousing the most laughable pseudoscientific notions as of late. Just the other day, he tried to convince me of the existence of leprechauns. His rationale? He came across a vibrant rainbow while exploring the woods behind his house, leading him to infer that leprechauns were supplying their signature colorful precipitation. I attemptedto illustrate the fundamentally flawed logic underpinning his leprechaun theory, but he was unswayed. Zach has steadfastly remained an ardent advocate for the leprechaun hypothesis, dismissing all counterarguments as being rooted in willful ignorance. Can you even imagine?!At the end of the day, people are certainly entitled to their own ideas and beliefs, no matter how wacky they may seem. As my grandpappy always reminds me, "That's what makes the world an interesting place - all the different perspectives!" Fair point, gramps. I may vehemently disagree with the vast majority of what my pals and teachers have been postulating, but I'll always respect their right be wrong.。

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