2013 ap physics c 力学 scoring guidelines答案及解析

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vlsi-2013

vlsi-2013UNIVERSITY OF GLASGOWDegree of MSc in EngineeringVLSI DESIGN AND CAD (ENG5092)Friday 13 December 201309:30-11:30Answer FOUR questionsAnswer only TWO questions from each of sections A and B Each question is worth 25 marksThe numbers in square brackets in the right-hand margin indicate the marks allotted to the part of the question against which the mark is shown. These marks are for guidance only.An electronic calculator may be used provided that it does not have a facility for either textual storage or display, or for graphical display.Continued overleafPage 1 of 6Continued overleaf Page 2 of 6Section A : Attempt any TWO questions [50 marks] Q1 (a)A pipelined system architecture must be able to arbitrarily shift data one bit to the left, one bit to the right, or not at all, in a single clock cycle. Sketch a circuit that will do this using pass-transistor logic. You may assume that there is an input and an output register associated with the device. [8] (b)A simple digital multiplier relies on a process of successive shifting of data to the left, and addition. (i) Show how you can express a m -bit unsigned binary number using radix-2 notation.[4] (ii) By expressing two unsigned binary numbers X and Y, oflength m and n respectively, in radix-2 notation, derive a formula for the product Z = XY . [8] (c)Using your answer for part (b(ii)) of this question, write down the Boolean expression for the partial products that would appear in a logical implementation of the multiplier, and sketch the logic circuit required to calculate a partial product. [5] Q2 (a) Sketch the circuit diagram for a CMOS circuit with the function: D C B A Z ).(++= [8] (b)A layout is required for the circuit. (i) In the layout for the circuit, what is the minimum number of regions of active required to make all the transistors? [2] (ii) Draw a stick diagram for the circuit, including features such as merged transistor active layers and bulk connections. Clearly label each part of your diagram. Coloured pens or pencils may be used, but are not essential. [9] (c)What is the advantage of using techniques such as placing more than one transistor on a single region of active. [3] (d) How are the standard cells designed in practice to achieve regular layouts for blocks? Illustrate your answer with a sketch if necessary. [3]Q3 (a) State the key dimensions th constructed us (b) The Elmore d between cells also be used, compared to u (c) Figure Q3 sho of three furthe the inputs layers of met connected usi interconnect, assume that al(d) Cell placemen how cell pla minimize delaTable Q3. InterconneM1 area capacitance = 0.2 fF/μm M2 edge capacitance = 0.05 fF/μM2 area capacitance = 0.1 fF/μm M2 edge cap acitance = 0.05 fF/μ Co Page 3 of 6e key MOSFET properties and their relationshi ons that determine the propagation delay a ted using them. more delay model can be used to estimate the int cells in a layout. Identify and describe two other m used, and say what advantages or disadvantages ed to using the Elmore method. Q3 shows the routing connecting the output of a cel further cells, labeled A, B and C. The load capaci uts is labeled in Figure Q3. The routing is requ f metal (M1 (horizontal) and M2 (vertical)) th ed using vias. Using Table Q3 for the electrical p nect, calculate the Elmore delay from Z to input A that all tracks are laid out to be of minimum width,cement strongly influences the overall delay of a c l placement affects delay, and what methods e delay by means of judicious cell placement. Figure Q3. Interconnect routing layout.nnect electrical properties.fF/μm 2 5 fF/μm fF/μm 2 5 fF/μm Via resistance = 0.5 ?M1 resistivity = 0.1 ?/square M2 resistivity = 0.1 ?/squareContinued overleafonship to the deviceof a digital circuit[5]he interconnect delayother methods that canages they have when[8]f a cell, Z, to the inputcapacitance at each ofrequired to use two) that are electricallyrical properties of thenput A only. You maywidth, which is 1 μm.[6] of a circuit. Describehods can be used to[6]Continued overleafPage 4 of 6Section B : Attempt any TWO questions [50 marks]Q4 (a)Draw a clearly labeled diagram showing the cross-section of a n-channel MOSFET in a p-type substrate. [4] (b)Explain what is meant by the term inversion in the operation of a MOSFET. [3] (c) Consider a MOSFET of gate length L and gate width W .(i) Write down an expression for the gate charge in terms of the gatecapacitance per unit area C ox , the applied gate-to-source voltageV GS and threshold voltage V th . [2](ii) Show that at very low drain-to-source voltage V DS (near 0 V) thedrain current I D is given by()DS th GS ox n D V V V L W C I ?=μwhere μn is the mobility of electrons near the si licon surface.[8](d) Sketch a transistor layout indicating the active region, the polysilicon gate, and the contact areas for the smallest transistor that can be realized in a CMOS process. Using this, list and explain at least three basic design rules for laying out transistorsassuming that each mask has a worst case misalignment of 0.75λ, where λ is half the gate length. [8]Q5 (a) Draw a labelled block diagram of a typical sampled data system. [6](b) Complex MOS ICs, such as microcontrollers, require on-chip dataconversion capabilities using only MOSFETs and capacitors.A weightedcapacitor digital-to-analog converter (DAC) is a good example of such aconverter.(i) Give the circuit diagram of a 3-bit weighted capacitor DAC andexplain its operation. [8] (ii) Comment on the drawbacks of this DAC architecture. [2](iii) What is the output voltage of a 3-bit weighted capacitor DACwhen the input word is 110 and the reference voltage V ref = 5V?[2](c) Sketch the schematic diagram of a potentiometric DAC using a 2-bit DACas an example. What is the main advantage of this DAC implementation?[7]Continued overleafPage 5 of 6Q6 (a) Flash analog-to-digital converters (ADC) are used in high-speed applications such as video and radar signal processing.(i) Sketch the schematic diagram of a flash ADC using a 3-bit ADC toillustrate your answer. Specify the relative reference resistor valuesof the ADC and explain how high conversion speed is achieved. [7] (ii) If the reference voltage for the ADC is 3 V, specify the actualreference voltage levels used in the conversion process. What willbe the digital output for an input voltage of 1 V? What range ofinput voltages would give the same digital output in this case?[6](b) Sigma-delta analog-to-digital converters (Σ-? ADC) are very popular forvery high resolution (≥16 bit) low-to-medium speed applications such asdigital audio.(i) Explain what is meant by the term quantization noise. [3](ii) State and briefly explain the two techniques employed in Σ-?ADCs to improve the signal-to-noise ratio. [6] (iii) The signal-to-noise (SNR) for a first order Σ-? ADC is given bySNR = 6.02(n + 1.5m) – 3.41 dB, where the basic ADC is n-bit andthe oversampling ratio (OSR) is given by 2m. What sample rate isrequired to obtain 16-bit resolution if the system uses a 1-bit ADCand the Nyquist sampling rate is 44 kHz? [3]End of question paperPage 6 of 6。

2013国际物理奥林匹克竞赛理论试卷(2)

IntroductionIn this problem we study an efficient process of steam production that has been demonstrated to work experimentally. An aqueous solution of spherical nanometer-sized silver spheres (nanoparticles) with only about particles per liter is illuminated by a focused light beam. A fraction of the light is absorbed by the nanoparticles, which are heated up and generate steam locally around them without heating up the entire water solution. The steam is released from the system in the form of escaping steam bubbles. Not all details of the process are well understood at present, but the core process is known to be absorption of light through the so-called collective electron oscillations of the metallic nanoparticles. The device is known as a plasmonic steam generator.Figure 2.1(a)A spherical charge-neutral nanoparticle of radius R placed at the center of the coordinate system. (b) A sphere with a positive homogeneous charge density (red), and containing a smaller spherical charge-neutral region (0, yellow) of radius , with its center displaced by. (c) The sphere with positive charge density of the nanoparticle silver ions is fixed in the center of the coordinate system. The center of the spherical region with negative spherical charge density –(blue) of the electron cloud is displaced by , where . (d)An external homogeneous electric field . For time-dependent , the electron cloud moves with velocity . (e) The rectangular vessel () containing the aqueous solution of nanoparticles illuminated by monochromatic light propagating along the -axis with angular frequency and intensity .A single spherical silver nanoparticleThroughout this problem we consider a spherical silver nanoparticle of radius and with its center fixed at the origin of the coordinate system, see Fig. 2.1(a). All motions, forces and driving fields are parallel to the horizontal -axis (with unit vector ). The nanoparticle contains free (conduction) electrons moving within the whole nanoparticle volume without being bound to any silver atom. Each silver atom is a positive ion that has donated one such free electron.The electric field in a charge-neutral region inside a charged sphereFor the rest of the problem assume that the relative dielectric permittivity of all materials is . Inside a charged sphere of homogeneous charge density and radius R is created a small spherical charge-neutral region of radius by adding the opposite charge density , with its center displa-ced by from the center of the R-sphere, see Fig. 2.1(b).The restoring force on the displaced electron cloudIn the following, we study the collective motion of the free electrons, and therefore model them as a single negatively charged sphere of homogeneous charge density with a center position , which can move along the x-axis relative to the center of the positively charged sphere (silver ions) fixed at the origin of the coordinate system, see Fig. 2.1(c). Assume that an external force displaces the electron cloud to a new equilibrium position with . Except for tiny net charges at opposite ends of the nanoparticle, most of its interior remains charge-neutral.The spherical silver nanoparticle in an external constant electric fieldA nanoparticle is placed in vacuum and influenced by an external force due to an applied static homogeneous electric field , which displaces the electron cloud the small distance , where .The equivalent capacitance and inductance of the silver nanoparticleFor both a constant and a time-dependent field , the nanoparticle can be modeled as an equivalent electric circuit.The equivalent capacitance can be found by relating the work , done on the separation of charges , to the energy of a capacitor, carrying charge . The charge separation will cause a certain equivalent voltage across the equivalent capacitor.For a time-dependent field ,the electron cloud moves with velocity , Fig. 2.1(d). It has the kinetic energy and forms an electric current flowing through the fixed yz-plane. The kinetic energy of the electron cloud can be attributed to the energy of an equivalent inductor of inductance carrying the current .The plasmon resonance of the silver nanoparticleFrom the above analysis it follows that the motion, arising from displacing the electron cloud from its equilibrium position and then releasing it, can be modeled by an ideal LC-circuit oscillating at resonance. This dynamical mode of the electron cloud is known as the plasmon resonance, which oscillates at the so-called angular plasmon frequency .The silver nanoparticle illuminated with light at the plasmon frequencyIn the rest of the problem, the nanoparticle is illuminated by monochromatic light at the angular plasmon frequency with the incident intensity . As the wavelength is large, , the nanoparticle can be considered as being placed in a homogeneous harmonical-ly oscillating field ( ) . Driven by , the center ( )of the electron cloud oscillates at the same frequency with velocity and constant amplitude . This oscillating electron motion leads to absorption of light. The energy captured by the particle is either converted into Joule heating inside the particle or re-emitted by the particle as scattered light.Joule heating is caused by random inelastic collisions, where any given free electron once in a while hits a silver ion and loses its total kinetic energy, which is converted into vibrations of the silver ions (heat). The average time between the collisions is , where for silver nanoparticle we use .The incident light beam loses some time-averaged power by scattering on the oscillating elec-tron cloud (re-emission). depends on the scattering source amplitude , charge , angular fre-quency and properties of the light (the speed of light and permittivity in vacuum). In terms of these four variables, is given by .The above equivalent circuit elements are combined into an LCR series circuit model of the silver nanoparticle, which is driven by a harmonically oscillating equivalent voltage ( ) determined by the electric field of the incident light.Steam generation by lightAn aqueous solution of silver nanoparticles is prepared with a concentration. It is placed inside a rectangular transparent vessel of size andilluminated by light at the plasmon frequency with the same intensity at normal incidence as above, see Fig. 2.1(e). The temperature of the water is and we assume, in fair agreement with observations, that in steady state all Joule heating of the nanoparticle goes tothe production of steam of temperature , without raising the temperature of the water. The thermodynamic efficiency of the plasmonic steam generator is defined by the power ratio , where is the power going into the production of steam in the entire vessel, while is the total power of the incoming light that enters the vessel.Most of the time any given nanoparticle is surrounded by steam instead of water, and it can thus be described as being in vacuum.。

APIO2013中文版

2013亚太地区信息学奥林匹克竞赛APIO 2013竞赛时间：2013年5月11日9:00-14:00编译器版本及编译选项见考试注意事项。

机器人【问题描述】VRI（V oltron机器人学会）的工程师建造了n个机器人。

任意两个兼容的机器人站在同一个格子时可以合并为一个复合机器人。

我们把机器人用1至n编号（n≤ 9）。

如果两个机器人的编号是连续的，那么它们是兼容的，可以合并成一个复合机器人。

最初这n个机器人各自都只有唯一的编号。

而一个由两个或以上的机器人合并构成的复合机器人拥有两个编号，分别是构成它的所有机器人中最小和最大的编号。

例如，2号机器人只可以与1号或3号机器人合并。

若2号机器人与3号机器人合并，可构成编号为2-3的复合机器人。

如果编号为2-3的复合机器人与编号为4-6的复合机器人合并，可构成编号为2-6的复合机器人。

当所有机器人合并以后则构成1-n复合机器人。

工程师把这n个机器人放在了一个封闭的房间中，房间四周均是墙。

该房间被划分成w ×h个方格。

有些方格有障碍物，机器人不可经过或停留；其余方格允许多个机器人停留，同时允许机器人经过。

任何时候一个机器人只占用一个方格。

初始时刻，所有机器人均在不同的方格中。

这些原始的机器人不会自发地移动。

它们只有被工程师沿x轴或y轴推动后，才会沿推动的方向不断向前直线移动，直至碰到障碍物或墙停止移动。

停止移动后，它会扫描当前的格子是否存在可以与它合并的机器人，如果有，则合并并继续检查，直至不能再合并为止。

工程师只能沿水平向左、水平向右、竖直向上、竖直向下四个方向推动机器人，并且，在机器人尚未停止移动时，不允许推动其它机器人，因此任何时刻，房间中都只能有一个机器人移动。

为了帮助机器人转向，工程师在一些格子中放置了转向器。

具体地说，转向器分为顺时针转向器（右转器）和逆时针转向器（左转器），顺时针转向器可以使到达该格子的机器人沿顺时针方向转向90°；逆时针转向器可以使到达该格子的机器人沿逆时针方向转向90°。

国外比较好的损伤力学教材

国外比较好的损伤力学教材以下是一些国外较为流行和高质量的损伤力学教材：1. "Mechanics of Composite Materials" by Robert M. Jones - 这本书是关于复合材料力学的经典教材，其中包括了对于损伤分析和断裂力学的深入讲解。

2. "Damage and Fracture Mechanics: Failure Analysis of Engineering Materials and Structures" by Taoufik Boukharouba -这本书提供了广泛的损伤和断裂力学理论的详细介绍，并通过案例研究来说明其在工程材料和结构分析中的应用。

3. "Applied Mechanics of Solids" by Allan F. Bower - 这本书讲解了固体力学中的基本原理和方法，包括损伤力学和断裂力学的内容，并给出了实际应用的例子。

4. "Fracture Mechanics: Fundamentals and Applications" by T.L. Anderson - 这本书详细介绍了断裂力学的基础理论和实际应用，包括对于裂纹扩展和损伤分析的深入探讨。

5. "Damage Mechanics with Finite Elements: Practical Applications with Python and MATLAB Programs" by Christian Linder - 这本书以Python和MATLAB程序为基础，介绍了有限元法在损伤力学中的应用，帮助读者理解和解决实际问题。

请注意，这些教材的选择还要根据你的具体需求和程度来决定。

对于初学者，推荐选择较为综合的教材以了解基本概念和原理；对于有一定背景的学者，可以选择更加专业和深入的教材来进一步研究和应用相关内容。

2013 ap physics c 力学 scoring guidelines答案及解析

Distribution of points (e) i. 1 point For the correct amplitude xm 0.25 m ii. 2 points For some work that uses a correct expression for the period of a spring m T 2p k For correct substitution of consistent values 0.40 kg T 2p 3.1 s 1.6 N m Alternate Solution 1 point 1 point
© 2013 The College Board. Visit the College Board on the Web: .
Filename: ap13_physics_CM_scoring_guidelines_q1_rev02_6.20 Directory: P:\Editorial\Summer Work\2013\SCORING GUIDELINES\PHYSICS C M Template: C:\Users\lhamilton\AppData\Roaming\Microsoft\Templates\Normal.dotm Title: 1998 Physics B Solutions Distribution Subject: Author: University Housing Keywords: Comments: Creation Date: 6/20/2013 5:42:00 PM Change Number: 4 Last Saved On: 6/21/2013 12:13:00 PM Last Saved By: Windows SOE Manager Total Editing Time: 10 Minutes Last Printed On: 7/10/2013 3:40:00 PM As of Last Complete Printing Number of Pages: 4 Number of Words: 465 (approx.) Number of Characters: 2,651 (approx.)

国际课程IGCSE剑桥物理chap13

•The angles are measured with respect to the normal line. This is the line perpendicular to the reflecting surface.
Application of Reflection: Mirrors •The mirror is a reflecting surface and using the Law of Reflection we
•Incoming parallel light rays are converged to into the focal point of the lens.
•Light rays that enter the lens through the centre are unaltered and proceed with their original path.
•Converging lenses: lenses that converge incoming parallel rays of light
•Diverging lenses: lenses that diverge incoming parallel rays of light
•In this chapter we focus on converging lenses. These lenses bend light in the following way:
The majority of light refracts and a minority will reflect if i < c
The majority of light refracts with r = 90° and a minority will reflect if i = c.

ASS-2013-1

Applied Surface Science 264 (2013) 633–635Contents lists available at SciVerse ScienceDirectApplied SurfaceSciencej o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /a p s u scInﬂuence of pulsed electron beam treatment on microstructure and properties of TA15titanium alloyYu-kui Gao ∗College of Aerospace Engineering and Applied Mechanics,Tongji University,No.100of Zhangwu Road,Shanghai 200092,Chinaa r t i c l ei n f oArticle history:Received 8June 2012Received in revised form 16July 2012Accepted 15October 2012Available online 23 October 2012Keywords:Pulsed electron beam treatment Grade characteristics Nanoindenta b s t r a c tThe surface of TA15titanium alloy was modiﬁed by pulsed electron beam and the hardness distribution along the treated surface layer was investigated by nanoindent technology.The grade characteristics were therefore analyzed by studying the distribution of hardness along surface layer of specimens.Moreover,the microstructure was investigated by OM,XRD and TEM techniques.Furthermore,the correlation of hardness to microstructure was analyzed.The results show that the grade ﬁne grain microstructure is formed in the upper surface layer and the temperature grade or heat effect caused by pulsed electron beam treatment is the main reason to form grade ﬁne grain microstructure in the surface layer.© 2012 Elsevier B.V. All rights reserved.1.IntroductionTitanium alloys are employed in aerospace industry because of their remarkable characteristics:the high ratio of strength to weight,excellent corrosion resistance and good fatigue perfor-mance.TA15titanium alloy is widely used in Chinese aircraft to make parts,which have lighter weight,longer life and good corro-sion properties [1].Surface determines performance and many components’prop-erties are affected by the surface.Wear,fatigue,and corrosion are the main properties of many metallic materials.The effect of sur-face integrity on fatigue was investigated by many researchers.Surface integrity is a comprehensive concept which includes the change of chemical and mechanical properties of materials at the surface layer.It has four main categories and microstructure is the critical one [2].The wear of TA15titanium alloy is bad due to its lower hardness and worse surface resistance to fretting.How to improve the wear property of TA15titanium alloy by increasing surface hardness is an important problem in its applications.Pulsed electron beam treatment is a new surface modiﬁca-tion process and can be applied in many ﬁelds [3–7].There are many investigations on the effects of pulsed electron beam for measurements of properties and microstructures of the titanium alloys [8–12].Therefore,the wear property may be improved with increasing hardness in surface layer by ﬁner grain modiﬁed by pulsed electron beam.The hardness is greater when the grain is∗Corresponding author.Tel.:+862165981290;fax:+862165983267.E-mail address:yukuigao@ﬁner,therefore the wear property could be modiﬁed with the hard-ness increase of surface layer.However,the effect of surface ﬁne grain microstructure by electron beam treatment on hardness has been less investigated and therefore it is interesting and impor-tant to study the change of hardness along surface layer by electron beam treatment and to obtain the characteristics of grade ﬁne grain microstructure in surface layer with the nanoindent technology.2.Experimental material and methods2.1.Experimental materialTA15titanium alloy was employed in this investigation.Its chemical composition is listed in Table 1.The metal was annealed at 800◦C for 1h then had an air cooling.Its microstructure is mainly ␣phase and a little ␤phase.The tensile property of TA15titanium alloy is listed in Table 2.2.2.Experimental methodsThe surfaces of specimens were pulsed electron beam treated by the Solo type pulsed electron beam machine.The parameters of pulsed electron beam treatment are the pulsed duration time,t =15␮s,pulsed times,N =3pulses,kinetic energy,E =10–40keV,and pulsed energy density,E S =15J/cm 2.The microstructure of pulsed electron beam treated specimens was analyzed by OM.The phases and their contents were deter-mined by the D/max-2500/PCX type XRD tester.Moreover,the ﬁne grain characteristics were also analyzed by TEM method.0169-4332/$–see front matter © 2012 Elsevier B.V. All rights reserved./10.1016/j.apsusc.2012.10.083634Y.-k.Gao /Applied Surface Science 264 (2013) 633–635Table 1Chemical composition of TA15titanium alloy (wt.%).AlZrMoVFeSiONCTi5.9 2.1 1.71.90.210.110.080.020.09BalTable 2Tensile property of TA15titanium alloy.Tensile strengthYield strengthElongation 985MPa881MPa14%The hardness distribution along surface layer was determined by the Tribolndente nanoindent tester.The maximum applied load is 1␮N,and the grade characteristics were analyzed based on the hardness distribution along surface layer.3.Results and discussion3.1.Microstructures and phases of TA15titanium alloyThe microstructure of pulsed electron beam treated specimens is shown in Fig.1and there are three zones in Fig.1.The three zones are melted layer,heat affected layer and substrate [3]from the upper or top surface layer to matrix illustrated in Fig.1.Fig.1also shows two special zones,the melt layer and the affected layer along the cross section surface of pulse electron beam treated spec-imens.In the melt layer,ﬁne grain microstructure can be found and the ␤phase cannot be clearly seen because of great resistance of sin-gle ␣phase corrosion in ﬁne grain microstructure layer,as shown in Fig.1.The ﬁne grain microstructure is determined by XRD peak width illustrated in Fig.2and the size of the diffraction grain is about 168nm for the pulsed electron beam treated specimens.The size of the diffraction grain for the unmodiﬁed specimens is also deter-mined by XRD peak width as shown in Fig.3.The size of the diffraction grain is about 310nm for the unmodiﬁed annealed spec-imens.The ﬁner grains or diffraction domains can increase the hardness and make surface have a good wear property.3.2.Nanoindent hardness and grade characteristicsTo determine the grade characteristics of ﬁne grain microstruc-ture in surface layer and the effect of ﬁne grain microstructure on hardness in surface layer of the pulsed electron beam treated specimens,the distribution of hardness along surface layer was determined by the nanoindent hardnessmeasurement.Fig.1.Microstructure of TA15titanium alloy treated by pulsed electronbeam.Fig.2.XRD of pulsed electron beam treated specimens.The hardness along the cross section surface of the pulsed elec-tron beam specimens is illustrated in Fig.4.The matrix hardness is about 4.62GPa and the surface hardness of pulsed electron beam specimens is about 7.11GPa,the increment of hardness is about 2.49GPa and the increase percentage is 53%.The grade characteristics of ﬁne grain microstructure in the sur-face layer and the effect of ﬁne grain microstructure on hardness in surface layer can be determined by nanoindentmeasurementFig.3.XRD of referenced annealedspecimens.Fig.4.Hardness along cross section surface of pulsed electron beam specimens.Y.-k.Gao/Applied Surface Science264 (2013) 633–635635Fig.5.TEM images of pulsed electron treated specimens.(a)BF image(b)SAED pattern(c)indexed diffraction pattern.technology.It can be seen that the gradient of hardness in surface layer about25␮m as shown in Fig.4is greater and this depth is equal to the depth of the melt layer,which is illustrated in Fig.1. The gradient of hardness beneath the melt layer between25␮m and50␮m is smaller and the gradient of hardness for the distance of50␮m from the surface to the distance of80␮m is about zero.The great increase in hardness of the surface melt layer should be related to the formation ofﬁne grain microstructure during pulsed electron beam treatment.The grain or domain size is gettingﬁner induced by pulsed electron beam treatment;the hardness will be higher because of the higher yield strength.The smaller width of martensite lentil microstructure can be found in the melt layer,as shown in Fig.5.The width of some martensite lathes is about90nm and the SAED pattern in Fig.5shows the lattice distort and the ﬁner grain which make the diffraction dots become the extended diffraction dots or even some short diffraction continue lines.The hardness is affected mainly by the factors ofﬁne grain microstructure and the heat effect during pulsed electron beam treating process.Theﬁne grain or small domain size can improve the hardness,and at the same time the surface melted layer has the less effect of heat after pulsed electron beam treatment due to short time,therefore,the gradient of hardness from surface to50␮m is great and mainly determined by theﬁne grain effect,althoughﬁne grains are formed through being re-melted with a high temperature induced by pulsed electron beam treatment.The gradient of hardness beneath the melt layer where from the surface between50␮m and80␮m is smaller and near to zero just because of a balance of theﬁne grain size effect and the heat effect induce by pulsed electron beam treatment.Theﬁne grain effect makes an increase in hardness,but the heat effect decreases hardness.The increase in hardness may also be related to the phase trans-formation,but the quantitative analysis of phases content by XRD illustrates that no any new phase occurs in the pulsed electron beam treated specimens and the change of phase content of both␣and␤is less than5%,therefore,the increase of hardness by pulsed electron modiﬁcation should be mainly due to theﬁne grain size effect.4.Conclusions(1)Theﬁne grain microstructure can be formed in melt layerinduced by pulsed electron beam treatment.(2)The grade characteristics ofﬁne grain microstructure in surfacelayer and the effect ofﬁne grain microstructure on hardness can be determined by nanoindent technology.(3)The great increment of hardness in the surface melt layer shouldbe related to the formation ofﬁne grain microstructure during pulsed electron beam treatment.(4)The gradient of hardness beneath the melt layer is greater dueto theﬁne grain size effect.AcknowledgementThe author is grateful for the foundation support from Pro-gram of Ministry of Science and Technology of China(contract nos. 200473-3641and08-039577).References[1]J.Y.Wang,Z.M.Ge,B.Y.Zhou,Titanium Alloys in Aeronautical Application,Shanghai Science Press,Shanghai,1985,p.68.[2]Y.K.Gao,X.B.Li,Q.X.Yang,M.Yao,Inﬂuence of surface integrity on fatiguestrength of42CrNi2Si2MoVA steel,Mater.Lett.61(2007)466–469.[3]A.D.Pogrebnyak, D.I.Proskurovskii,Modiﬁcation of metal surface layerproperties using pulsed electron beams,Phys.Status Solidi A145(1994) 9–49.[4]D.I.Proskurovsky,V.P.Rotshtein,G.E.Ozur,A.B.Markov,D.S.Nazarov,Pulsedelectron-beam technology for surface modiﬁcation of metallic materials,J.Vac.Sci.Technol.A16(1998)2480–2488.[5]A.D.Pogrebnjak,Metastable states and structural phase change in metals andalloys exposed to high power pulsed ion beams,Phys.Stat.Sol.117A(1990) 17–35.[6]V.P.Rotshtein,D.I.Proskurovsky,G.E.Ozur,Yu.F.Ivanov,A.B.Markov,Surfacemodiﬁcation and alloying of metallic materials with low-energy high-current electron beams,Surf.Coat.Technol.180–181(2004)377–381.[7]Y.K.Gao,Surface modiﬁcation of TA2pure titanium by low energy highcurrent pulsed electron beam treatments,Appl.Surf.Sci.257(2011) 7455–7460.[8]A.D.Pogrebnjak,A.P.Kobzev,B.P.Gritsenko,Effect of Fe and Zr ion implantationand high-current electron irradiation treatment on chemical and mechanical properties of Ti–V–Al Alloy,J.Appl.Phys.87(2000)2142–2148.[9]A.D.Pogrebnjak,E.A.Bazyl,Modiﬁcation of wear and fatigue characteristics ofTi–V–Al alloy by Cu and Ni ion implantation and high-current electron beam treatment,Vacuum64(2002)1–7.[10]A.D.Pogrebnjak,S.Bratushka,V.I.Boyko,et al.,A review of mixing processes inTa/Fe and Mo/Fe systems treated by high current electron beams,Nucl.Instrum.Meth.B B145(1998)373–390.[11]T.Grosdidier,J.X.Zou,B.Bolle,S.Z.Hao,C.Dong,Grain reﬁnement,hardeningand metastable phase formation by high current pulsed electron beam(HCPEB) treatment under heating and melting modes,J.Alloys Compd.504S(2010) S508–S511.[12]X.D.Zhang,S.Z.Hao,X.N.Li,C.Dong,T.Grosdidier,Surface modiﬁcation of puretitanium by pulsed electron beam,Appl.Surf.Sci.257(2011)5899–5902.。

AP物理C力学模拟卷MultipleChoiceQuestions

AP物理C⼒学模拟卷MultipleChoiceQuestionsMultiple Choice QuestionsTime: 45 minutes. You may refer to the Constants sheet. However, you may not use the Equations sheet, and you may not use a calculator on this portion of the exam.1. A cannon is mounted on a truck that moves forward at a speed of 5m/s. The operator wants to launch a ball from a cannon so the ball goes as far as possible before hitting the level surface. The muzzle velocity of the cannon is 50 m/s. What angle from the horizontal should the operator point the cannon?A.5°B.41°C.45°D.49°E.85°2. A car moving with speed v reaches the foot of an incline of angleθ. The car coasts up the incline without using the engine.Neglecting friction and air resistance, which of the following is correct about the magnitude of the car's horizontal acceleration aand vertical acceleration a y?xA.a x = 0; a y < gB.a x = 0; a y = gC.a x < g ; a y < gD.a x < g ; a y = gE.a x < g ; a y > g3. A bicycle slows down with an acceleration whose magnitude increaseslinearly with time. Which of the following velocity–time graphs could represent the motion of the bicycle?4. A cart is sliding down a low friction incline. A device on the cartlaunches a ball, forcing the ball perpendicular to the incline, as shown above. Air resistance is negligible. Where will the ball land relative to the cart, and why?A.The ball will land in front of the cart, because the ball'sacceleration component parallel to the plane is greater thanthe cart's acceleration component parallel to the plane.B.The ball will land in front of the cart, because the ball hasa greater magnitude of acceleration than the cart.C.The ball will land in the cart, because both the ball and thecart have the same component of acceleration parallel to theplane.D.The ball will land in the cart, because both the ball and thecart have the same magnitude of acceleration.E.The ball will land behind the cart, because the ball slowsdown in the horizontal direction after it leaves the cart.5.The quantity "jerk," j, is defined as the time derivative of anobject's acceleration,What is the physical meaning of the area under a graph of jerk vs.time?A.The area represents the object's acceleration.B.The area represents the object's change in acceleration.C.The area represents the object's change in velocity.D.The area represents the object's velocity.E.The area represents the object's change in position.6. A particle moves along the x-axis with a position given by theequation x(t) = 5 + 3t, where x is in meters, and t is in seconds.The positive direction is east. Which of the following statements about the particle is FALSE.0.The particle is east of the origin at t = 0.1.The particle is at rest at t = 0.2.The particle's velocity is constant.3.The particle's acceleration is constant.4.The particle will never be west of position x = 0.7. A mass hangs from two ropes at unequal angles, as shown above. Whichof the following makes correct comparisons of the horizontal and vertical components of the tension in each rope?8.The force of air resistance F on a mass is found to obey the equationF = bv2, where v is the speed of the mass, for the range of speedsinvestigated in an experiment. A graph of F N vs. v2 is shown above.What is the value of b?.0.83 kg/mA. 1.7 kg/mB. 3.0 kg/mC. 5.0 kg/mD. 1.0 kg/mE.zero9. A box sits on an inclined plane without sliding. As the angle ofthe plane (measured from the horizontal) increases, the normal force.increases linearlyA.decreases linearlyB.does not changeC.decreases nonlinearlyD.increases nonlinearly10.Which of the following conditions are necessary for an object tobe in static equilibrium?.The vector sum of all torques on the object must equal zero.I.The vector sum of all forces on the object must equal zero.II.The sum of the object's potential and kinetic energies must be zero.C.I onlyD.II onlyE.III onlyF.I and II onlyG.I, II, and III11.A student pushes a big 16-kg box across the floor at constant speed.He pushes with a for ce of 50 N angled 35° from the horizontal, as shown in the diagram above. If the student pulls rather than pushes the box at the same angle, while maintaining a constant speed, what will happen to the force of friction?.It must increase.A.It must decrease.B.It must remain the same.C.It will increase only if the speed is greater than 3.1 m/s.D.It will increase only if the speed is less than 3.1 m/s.12.Consider a system consisting only of the Earth and a bowling ball,which moves upward in a parabola above Earth's surface. The downward force of Earth's gravity on the ball, and the upward force of the ball's gravity on the Earth, form a Newton's third law force pair.Which of the following statements about the ball is correct?.The ball must be in equilibrium since the upward forces must cancel downward forces.A.The ball accelerates toward the Earth because the force ofgravity on the ball is greater than the force of the ball onthe Earth.B.The ball accelerates toward the Earth because the force ofgravity on the ball is the only force acting on the ball.C.The ball accelerates away from Earth because the forcecausing the ball to move upward is greater than the force ofgravity on the ball.D.The ball accelerates away from Earth because the forcecausing the ball to move upward plus the force of the ballon the Earth are together greater than the force of gravityon the ball.13.A mass m is attached to a mass 3m by a rigid bar of negligible massand length L. Initially, the smaller mass is located directly above the larger mass, as shown above. How much work is necessary to flip the rod 180° so that the lar ger mass is directly above the smaller mass?.4mgLA.2mgLB.mgLC.4pmgLD.2pmgL14.A ball rolls horizontally with speed v off of a table a height habove the ground. Just before the ball hits the ground, what is its speed?.A.B.C.vD.15.A pendulum is launched into simple harmonic motion in two differentways, as shown above, from a point that is a height h above its lowest point. During both launches, the bob is given an initial speed of3.0 m/s. On the first launch, the initial velocity of the bob isdirected upward along the pendulum's path, and on the second launch it is directed downward along the pendulum's path. Which launch will cause the pendulum to swing with the larger amplitude?.the first launchA.the second launchB.Both launches produce the same amplitude.C.The answer depends on the initial height h.D.The answer depends on the length of the supporting rope.16.The mass M is moving to the right with velocity v0 at position x= x0. Neglect friction. The spring has force constant k. What is the total mechanical energy of the block at this position?17.A sphere, a cube, and a cylinder, all of equal mass, are releasedfrom rest from the top of a short incline. The surface of the incline is extremely slick, so much so that the objects do not rotate when released, but rather slide with negligible friction. Which reaches the base of the incline first?.the sphereA.the cubeB.the cylinderC.All reach the base at the same time.D.The answer depends on the relative sizes of the objects.18.Block B is at rest on a smooth tabletop. It is attached to a longspring, which is in turn anchored to the wall. Block A slides toward and collides with block B. Consider two possible collisions: Collision I: Block A bounces back off of block B.Collision II: Block A sticks to block B.Which of the following is correct about the speed of block Bimmediately after the collision?.It is faster in case II than in case I ONLY if block B is heavier.A.It is faster in case I than in case II ONLY if block B isheavier.B.It is faster in case II than in case I regardless of the massof each block.C.It is faster in case I than in case II regardless of the massof each block.D.It is the same in either case regardless of the mass of eachblock.19.A 0.30-kg bird is flying from right to left at 30 m/s. The birdcollides with and sticks to a 0.50-kg ball which is moving straight up with speed 6.0 m/s. What is the magnitude of the momentum of the ball/bird combination immediately after collision?.12.0 N?sA.9.5 N?sB.9.0 N?sC. 6.0 N?sD. 3.0 N?s20.The force F on a mass is shown above as a function of time t. Whichof the following methods can be used to determine the impulse experienced by the mass?.multiplying the average force by t maxI.calculating the area under the line on the graphII.taking the integralC.II onlyD.III onlyE.II and III onlyF.I and II onlyG.I, II, and III21.A projectile is launched on level ground in a parabolic path so thatits range would normally be 500 m. When the projectile is at the peak of its flight, the projectile breaks into two pieces of equal mass. One of these pieces falls straight down, with no further horizontal motion. How far away from the launch point does the other piece land?.250 mA.375 mB.500 mC.750 mD.1000 mQuestions 22 and 23A rigid rod of length L and mass M is floating at rest in space farfrom a gravitational field. A small blob of putty of mass m < M is moving to the right, as shown above. The putty hits and sticks to the rod a distance 2L/3 from the top end.22.How will the rod/putty contraption move after the collision?.The contraption will have no translational motion, but will rotate about the rod's center of mass.A.The contraption will have no translational motion, but willrotate about the center of mass of the rod and putty combined.B.The contraption will move to the right and rotate about theposition of the putty.C.The contraption will move to the right and rotate about thecenter of mass of the rod and putty combined.D.The contraption will move to the right and rotate about therod's center of mass.23.What quantities are conserved in this collision?.linear and angular momentum, but not kinetic energyA.linear momentum onlyB.angular momentum onlyC.linear and angular momentum, and linear but not rotationalkinetic energyD.linear and angular momentum, and linear and rotationalkinetic energy24.A car rounds a banked curve of uniform radius. Three forces act onthe car: a friction force between the tires and the road, the normal force from the road, and the weight of the car. Which provides the centripetal force which keeps the car in circular motion?.the friction force aloneA.the normal force aloneB.the weight aloneC. a combination of the normal force and the friction forceD. a combination of the friction force and the weight25.A ball of mass m anchored to a string swings back and forth to amaximum position A, as shown above. Point C is partway back to the vertical position. What is the direction of the mass's acceleration at point C?.along the mass's path toward point BA.toward the anchorB.away from the anchorC.between a line toward the anchor and a line along the mass'spathD.along the mass's path toward point A26.In a carnival ride, people of mass m are whirled in a horizontalcircle by a floorless cylindrical room of radius r, as shown in the diagram above. If the coefficient of friction between the people and the tube surface is µ, what minimum speed is necessary to keep the people from sliding down the walls?Questions 27 and 28The uniform, rigid rod of mass m, length L, and rotational inertiaI shown above is pivoted at its left-hand end. The rod is released from rest from a horizontal position.27.What is the linear acceleration of the rod's center of mass the moment after the rod is released?28.What is the linear speed of the rod's center of mass when the mass passes through a vertical position?29.The 1.0-m-long non-uniform plank, shown above, has weight 1000 N.It is to be supported by two rods, A and B, as shown above. The center of mass of the plank is 30 cm from the right edge. Each support bears half the weight of the plank. If support B is 10 cm from the right-hand edge, how far from the left-hand edge should support A be?.0 cmA.10 cmB.30 cmC.50 cmD.70 cm30.A mass m on a spring oscillates on a horizontal surface with periodT. The total mechanical energy contained in this oscillation is E.Imagine that instead a new mass 4m oscillates on the same springwith the same amplitude. What is the new period and total mechanical energy?31.A mass m is attached to a horizontal spring of spring constant k.The spring oscillates in simple harmonic motion with amplitude A.What is the maximum speed of this simple harmonic oscillator?32.An empty bottle goes up and down on the surface of the ocean, obeyingthe position function x= Acos(t). How much time does this bottle take to travel once from its lowest position to its highestposition?33.The Space Shuttle orbits 300 km above the Earth's surface; theEarth's radius is 6400 km. What is the acceleration due to Earth's gravity experienced by the Space Shuttle?. 4.9 m/s2A.8.9 m/s2B.9.8 m/s2C.0.8 m/s2D.zero34.An artificial satellite orbits Earth just above the atmosphere ina circle with constant speed. A small meteor collides with thesatellite at point P in its orbit, increasing its speed by 1%, but not changing the instantaneous direction of the satellite's velocity. Which of the following describes the satellite's new orbit?.The satellite now orbits in an ellipse, with P as the farthest approach to Earth.A.The satellite now orbits in an ellipse, with P as the closestapproach to Earth.B.The satellite now orbits in a circle of larger radius.C.The satellite now orbits in a circle of smaller radius.D.The satellite cannot maintain an orbit, so it flies off intospace.35.Mercury orbits the sun in about one-fifth of an Earth year. If 1AU is defined as the distance from the Earth to the sun, what is the approximate distance between Mercury and the sun? .(1/25) AUA.(1/9) AUB.(1/5) AUC.(1/3) AUD.(1/2) AU。

ap-physics-1-syllabus-development-guide

The course design provides opportunities for students to develop understanding of the AP Physics 1 foundational physics principles in the context of the big ideas that organize the curriculum framework. The course design provides opportunities for students to develop understanding of the foundational principles of dynamics in the context of the big ideas that organize the curriculum framework. The syllabus must identify all of the big ideas connected to dynamics. The syllabus must explicitly include Newton’s laws. Big ideas: encompass the core scientific principles, theories, and processes of physics that cut across traditional content boundaries and provide students a broad way of thinking about the physical world. 1. In a list or chart of topics covered, dynamics is included and connected to Big Ideas 1, 2, 3, and 4. Unit: Dynamics (Big Ideas 1, 2, 3, and 4). • Newton’s laws 2. The syllabus indicates instruction in Newton’s laws and connects these to Big Ideas 1, 2, 3, and 4. 3. The laboratory section of the syllabus includes investigative questions related to the relationship between force and motion (Newton’s laws) and connects them to Big Ideas 1, 2, 3, and 4.

AP物理C力学必备知识梳理

AP物理C力学对于目标工科的留学党来讲，AP物理C几乎是必学科目。

当然还有纯粹对AP物理C是爱好的小伙伴们，今天小编为小伙伴们梳理了AP 物理C力学的考点，内容很全，尤其适合考前梳理，一起来看一下吧。

Newtonian Mechanics牛顿力学、占整个PhysicsC力学考试的100%Kinematics运动学占18%“矢量（vectors）的概念既有大小，又有方向；矢量代数（vector algebra）.矢量和的三角形法则是必须熟练掌握的，最简单的记忆方法就是花萌萌面对两段直的折线路径（对应两段位移矢量之和），她会选择直接连接出发点和终点的直线捷径（等效的对应两个位移矢量和），这样构成了一个矢量和三角形。

“矢量的点乘A·B=ABcosΘ（加重符号都表示矢量）和叉乘（大小）／A×B／=／ABsinΘ／（叉乘结果是矢量，方向为从A绕到B的右手螺旋系大拇指方向），Θ为矢量A和B的夹角。

矢量的加减，点乘和叉乘，是矢量分析的基础，是我们学习AP物理C的基本数学框架一定要熟练掌握。

矢量在直角坐标系中的分量（components of vectors, coordinate systems）,特别强调的是物理上只会用“右手系”，也就是从X轴到Y轴的右手螺旋拇指指向Z轴，这个和叉乘的定义是一样的，好记！有了ta，大家在学电磁学的时候就不用左右手的拧麻花了。

AP 物理C还需要掌握柱坐标和球坐标，这在需要柱对称和球对称的积分问题时，就很有用了。

“运动学中要用到的三大矢量位移、速度和加速度（displacement, velocity and acceleration)，特别要注意别把距离（或者叫路程distance），速率（speed）和前面的概念搞混了，后两个概念是标量，只有在一些特殊情况下才和对应矢量的模（大小）相等。

“一维运动（Motion in one dimension）一维运动的矢量性就记住有正负的方向就行，对于一维匀加速直线运动，务必掌握其最重要的三个方程：第一,求速度的公式Vf=V i+at角标i（initial）和f（final）总是代表初和末，这个公式只要从匀加速度等于平均加速度的定义就可以得到：第二,求位移的公式ΔX= V it + 1/2 at2这个公式可以理解为保持初速度的匀速运动位移和初速为零的匀加速运动位移之和第三,2aΔX= Vf2-Vi 2公式是把前面两个公式消去变量⊿t，得：更方便的记忆方法是公式左边用牛顿第二定律F=ma，变成外力做功的形式：F⊿x, 左边多出来的2/m转到右边，右边就正好得到物体动能的变化。

弹性力学基础-中英

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

AP Physics C – Mechanics：AP物理C–力学

COURSE DESCRIPTIONThe New York State course in Regents Physics is an excellent introduction to physics for the college bound senior. Many students embark on their university career without knowing exactly what they want to study. Taking physics in high school can open many doors for students who find that they want to major in a technical area. Students who take high school physics can obviously expect to do far better in university physics courses than those students who have not.Taking a course in physics gives the student a stronger foundation in problem-solving strategies and critical thinking. These are exactly the areas in which many universities and employers are complaining that candidates are not skilled enough!The Regents course is comprehensive in scope with each subject is treated with the proper depth for the average student. Students are prepared for, and expected to take, the Regents Physics exam in June.There are two prerequisites for this course. First, students should have completed Regents Biology, Regents Earth Science and Regents Chemistry. Without previous science experience, it will be difficult to do well in this class. Second, students should have completed two Regents Math exams. This course requires the understanding of algebra and fundamental knowledge of geometry that you gain from your math class.We meet every day for 40 minutes with an additional 40 minute lab period every-other day. At the completion of this course students should have a strong conceptual understanding of required topic and be able to complete all required physics laboratory experiments.COURSE TOPICS1. The science of physics2. Kinematics and Mechanics3. Energy and Momentum4. Electricity and Magnetism5. Vibration and Waves6. Modern PhysicsRESOURCES AND HELPFUL LINKSTextbook - Holt Physics, by Raymond A Servway and Jerry Faughn,/physics//.au/online/sciences/physics/t utes1.html/en/simulations/category/physics //Domain/248/physics/http://hyperphysics.phy-/hbase/hph.html#mechcon/physlet_resources/bu_ semester1/index.html/mathphysics.htmlhttp://www.walter-fendt.de/ph14e/stwaverefl.htmGRADING POLICYCategory 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter Tests & Exams 60% 40% 60% 60% Lab 5% 5% 5% 5% Project/formal lab 5% 5% 5% 5% Class work/ Participation 10% 10% 10% 10% Homework 20% 20% 20% 20%Midterm Exam 20%Course GradeStudents will receive a course grade that is an average of their grade for each of the four quarters and their score on the Regents Exam. Thus, each quarter and the Final Exam will comprise 20% of the final course grade.MidtermThe physics department administers a district-wide midterm exam during "Midterm Week" in January. This exam includes Regents level questions and will count for 20% of the student's second quarter grade.Tests and ExamsA test is a 25 point assessment with a blend of multiple choice and extended response questions. Tests are typically given in the middle of a large unit of instruction. An exam is given at the end of each unit and is a two part assessment. Part One of the assessment will consist of 30 multiple choice questions. Part Two of the assessment will consist of 20 points worth of extended response questions. All tests and exams are built using questions from past Regents exams and/or questions based directly on Regents exam questions.LabAll labs will be documented in a personal lab-notebook which will be kept in the classroom. Students will be required to complete at least 1200 minutes of lab (about 30 labs) time with a complete lab report in order to pass the course.Project/Formal LabOne lab per quarter will be designated as a "formal lab". This lab will be subjected to strict grading criteria and will be important in teaching students how to produce high quality lab reports.One project is also assigned every quarter. This project is for students to construct some type of device after school and write a report about the project.Class work / ParticipationClass work includes any formal or informal assessment of student work or preparedness for class. Most of the class work grades will consist of "Do Now's", "Exit Slips", and "Activities". Participation includes attendance, attentiveness to tasks during class and ability to work well with others. Participation grade heavily rewards effort on the part of the student.HomeworkHomework is assigned every day; it will take an average student about half an hour to complete. Homework will be collected and graded daily. According to research, completion of homework in high school produces a gain of about 24 percentile points.REQUIRED SUPPLIES▪Lab notebook▪Binder for class notes and homework▪Protractor with ruler▪CalculatorTENTATIVE SCHEDULE。

2013-Yuanshen Huang-APPLIED OPTICS-Calculation of the

Calculation of the diffraction efficiency on concave gratings based on Fresnel–Kirchhoff’sdiffraction formulaYuanshen Huang,1,*Ting Li,1Banglian Xu,1Ruijin Hong,1Chunxian Tao,1 Jinzhong Ling,1Baicheng Li,1Dawei Zhang,1,2Zhengji Ni,1and Songlin Zhuang1 1Engineering Research Center of Optical Instrument and System,Ministry of Education and Shanghai Key Laboratory of Modern Optical Systems,University of Shanghai for Science and Technology,No.516JunGong Road,Shanghai200093,China2School of Electrical and Electronic Engineering,Nanyang Technological University,50Nanyang Avenue,Singapore639798,Singapore*Corresponding author:hyshyq@Received19October2012;revised29December2012;accepted8January2013;posted9January2013(Doc.ID178382);published8February2013Fraunhofer diffraction formula cannot be applied to calculate the diffraction wave energy distribution ofconcave gratings like plane gratings because their grooves are distributed on a concave spherical surface.In this paper,a method based on the Kirchhoff diffraction theory is proposed to calculate the diffractionefficiency on concave gratings by considering the curvature of the whole concave spherical surface.Ac-cording to this approach,each groove surface is divided into several limited small planes,on which theKirchhoff diffraction field distribution is calculated,and then the diffraction field of whole concave grat-ing can be obtained by superimposition.Formulas to calculate the diffraction efficiency of Rowland-typeand flat-field concave gratings are deduced from practical applications.Experimental results showedstrong agreement with theoretical computations.With the proposed method,light energy can be opti-mized to the expected diffraction wave range while implementing aberration-corrected design of concavegratings,particularly for the concave blazed gratings.©2013Optical Society of AmericaOCIS codes:300.6190,090.2890,120.4820,050.1950.1.IntroductionConcave gratings play an important role in spectro-scopy field since they integrate the functionality of dispersion and focus together.In most cases high re-solution is a quite important indicator to evaluate the performance of gratings,but it is not the unique criterion,especially in the situation of weak spectral energy,more attention should be paid to concentrate the diffraction light energy on the specific wave-length range.Therefore,calculation for the energy distribution of the diffraction field is also a signifi-cant task.The theoretical system for plane gratings was established based on the Fraunhofer diffraction theory.Born and Wolf[1]calculated the diffraction efficiency of a plane grating by solving the transmis-sion field of multiple slits.As for many different kinds of plane gratings,blazed grating is regarded as a vital one because its diffraction energy can be concentrated near an expected wavelength just by changing the angle of groove surfaces,which is de-scribed in detail by Hutley[2]for both transmission and reflection plane blazed gratings.For a more ac-curate calculation,the groove patterns and material properties of gratings must be bine with the boundary condition of grating,diffraction fields of transverse electric and transverse magnetic polarization are first obtained by solving the Maxwell’s equations,after which the diffraction1559-128X/13/051110-07$15.00/0©2013Optical Society of America1110APPLIED OPTICS/Vol.52,No.5/10February2013efficiency is computed[3].Moharam and Gaylord proposed the rigorous coupled-wave theory and set up the theoretical model on calculating diffraction ef-ficiency of one-dimensional rectangular gratings[4]. This theory was developed for suiting arbitrary grat-ing groove profile later[5–8].The above-mentioned theories are just fit for plane gratings with equidi-stant and straight grooves.Although the concave grating was first introduced by Rowland as early as1882[9],only a few studies on the calculation of its diffraction efficiency were reported.One reason is that grooves of a concave grating are distributed on a concave substrate,wherein the Fraunhofer dif-fraction equation cannot be used.Moreover,if vector diffraction theory is selected,the two-dimensional groove surfaces must be divided into a finite number of small units,and then the diffraction field on each unit is calculated with considering the boundary con-dition among adjacent units.Obviously the more units we divided,the more accurate result can be got,but the data volume is becoming larger at the same time,which means a more complex computa-tion.Another reason is that in the concave grating application,the incident wave is divergent spherical wave emitted by point light source and becomes con-vergent after the grating diffraction.Therefore,the positions of both source and receiving surface have to be considered simultaneously in the diffraction efficiency calculation,which will also increase the difficulty of the process.At present,most fabricants and users of concave gratings generally use the ac-tual measuring instruments to obtain the diffraction efficiency.As a result,diffraction energy cannot be designed to concentrate in the specific wavelength range before manufacturing,which will cause a waste of resource and time.Few studies have been published about the diffrac-tion efficiency of concave gratings.Hunter and co-workers[10,11]reported the differences of diffrac-tion efficiency between holographic lithography grating and mechanical ruled grating based on the-oretical calculations and experimental results.But the authors adopted plane grating model for approx-imation due to the small curvature of the selective concave grating.Bazhanov and Kulakova[12]estab-lished the functional relation between grooves at arbitrary position and the apex of the concave grat-ing.Analytic expressions of diffraction energy distri-bution were derived by utilizing the geometrical relation between incident rays of arbitrary grooves and principle one.Kulakova et al.[13]set up the mathematic model on a concave grating when the spherical wave was incident.The analysis on the dis-tribution as well as variable spacing of grooves was added,and then the diffraction efficiency distribu-tion in the principal section was discussed by both the scalar and vector method.Ko et al.[14]first discovered the double-reflection phenomenon of the concave blazed grating and simulated the diffrac-tion efficiency of Rowland-type concave grating by PCGrate software.However,all the calculation models on diffraction efficiency discussed above were established in the principal section of a concave grating,which ignored the influence of the nonprincipal section.This pre-supposition will cause large errors when the grating curvature is big.An ideal calculation model should consider the influence of the entire concave surface on the diffraction efficiency.According to this thought,a calculation model on the concave grating with sawtooth grooves is going to be established un-der spherical wave incidence.The whole procedure can be described as three main steps:first,an arbitrary grating groove was divided into finite dif-fraction apertures and the diffraction complex ampli-tude on each aperture was calculated based on the Fresnel–Kirchhoff’s diffraction formula.Then the total complex amplitude of the whole concave grating is got by superimposing the results from all aper-tures of every groove.Finally,the diffraction effi-ciency of a concave grating is obtained by a simple transformation from the complex amplitude.In this article,the relationship between the diffraction efficiency of a Rowland-type concave grating and different parameters,i.e.,incident angle,F number, number of grooves,is analyzed,respectively.The calculation method of diffraction efficiency for a flat-field concave grating is illustrated,and the peak variations are compared among different usage con-ditions.Experimental results are also given in the end,which show basically coincident with the theo-retical computation,and hence the proposed method will provide some certain reference values to the design and fabrication of a concave grating.2.PrincipleSupposing grooves of a concave grating are formed on the reflective coating that is deposited on the concave substrate.Due to mechanical ruling with a diamond graver is a commonly used manufacturing way,groove shapes are sawtooth with a definite an-gle or triangular which is consistent with the cutter edge of graver.Generally,all grooves are parallel and distributed along a certain orientation,so the projec-tions on the tangent plane of the grating vertex are straight lines that are either equidistant or nonequi-distant.According to different operating conditions, the grating grooves can also be equidistant or none-quidistant curves after carrying out aberration-corrected design.In this article we focus on the former situation.A.Rowland-Type Concave GratingIf the incident slit is set on the Rowland circle,the diffraction image will focus automatically on the same circle[9].Sharp spectral lines can be obtained in this situation since the meridional astigmatic is zero on the Rowland circle.This kind of device has wide applications due to its simple structure and con-venient adjustment.As shown in Fig.1,first we assume the N pieces of sawtooth grooves are equidistant and parallel to 10February2013/Vol.52,No.5/APPLIED OPTICS1111each other.A coordinate system is set up with the ori-gin at the vertex O 0;0;0 of the concave grating,Xaxis points to the normal direction at vertex while Z axis parallels to the tangential direction of grooves.Grating substrate is a spherical surface with curva-ture radius R ,and its center is at C 0;0;R .In the principal section (XOY plane),a spherical wave emitted from A r cos θ;−r sin θ;0 is diffracted when encountering an arbitrary point P x;y;z on any groove surface,and the image point for a certain wavelength will be focused on A 0 r 0cos θ0;r 0sin θ0;0 ,which lies on the Rowland circle too.According to the characteristic of fabrication,each groove surface is a cone surface rotating about a cer-tain rotor,with the diamond blade used as genera-trix.Different groove faces have different rotating shafts,but they are all parallel to the Y axis and the distance from them to the bottom of their corre-sponding groove is equal to R .Therefore,grating pro-files ruled in this way are parallel straight grooves.As point P x;y;z located on the spherical surface,its coordinate values must satisfy the spherical equationx −R 2 y 2 z 2 R 2:(1)Then since principal rays meet the grating equa-tion,which can be denoted bysin θ−sin θ01e 0k λ;(2)where e 0is the grating constant at vertex O ,k is the diffraction order,λis the diffraction wavelength,θand θ0are the incident and diffraction angles,respec-tively.Each groove face is equally divided into n pieces of small diffraction units,each of which can be considered approximately as a small plane.The dimension of these small planes is larger than wave-length,but much smaller than the distance from A or A 0to points on these diffraction units.Assuming n p represents the normal vector of a small plane at point P ,so the Fresnel –Kirchhoff ’s diffraction formula corresponding to this plane can be expressed as~E i A 0B i λZZ Σexp ikr r exp ikr 0 r 0×cos n p ;r −cos n p ;r 02d σ;(3)wherer j AP j x −r cos θ 2 y −r sin θ 2 z 2 12;(4)r 0 j A 0P j x −r 0cos θ0 2 y −r 0sin θ0 2 z 2 12;(5)cos n p ;rnp ·r j np j ·j r j ;(6)cos n p;r 0np ·r 0j np j ·j r 0j :(7)As shown in Fig.2,αis the angle between groovesurface at vertex O and Y axis,then the normal vector n p is got by using space analytic geometry np −cos αR −x zR ;sin αcos θR −x zR sin αsin θR ;cos αR: 8Assuming that the grating width and height are W and H ,respectively,then the grating constant e 0for equidistant grating can be written as:e 0 w ∕N ,and the height of each small diffraction unit is H ∕n .Obviously ,the larger the n chosen,the more accurate the calculation results will be.The complex ampli-tude of a single groove at point A 0can be expressed as follows:~E j A 0 X n i 1~E i A 0 :(9)Fig.1.Structure of Rowland-type concavegrating.Fig.2.Principal section of concave grating.1112APPLIED OPTICS /Vol.52,No.5/10February 2013Then the total complex amplitude at point A0for the whole N pieces of groove can be written as~E A0X Nj 1~EjA0 :(10)The diffraction field distribution of Rowland-type concave gratings can be calculated by Eqs.(1)–(10). At a certain order,the light intensity distribution for different wavelengths can be obtained by squar-ing the relevant total complex amplitude,which pro-vides significant reference values to the design of concave grating with high resolution and reasonable energy distribution.B.Flat-Field Concave GratingWith the extensive applications of linear and area-array detectors,optical spectrum instruments are developed to the direction of miniaturization,high-speed,and simultaneous multichannel detection. These instruments need to focus the detected spec-trums onto a plane.In this case,flat-field concave grating is considered as an ideal spectral component which can disperse the incident light in one plane after aberration-corrected design and precision grat-ing fabrication.For a flat-field concave grating with given incident slit and image position,if we take an astigmatism-corrected design for the most signifi-cant astigmatism,the grating grooves will change into nonequidistant parallel straight lines,and its distribution function is defined asy 12u20y2 e0m;(11)where m 0; 1; 2…,e0is the effective grating constant at the grating vertex,and u20is a constant getting from the astigmatism-corrected calcula-tion[15,16].Figure3shows the schematic diagram of the flat-field concave grating,where A is the midpoint of in-cident slit,A0is a diffraction image focused on the plane L for a certain wavelength,and r0is the dis-tance from an arbitrary point P of grooves to the im-age point on the plane L.The method of calculating the diffraction efficiency is the same as that dis-cussed in Subsection2.A,except that the grooves are no longer equidistant.The distribution of gratinggrooves must be calculated first by Eq.(11)and thencombined with Eqs.(3)and(10)to obtain the finalresult.3.Simulation and ExperimentsA.Software Simulation by MatlabAccording to the theoretical model presented above,we simulated the diffraction efficiencies of Rowland-type and flat-field concave gratings with sawtoothgrooves at visible wavelengths(400–700nm).The in-fluence of several parameters,like incident angle,Fnumber,and number of grooves on diffractionefficiency,is discussed separately.1.Effects of Incident Angle on Diffraction EfficiencyFigure4shows the 1st-order diffraction efficiencycurves of Roland-type concave grating,which varies with wavelength at different incident angles.Thegrating grooves are parallel and equidistant with adensity of600g∕mm,the angles of their surfacesare all equal to10°.Grating substrate size is 10mm×10mm.The selected incident angles are 6°,8°,and10°.As we can see from Fig.4,the peak of diffractionefficiency shifts to the longer wavelength as the inci-dent angle gradually increases.According to this reg-ulation,maximum diffraction efficiency can be optimized to the necessary spectrum range by adjust-ing the incident angle,which will greatly increase the utilization of energy.2.Effects of F Number on Diffraction EfficiencyF number is one of the most important factors that influence the diffraction efficiency.It is defined by f∕d for gratings,where f is the focal length and d is the clear aperture of gratings.Once the grating aperture size is determined,a short curvature radius will correspond to a small F number.Figure5shows the 1st-order diffraction efficiency curvesof Fig.3.Structure of flat-field concavegrating.Fig.4.(Color online)Diffraction efficiency versus wavelength atdifferent incident angles.10February2013/Vol.52,No.5/APPLIED OPTICS1113Roland-type concave grating,which varies with wavelength at different F numbers.The grating grooves are parallel and equidistant with a density of 600g ∕mm,both incident angle and groove surface angle are 10°.Grating substrate size is 10mm ×10mm.The chosen F numbers are 7.1,7.8,and 8.5.According to Fig.5,the peak of diffraction effi-ciency shifts to the longer wavelength as the F num-ber gradually increases.With this regulation,energy on the expected spectral range can be optimized dur-ing the course of aberration-corrected design.Higher diffraction efficiency as well as optimization for reso-lution and dispersion can be obtained by changing the F number.3.Effects of Number of Grating Grooves on Diffraction EfficiencyFor the concave grating,the usage spectrum range,dispersion,and resolution are partly determined by the total number of grating grooves.Moreover,dif-fraction efficiency will also be affected by the density of grating grooves for a specified spectral range.Figure 6shows the 1st-order diffraction efficiency curves of Roland-type concave grating,which varies with wavelength at different densities of grating grooves.The grating grooves are parallel and equidi-stant,both incident angle and groove surface angle are 10°.Grating substrate size is 10mm ×10mm.The densities of grating grooves are 600g ∕mm,650g ∕mm,and 700g ∕mm.From Fig.6,we can see that the peak of diffraction efficiency shifts toward the shorter wavelength as the densities of grating grooves gradually decrease,which provide some definite reference values to the design of the concave grating.For the situations discussed in Figs.5and 6,if the incident angle is reduced from 10°to 6°,then the peak position of diffraction efficiency will all shift to the shorter wavelength.This is corresponding to the conclusion given in Fig.4.Besides the bandwidth of each curve becomes relatively narrower.The simu-lation results are shown in Figs.7and 8,respectively.It can be deduced that if the F number or density of grating grooves is determined,a decrease in incident angle will cause the peak position to shift to the shorter wavelength and narrower bandwidth.4.Diffraction Efficiency Curve of Flat-Field Concave GratingThe groove distribution function of aberration-corrected flat-field concave grating is dependent on the usage condition,such as spectrum range,density of grating groove,detector size on image plane,cur-vature radius of grating,and position of incident slit.Although the effects of those parameters on the calculation of diffraction efficiency are rather complex,the method introduced in Section 2can obtain the diffraction efficiency of a given flat-field concave grating conveniently with the aid of software such as Matlab.Figure 9shows the calculated result of the −1st order diffraction efficiency curve for a flat-field concave grating,where the curvature ra-dius is 120mm,both incident angle and groove surface angles are 10°,grating substrate sizeisFig.5.(Color online)Diffraction efficiency versus wavelength at different F numbers with incident angle equal to10°.Fig.6.(Color online)Diffraction efficiency versus wavelength at different densities of grating grooves with incident angle equal to10°.Fig.7.(Color online)Diffraction efficiency versus wavelength at different F numbers with incident angle equal to 6°.1114APPLIED OPTICS /Vol.52,No.5/10February 201310mm ×10mm,and density of grating grooves is 500g ∕mm.The groove distribution function deduced from the given grating is written asy 0.5×0.0056y 2 e 0m;(12)where e 0is the effective grating constant at vertex,m 0; 1; 2….The peak of diffraction efficiency in Fig.9lies at about ing this method,the energy distri-bution can be acquired quickly while carrying out the optimization design of aberration.Moreover,flat-field concave gratings with high resolution and rea-sonable energy distribution can be obtained through repeated trials.B.Experimental ResultA Rowland-type concave grating was designed and fabricated with the following parameters:curvature radius at 110mm,density of grating grooves at 600g ∕mm,both groove surface angle and incident angle at 10°,and grating substrate size at10mm ×10mm.Figure 10shows the diffraction ef-ficiency curves of both practical measurement and theoretical calculation.A flat-field concave grating was also designed and fabricated with the following parameters:curvature radius at 120mm,density of grating grooves at 500g ∕mm,both groove surface angle and incident angle at 10°,and grating substrate size at 10mm ×10mm.Figure 11shows the diffraction ef-ficiency curves of both practical measurement and theoretical calculation.As shown in Figs.10and 11,both curves in each figure appear as a similar trend.The noncoincidence between the theoretical and the practical result is caused by the approximation made in the theoretical analysis,fabrication as well as measurement errors,and so on.4.ConclusionWe have successfully calculated the diffraction effi-ciency of concave gratings with sawtoothgroovesFig.8.(Color online)Diffraction efficiency versus wavelength at different densities of grating grooves with incident angle equal to6°.Fig.9.Diffraction efficiency versus wavelength for flat-field concavegrating.Fig.10.(Color online)Diffraction efficiency curves of both theo-retical calculation and experimental measurement for Rowland-type concavegrating.Fig.11.(Color online)Diffraction efficiency curves of both theo-retical calculation and experimental measurement for flat-field concave grating.10February 2013/Vol.52,No.5/APPLIED OPTICS1115based on the Fresnel–Kirchhoff’s diffraction formula. This achievement fills a theoretical gap with taking the influence of grooves in nonprincipal section into consideration.The diffraction efficiency curves, which vary with wavelength at different parameters, such as incident angle,F number,and number of grating grooves,is also analyzed.The consistency be-tween theoretical simulation by Matlab and practical measurement results illustrates that our proposed method is a new and useful approach to solve the dif-fraction efficiency on concave ing this calculation method,the distribution of diffraction ef-ficiency with wavelength can be solved accurately and quickly while the design and usage parameters are given;therefore,the efficiency peak is easy to be optimized to the desired wavelength and the purpose of blazing will be achieved.This work is partly supported by the National Natural Science Foundation of China(60908021, 61176085),the National Key Technologies R&D Program(2011BAF02B00),the National Science Instrument Important Project(2011YQ15004),the Singapore National Research Foundation(CRP Award No.NRF-G-CRP2007-01),the programs (11DZ2290301)from Shanghai Committee of Science and Technology,the Leading Academic Discipline Project of Shanghai Municipal Government (S30502),and the Innovation Fund Project For Grad-uate Student of Shanghai(JWCXSL1101). References1.M.Born and E.Wolf,Principles of Optics(Macmillan,1964),Chap.8.2.M.C.Hutley,Diffraction Gratings(Academic,1982).3.R.Petit,Electromagnetic Theory of Gratings(Springer-Verlag,1980).4.M.G.Moharam,E.B.Grann,and D.A.Pomment,“Formula-tion for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,”J.Opt.Soc.Am.12,1068–1076(1995).5.M.G.Moharam,D.A.Pomment,and E.B.Grann,“Stableimplementation of the rigorous coupled-wave analysis for surface-relief gratings:enhanced transmittance matrix ap-proach,”J.Opt.Soc.Am.12,1077–1086(1995).6.M.G.Moharam and T.K.Gaylord,“Planar dielectricdiffraction theories,”Appl.Phys.B28,1–14(1982).7.M.G.Moharam and T.K.Gaylord,“Rigorous coupled-waveanalysis of planar-grating diffraction,”J.Opt.Soc.Am.71, 811–818(1981).8.M.G.Moharam and T.K.Gaylord,“Coupled-wave analysis ofreflection gratings,”Appl.Opt.20,240–244(1981).9.H. A.Rowland,“Preliminary notice of the results accom-plished in the manufacture and theory of gratings for optical purposes,”Phil.Mag.13(84),469–474(1882).10.M.Neviere and W.R.Hunter,“Analysis of the changes in ef-ficiency across the ruled area of a concave diffraction grating,”Appl.Opt.19,2059–2065(1980).11.M. C.Hutley and W.R.Hunter,“Variation of blaze ofconcave diffraction gratings,”Appl.Opt.20,245–250 (1981).12.Yu.V.Bazhanov and N.A.Kulakova,“Analysis of the effi-ciency of concave diffraction gratings in the scalar approxima-tion,”J.Opt.Technol.69,886–888(2002).13.N. A.Kulakova,S.O.Mirumyants,and A.G.Bugaenko,“Characteristics of a concave diffraction grating on which a spherical wave is incident,”J.Opt.Technol.73,682–686 (2006).14.C.-H.Ko,W.-C.Liu,N.-P.Chen,J.-L.Shen,and J.-S.Lin,“Double reflection in the concave reflective blazed grating,”Opt.Express15,10498–10530(2007).15.H.Noda,T.Namioka,and M.Seya,“Geometric theory of thegrating,”J.Opt.Soc.Am.64,1031–1036(1974).16.D.Pi,Y.Huang,D.Zhang,Z.Ni,and S.Zhuang,“Optimizationof the flat-field holographic concave grating in wide spectral range,”Acta Phys.Sinica59,1009–1016(2010).1116APPLIED OPTICS/Vol.52,No.5/10February2013。

US20130291598A1翻译

A method of cutting a strengthened glass including, a front surface layer and a back surface layer each having a remaining compression stress, respectively, and an intermediate layer formed between the front surface layer and the back surface layer, having an internal remaining tensile stress, the method includes heating the intermediate layer at an irradiation area of a laser beam at a temperature less than or equal to an annealing point to generate a tensile stress less than a value of the internal remaining tensile stress of the intermediate layer or a compression stress at the center of the irradiation area for suppressing the propagation of the crack.切割的方法强化玻璃,包括表层前面和背面层各有一个剩余压缩应力,分别和中间层之间形成正面层和表层,内部剩余的拉应力,该方法包括加热中间层的一束激光辐照区域的温度小于或等于一个退火点产生拉伸应力小于剩余价值的内部中间层的拉应力或压应力的中心辐射抑制裂纹的传播区域。

METHOD OF CUTTING STRENGTHENED GLASS PLATEBACKGROUND OF THR INVENTION[0003]The present invention relates to a method of cutting a strengthened glass plate.[0004]2. Description of the Related Art[0005]Recently, in mobile devices such as mobile phones, PDAS or the like, a cover glass (protection glass) is often used in order to protect displays (including touch panels) and increase good appearances. Further, glass substrates are widely used as substrates for displays.最近,在移动设备如手机、掌上电脑或类似的,封面玻璃(保护玻璃)是经常使用以保护显示(包括触摸面板)和增加好的外表。

弹性力学专业英语文档

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