關(guān)于力的外文文獻(xiàn)翻譯@中英文翻譯@外文翻譯

五、外文資料翻譯 Stress and Strain 1. Introduction to Mechanics of Materials Mechanics of materials is a branch of applied mechanics that deals with the behavior of solid bodies subjected to various types of loading. It is a field of study that is known by a variety of names, including “strength of materials” and “mechanics of deformable bodies”. The solid bodies considered in this book include axially-loaded bars, shafts, beams, and columns, as well as structures that are assemblies of these components. Usually the objective of our analysis will be the determination of the stresses, strains, and deformations produced by the loads； if these quantities can be found for all values of load up to the failure load, then we will have obtained a complete picture of the mechanics behavior of the body. Theoretical analyses and experimental results have equally important roles in the study of mechanics of materials . On many occasion we will make logical derivations to obtain formulas and equations for predicting mechanics behavior, but at the same time we must recognize that these formulas cannot be used in a realistic way unless certain properties of the been made in the laboratory. Also , many problems of importance in engineering cannot be handled efficiently by theoretical means, and experimental measurements become a practical necessity. The historical development of mechanics of materials is a fascinating blend of both theory and experiment, with experiments pointing the way to useful results in some instances and with theory doing so in others . Such famous men as Leonardo da Vinci(1452-1519) and Galileo Galilei (1564-1642) made experiments to adequate to determine the strength of wires , bars , and beams , although they did not develop any adequate theories (by todays standards ) to explain their test results . By contrast , the famous mathematician Leonhard Euler(1707-1783) developed the mathematical theory any of columns and calculated the critical load of a column in 1744 , long before any experimental evidence existed to show the significance of his results . Thus , Eulers theoretical results remained unused for many years, although today they form the basis of column theory. The importance of combining theoretical derivations with experimentally determined properties of materials will be evident theoretical derivations with experimentally determined properties of materials will be evident as we proceed with our study of the subject . In this section we will begin by discussing some fundamental concepts , such as stress and strain , and then we will investigate bathe behaving of simple structural elements subjected to tension , compression , and shear. 2. Stress The concepts of stress and strain can be illustrated in elementary way by considering the extension of a prismatic bar see Fig.1.4(a). A prismatic bar is one that has cross section throughout its length and a straight axis. In this illustration the bar is assumed to be loaded at its ends by axis forces P that produce a uniform stretching , or tension , of the bar . By making an artificial cut (section mm) through the bar at right angles to its axis , we can isolate part of the bar as a free bodyFig.1.4(b). At the right-hand end the force P is applied , and at the other end there are forces representing the action of the removed portion of the bar upon the part that remain . These forces will be continuously distributed over the cross section , analogous to the continuous distribution of hydrostatic pressure over a submerged surface . The intensity of force , that is , the per unit area, is called the stress and is commonly denoted by the Greek letter . Assuming that the stress has a uniform distribution over the cross sectionsee Fig.1.4(b), we can readily see that its resultant is equal to the intensity times the cross-sectional area A of the bar. Furthermore , from the equilibrium of the body show in Fig.1.4(b), Fig.1.4 Prismatic bar in tension we can also see that this resultant must be equal in magnitude and opposite in direction to the force P. Hence, we obtain =P/A ( 1.3 ) as the equation for the uniform stress in a prismatic bar . This equation shows that stress has units of force divided by area -for example , Newtons per square millimeter(N/mm) or pounds of per square inch (psi). When the bar is being stretched by the forces P ,as shown in the figure , the resulting stress is a tensile stress； if the force are reversed in direction, causing the bat to be compressed , they are called compressive stress. A necessary condition for Eq.(1.3) to be valid is that the stress must be uniform over the cross section of the bat . This condition will be realized if the axial force p acts through the centroid of the cross section , as can be demonstrated by statics. When the load P doses not act at thus centroid , bending of the bar will result, and a more complicated analysis is necessary . Throughout this book , however , it is assumed that all axial forces are applied at the centroid of the cross section unless specifically stated to the contrary . Also, unless stated otherwise, it is generally assumed that the weight of the object itself is neglected, as was done when discussing this bar in Fig.1.4. 3. Strain The total elongation of a bar carrying force will be denoted by the Greek letter see Fig .1.4(a), and the elongation per unit length , or strain , is then determined by the equation =/L (1.4) Where L is the total length of the bar . Now that the strain is a nondimensional quantity . It can be obtained accurately form Eq.(1.4) as long as the strain is uniform throughout the length of the bar . If the bar is in tension , the strain is a tensile strain , representing an elongation or a stretching of the material； if the bar is in compression , the strain is a compressive strain , which means that adjacent cross section of the bar move closer to one another. ( Selected from Stephen P.Timoshenko and James M. Gere, Mechanics of Materials,Van NostrandReinhold Company Ltd.,1978.) 應(yīng)力應(yīng)變 1、 材料力學(xué)的介紹 材料力學(xué)是應(yīng)用力學(xué)的分支，它是研究受到各種類(lèi)型載荷作用的固體物。材料力學(xué)所用的方面就我們所知道的類(lèi)型名稱(chēng)包括：材料強(qiáng)度和可變形物體 的力學(xué)。在本書(shū)中考慮的固體物有受軸向載荷的桿、軸、梁和柱以及用這些構(gòu)件所組成的結(jié)構(gòu)。通常我們分析物體由于載荷所引起的應(yīng)力集中、應(yīng)變和變形作為目的。如果這些是能夠獲得增長(zhǎng)直到超載的重要性。我們就能夠獲得這種物體的完整的機(jī)械行為圖。 理論分析和實(shí)驗(yàn)結(jié)論是研究材料力學(xué)的相當(dāng)重要的角色。在許多場(chǎng)合，我們要做出邏輯推理獲得機(jī)械行為的公式和方程。但是同時(shí)我們必須認(rèn)識(shí)到這些公式除非已知這些材料的性質(zhì)，否則不能用于實(shí)際方法中，這些性質(zhì)只有通過(guò)一些合適的實(shí)驗(yàn)之后才能用。同樣的，許多重要的問(wèn)題也不能用理論的方法有效的處理 ，只有通過(guò)實(shí)驗(yàn)測(cè)量才能實(shí)際應(yīng)用。材料力學(xué)的發(fā)展歷史是理論與實(shí)驗(yàn)極有趣的結(jié)合。在一些情況下是指明了得以有用結(jié)果的道路，在另一些情況下則是理論來(lái)做這些事。例如著名人物萊昂納多 達(dá) 芬奇（ 1452-1519）和 伽利略 加能（ 1564-1642）做實(shí)驗(yàn)以確定鐵絲、桿、梁的強(qiáng)度。盡管他們沒(méi)有得出足夠的理論（以今天的標(biāo)準(zhǔn)）來(lái)解釋他們的那些實(shí)驗(yàn)結(jié)果。相反的，著名的數(shù)學(xué)家利昴哈德 尤勒 （ 1707-1783）在 1744 年就提出了柱體的數(shù)學(xué)理論計(jì)算出其極限載荷，而過(guò)了很久才有實(shí)驗(yàn)證明其結(jié)果的重要性。雖然其理論結(jié)果并沒(méi)有留存多 少年，但是在今天他仍是柱體理論的基本形式。 隨著研究的不斷深入，把理論推導(dǎo)和在實(shí)驗(yàn)上已確定的材料性質(zhì)結(jié)合起來(lái)形容的重要性是很顯然的。然后，調(diào)查研究簡(jiǎn)單結(jié)構(gòu)元件承受拉力、壓力和剪切的性質(zhì)。 2、 應(yīng)力 應(yīng)力和應(yīng)變的概念可以用圖解這種方法。考慮等截面桿發(fā)生的延伸。 如圖1.4(a).等截面桿沿長(zhǎng)度方向和軸線方向延伸。在這個(gè)圖中的桿假設(shè)在它的兩端承受軸向載荷 P 致使產(chǎn)生一致的延伸，即桿的拉力。通過(guò)桿的假想（ mm）截面是垂直于軸的直角面。 我們可以分離出桿的一個(gè)自由體作為研究對(duì)象 圖1.4(b). 在右邊的 端點(diǎn)上是拉力 P 的作用，而在另一端是被移走的桿上的一部分作用在這部分上的力。這些力分布在水的表面上。強(qiáng)度就是單位面積上的載荷叫應(yīng)力，用希臘字母表示。假設(shè)應(yīng)力均勻連續(xù)分布在橫截面上 看圖1.4(b)。而且在圖 1.4(b)中看到物體的平衡，我們能夠得出這樣的合力在大小上必須等于相反方向的載荷 P。我們得到等截面桿的應(yīng)力均勻分布的方程式： =P/A 這個(gè)方程式表明應(yīng)力是在面積上分成微分載荷。例如 N/mm 或 psi。當(dāng)桿被載荷 P拉伸，可以用數(shù)值來(lái)表示。因此產(chǎn)生的應(yīng)力為拉應(yīng)力。如果載荷是相反的方向，造成桿的壓縮 ，這就叫壓應(yīng)力。 方程（ 1.3）所必須具備的條件就是應(yīng)力均勻分布在桿的面上。軸向載荷 P通過(guò)截面的形心，這個(gè)條件必須實(shí)現(xiàn)。可以用靜力學(xué)來(lái)說(shuō)明：當(dāng)加載 P 不能經(jīng)過(guò)形心，將會(huì)導(dǎo)致桿的彎曲，而且有一個(gè)更復(fù)雜的分析。在本書(shū)過(guò)程中，如果沒(méi)有特別說(shuō)明，我們假定的所有軸向力都作用在橫截面的形心上。同樣的，除另外的狀態(tài)，當(dāng)我們對(duì)圖 1.4 討論時(shí)同，對(duì)于一般地物體本身是重可忽略。 3、 應(yīng)變 由于軸向載荷使桿伸長(zhǎng)的總量是用希臘字母表示 看圖 1.4(a)。單位長(zhǎng)度的伸長(zhǎng)即應(yīng)變。得到方程式 = /L L 為桿的長(zhǎng)度。 注 意到應(yīng)變是非空間的量，從方程 (1.4)可以獲得準(zhǔn)確的應(yīng)變。應(yīng)變?cè)谡麄€(gè)桿的長(zhǎng)度上是一致的。如果拉伸，應(yīng)變莊稼漢叫拉應(yīng)變，它使材料伸長(zhǎng)或延長(zhǎng)；如果桿是縮短的，應(yīng)變就叫壓應(yīng)變，將會(huì)使桿的兩端距離縮小。 （ 從選出 ： 史蒂芬 .Timoshenko 和詹姆士 M.蓋爾，材料力學(xué)， NostrandReinhold 廂式客貨兩用車(chē)有限公司， 1978） Shear Force and Bending Moment in Beams Let us now consider, as an example , a cantilever beam acted upon by an inclined load P at its free end Fig.1.5(a). If we cut through the beam at a cross section mn and isolate the left-hand part of the beam as free body Fig.1.5(b), we see that the action of the removed part of the beam (that is , the right-hand part)upon the left-hand part must as to hold the left-hand in equilibrium. The distribution of stresses over the cross section mn is not known at this stage in our study , but wee do know that the resultant of these stresses must be such as to equilibrate the load P. It is convenient to resolve to the resultant into an axial force N acting normal to the cross section and passing through the centriod of the cross section , a shear force V acting parallel to the cross section , and a bending moment M acting in the plane of the beam. The axial force , shear force , and bending moment acting at a cross section of a beam are known as stress resultants. For a statically determinate beam, the stress resultants can be determined from equations of equilibrium. Thus , for the cantilever beam pictured in Fig.1.5, we may writer three equations of stactics for the free-body diagram shown in the second part of the figure. From summations of forces in the horizontal and vertical directions we find, respectively, N=Pcos V=Psin and ,from a summation of moments about an axis through the centroid of cross section mn, we obtain M=Pxsin where x is the distance from the free end to section mn. Thus ,through the use of a free-body diagram and equations of static equilibrium, we are able to calculate the stress resultants without difficulty. The stress in the beam due to the axial force N acting alone have been discussed in the text of Unit.2； Now we will see how to obtain the stresses associated with bending moment M and the shear force V. The stress resultants N, V and M will be assumed to be positive when the they act in the directions shown in Fig.1.5(b). This sign convention is only useful, however , when we are discussing the equilibrium of the left-hand part of the beam is considered, we will find that the stress resultants have the same magnitudes but opposite directionssee Fig.1.5(c). Therefore , we must recognize that the algebraic sign of a stress resultant does not depend upon its direction in space , such as to the left or to the right, but rather it depends upon its direction with respect to the material against , which it acts. To illustrate this fact, the sign conventions for N, V and M are repeated in Fig.1.6, where the stress resultants are shown acting on an element of the beam. We see that a positive axial force is directed away from the surface upon which is acts(tension), a positive shear force acts clockwise about the surface upon which it acts , and a positive bending moment is one that compresses the upper part of the beam. Example A simple beam AB carries two loads , a concentrated force P and a couple Mo, acting as shown in Fig.1.7(a). Find the shear force and bending moment in the beam at cross sections located as follows: (a) a small distance to the left of the middle of the beam and (b) a small distance to the right of the middle of the beam . Solution The first step in the analysis of this beam is to find the reactions RA and RB. Taking moments about ends A and B gives two equations of equilibrium, from which we find RA=3P/4 Mo/L RB=P/4+mo/L Next, the beam is cut at a cross section just to the left of the middle, and a free-body diagram is drawn of either half of the beam. In this example we choose the left-hand half of the bean, and the corresponding diagram is shown in Fig.1.7(b). The force p and the reaction RA appear in this diagram, as also do the unknown shear force V and bending moment M, both of which are shown in their positive directions. The couple Mo does not appear in the figure because the beam is cut to the left of the point where Mo is applied. A summation of forces in the vertical direction gives V=R P= -P/4-M0/L Which shown that the shear force is negative； hence, it acts in the opposite direction to that assumed in Fig.1.7(b). Taking moments about an axis through the cross section where the beam is cut Fig.1.7(b) gives M = RAL/2-PL/4=PL/8-Mo/2 Depending upon the relative magnitudes of the terms in this equation, we see that the bending moment M may be either positive or negative . To obtain the stress resultants at a cross section just to the right of the middle, we cut the beam at that section and again draw an appropriate free-body diagram Fig.1.7(c). The only difference between this diagram and the former one is that the couple Mo now acts on the part of the beam to the left of the cut section. Again summing force in the vertical direction, and also taking moments abo ut an axis through the cut section , we obtain V= - P/4- Mo/L M=PL/8+Mo/2 We see from these results that the shear force does not change when the section is shifted from left to right of the couple Mo, but the bending moment increases algebraically by an amount equal to Mo . ( Selected from: Stephen P.Timosheko and James M. Gere,Mechanics of materials, Van Nostrand reinhold Company Ltd.,1978.) 平衡梁的剪力和彎矩 讓我們來(lái)共同探討像圖 1.5(a)所示懸梁自由端在傾斜拉力 P的作用下的問(wèn)題。如果將平衡梁在截面 mn 處截?cái)嗲覍⑵渥筮叢糠肿鳛楦綦x體（圖 1.5（ b）?？梢钥闯龈綦x體截 面（右邊）的作用國(guó)必須和左邊的作用力平衡，截面 mn 處應(yīng)力的分布情況我們現(xiàn)階段是不知道的，但我們知道這些應(yīng)力的合力必須和拉力 P 平衡。按常規(guī)可將合力分解成為通過(guò)質(zhì)點(diǎn)作用于橫截面的軸向應(yīng)力 N、平行于截面的剪切力 V 和作用在平衡梁平面中的彎矩 M。 作用在截面上的軸向應(yīng)力、剪切力和彎曲應(yīng)力就是應(yīng)力的合成力。比如靜止的固定梁合成力可由平衡方程得出，如圖 1.5 所示懸臂梁結(jié)構(gòu)。這樣就可以得到圖形另一部分中的圖示自由部分的三個(gè)平衡方程式。由水平合力和垂直合力的方向，可得： N=Pcos 如果將平衡梁在截面 mn 處截?cái)嗲覍⑵?左邊部分作為隔離體（圖 1.5（ b）?？梢钥闯龈綦x體截面（右邊）的作用國(guó)必須和左邊的作用力平衡，截面 mn 處應(yīng)力的分布情況我們現(xiàn)階段是不知道的，但我們知道這些應(yīng)力的合力必須和拉力 P平衡。按常規(guī)可將合力分解成為通過(guò)質(zhì)點(diǎn)作用于橫截面的軸向應(yīng)力 N、平行于截面的剪切力 V 和作用在平衡梁平面中的彎矩 M。 作用在