38英汉双语弹性力学1
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38英汉双语弹性力学1
Elasticity；2；Chapter1Introduction；§1-1TheModelingoftheEngi；第一章；§1-1工程力学问题的建模§1-2§1-3§1-；弹性力学的基本内容弹性力学问题的基本假设弹性力学；Theelasticityisabrancho；弹性力学是固体力学的一个分支,研究弹性体由于外；本课程较为完整的表现了力学问
Elasticity12Chapter 1 Introduction§1-1 The Modeling of the Engineering Mechanics Problem §1-2 The Basic Contents of the Elasticity §1-3 The Basic Assumption of the Elasticity Problem §1-4 The Several Basic Concepts of Elasticity §1-5 The Study Method of the Elasticity Exercises Lesson3第一章绪论§1-1 工程力学问题的建模 §1-2 §1-3 §1-4 §1-5 习题课4弹性力学的基本内容 弹性力学问题的基本假设 弹性力学中的几个基本概念 弹性力学的学习方法The elasticity is a branch of the solid mechanics, the task of it is to research the elasticity object's stress, deformation and displacement due to external force or change of temperature. This course shows the mathematics modeling process of mechanics problems completely, and establishes the basic equation and boundary condition of the elasticity and proceeds to beg the solutions of some problem. The foundation of the elasticity basic equation lays a foundation for further number method. The elasticity is the foundation of studying plasticity, fracture mechanics and finite element method.5弹性力学是固体力学的一个分支,研究弹性体由于外 力作用或温度改变等原因而发生的应力,形变和位移.本课程较为完整的表现了力学问题的数学建模过程, 建立了弹性力学的基本方程和边值条件,并对一些问题进 行了求解.弹性力学基本方程的建立为进一步的数值方法 奠定了基础. 弹性力学是学习塑性力学,断裂力学,有限元方法的 基础.6§1-1 The Modeling of the Engineering Mechanics Problem1,The Modeling Process of the Engineering Mechanics ProblemThrough the process of establishing the mechanics model in the engineering mechanics problem, generally three parts should be simplified: Construction Simplification Suffering Force Simplification Material SimplificationFig.1Fig.1-17§1-1工程力学问题的建模工程力学问题建立力 学模型的过程中,一般要 对三方面进行简化:一,工程力学问题的建模过程结构简化 受力简化 材料简化图1-18(1)Construction Simplification )Such as space problem is simplified to flat surface problem and symmetry problem in axis, and entity construction is simplified to plate construction(2)Suffering Force Simplification )According to the Saint-Venant's principle, the complex force system is simplified to an equivalent force system.(3)Material simplification )Material is simplified according to these hypothesises of the same kind, consecution and uniformity in each direction.9(1)结构简化如空间问题向平面问题的简化,向轴对称问题的简化,实 体结构向板,壳结构的简化.(2)受力简化根据圣维南原理,复杂力系简化为等效力系.(3)材料简化根据各向同性,连续,均匀等假设进行简化.102,Advertent Problem in Modeling Process , (1)Linearization ) Proceed to handle to the smallquantity in high level. Proceed the linearization that may be linearized. (2)Experiment Verification ) After the model is established, proceed to analyse and neaten to the result of the computation, and return the actual problem and proceed the verification. Generally and mostly it is proceeded through experiment.11二,建模过程中注意的问题 (1)线性化对高阶小量进行处理,能进行线性化的,进行线性化.(2)实验验证模型建立以后,对计算的结果进行分析整理,返回实际问 题进行验证,一般主要通过实验进行.12§1-2 The Basic Contents of the Elasticity1,Investigative task , The elasticity is a branch of the solid mechanics, the task of it is to research the elasticity object's stress, deformation and displacement due to external force or change of temperature. 2,Investigative object , The research object of the elasticity is general and complicated shape structure piece, entity structure, plate shell etc.13§1 - 2一,研究任务弹性力学的基本内容弹性力学是固体力学的一个分支,研究弹性体由于受 外力作用或由于温度改变等原因而发生的应力,形变和位 移. 二,研究对象 弹性力学的研究对象为一般及复杂形状的构件,实体 结构,板壳等.143,The relation about the other course: , : Theoretical mechanics: Study statics and dynamics of the rigid body(constraint force,velocity,acceleration). Material mechanics: research stress and displacement of the bar structure piece that is pulled, pressed, sheared, bent or turned. Structual mechanics: research internal force and displacement of the bar structure. Plasticity: plasticity analysis and design of the structure. Elasticity: stress and displacement analysis of general plane problem, plate, shell and entity structure etc.15三,与其他学科的关系: 与其他学科的关系: 理论力学:研究刚体的静,动力学(约束力,速度, 加速度). 材料力学:研究杆状构件在拉,压,剪,弯,扭状态 下的应力和位移; 结构力学:研究杆系结构的内力与位移; 塑性力学:结构的塑性分析,设计; 弹性力学:一般平面问题,板,壳和实体结构等的 应力和位移分析.16§1-3 The Basic Assumption of the ElasticityIn elasticity, doing some necessary assumptions under the premise that can satisfy the practical needing precision and making the problem solved. The basic assumption of the elasticity: (1)Consecution assumption:Some physics measures inside the object, for example stress, strain and displacement etc.whose variety regulation may be denoted by continuous function in coordinate. (2)Ideal elasticity assumption: supposing that the object is a ideal elastic body,then the elastic body obey the Hooke's law---the stress becomes the direct proportation with homologous deformation.And the elasticity constant doesn't change along with the variety of stress and deformation. (3)Even assumption:supposing the object be constituted by the same material, the elasticity of the object would not 17 change along with position coordinates change.§1 - 3弹性力学的基本假设在弹性力学中,在满足实用所需精度的前提下做一些 必要的假设,使问题得以求解. 弹性力学的基本假设为: (1)连续性假设:这样物体内的一些物理量,例如 应力,应变和位移等可用坐标的连续函数表示它们的变 化规律. (2)完全弹性假设:假定物体为完全弹性体,则 服从虎克定律---应力和相应的形变成正比,弹性常数 不随应力或形变的大小而变化. (3)均匀性假设:假定物体由同一材料组成,这 样物体的弹性不随位置坐标而变化.18(4)Isotropy assumption: The elastic properties of one point in object are the same in every direction. (5)Assumption of small deformation: supposing displacement and deformation is very small.Then using the dimension before deformation instead of the one after deformation. The small quantity in high level may be ignored when investigating strain and displacement of the object.Which is very important to the linearization of the equation. The assumptions above are suitable for many problems in engineering, but they exist errors much differently for some problems, then it is necessary to use another brief method.But it is still the same for the basic theories of many concepts.The elasticity is the foundation of the subjects of learning plasticity,fracture mechanics and finite element method and etc.19(4)各向同性假设:物体内一点的弹性性质在所有 各个方向都相同. (5)小变形假设:假定位移和形变是微小的.这样, 可以用变形前的尺寸代替变形后的尺寸,在考察物体的 应变和位移时,可以略去高阶小量,这对于方程的线性 化十分重要. 以上的假设对于工程中不少问题是适用的,但对于 一些问题的误差太大,就必须用另外的简化方案,但许 多概念基本理论仍然是共同的,弹性力学是学习塑性力 学,断裂力学,有限元方法等学科的基础.20§1-4 The Several Basic Concepts of the Elasticity1.External stress It can be divided into the stress of volume and plane according to the different distribution of the external function, which are called volumetric force and surface force respectively. 1.Volumetric force z△VZFPQYXOyFig.1-2x(1)Definition:It is the stress distributed in volume of the object that is called volumetric force,for example,gravity and inertia force.It is shown in Fig.1-2. Q (2)Property:volumetric force is different from the differentthe volumetric force is continuous in distribution. 21§1 - 4 (一)外力弹性力学中的几个基本概念按照外力作用的不同分布方式,可分为体积力和表面力, 分别简称体力和面力. 1.体力 z△VZFPQ(1)定义:所谓体力是分布在物 体体积内的力,如重力和惯性力. 如图1-2所示 Q. (2)性质:体力随点的位置不同 而不同;体力是连续分布的.22YXOy图1 - 2x(3)Gather degree: ) : The average gather degree of volumetric force:
Q VQ VThe gather degree of volumetric force at point P:F = lim V → 0 The direction of F is the limited one of
Q (4)The component of volumetric force: ) : The force of F is resolved along with the three coordinates, which will get the three components of straight intersection: F = X i + Yj + Z k X,Y,Z are called the components of volumetric force at point P.Plus sign and negative sign are separately determined by the direction of components,and then is[Force][Length]-3.23(3)集度: 集度:Q 体力的平均集度为: VQ F P点所受体力的集度为: = lim V →0 VF的方向就是
Q 的极限方向.(4)体力分量: 体力分量: 将F沿三个坐标轴分解,可得到三个正交的分力:F = Xi + Yj + ZkX,Y,Z称为物体在P点的体力分量,正负号视分 力指向而定,因次是[力][长度]-3.242. Surface force (1) Definition:surface force is distributed one in the surface of the object.For instance,liquid stress and contact stressQ . It is shown in Fig.1-3. (2) Property:In general, surface force is the function of located coordinates at point in the surface of the object. (3) Gather degree of surface force:the average gather degree of the surface force above
S Q The gather degree of the surface z Z force at P: F Q △S F = lim S → 0
S Y P (4) The components of surface force: X y The components of surface force Fig.1-3 are X , Y , Z,and then are 25 [Force][Length]-2 x2. 面力(1)定义:分布在物体表面上的力.如流体压力和接触力
Q .如图1-3所示 . (2)性质:面力一般是物体表面点的位置坐标的函数.
Q (3)面力集度:
S 上面力的平均集度为:
S z△SQZPP点所受面力的集度为:FYyQ F = lim S → 0
SX图1-3(4)面力分量: P点的面力分量为 X,Y,, Z 因次是[力][长度]-2.26x2.stress1.Definition:The object bears the external force function.Additional internal force is produced among every cross sections of the object interior.For displaying these internal forces,we use a cross section to cut the object open, and then take out a part among them.The function of a part to another part among them that expresses for internal force, which are resultant force of distributed forces that distribute on the cross section.When the area of cross section incline to the zero,the distributed force on the cross section is shown as Fig.1-4s. 2.Property:The same point in the object,whose stress of different cross sections is different. 3.Stress gather degree:zm△AB Q σsThe average gather degree of internal force above :
A QP o xτnylim The stress at point P: s =
A → 0AAFig.1-4The stress component at point P is σ ,Q Aσ---Positive stressτ ---Shearing strength27τ.And then are[Force][Length]-2(二)应力1.定义:物体承受外力作用,物体内部各截面之间产生附加内 力,为了显示出这些内力,我们用一截面截开物体,并取出其 中一部分,其中一部分对另一部分的作用,表现为内力,它们 是分布在截面上分布力的合力.当截面面积趋于零时截面上的 分布力.如图1-4所示 s . 2.性质:在物体内的同一点,不同截面上的应力是不同的. zm△AσPBsQτnyQ
A上的内力的平均集度为: A3.应力集度:oA图1 - 4σP点的应力分量为 σ, τ ---正应力Q s lim P点的应力为: =
A → 0 Aτ ---切应力28因次是[力][长度]-2.x4.The component of the stress Stress is relevant with not only the position of point but also the direction of the cross section. It is not a general vector but is two rank tensor. (1) For analyzing the state of one C point,one small positive parallel hexahedron is taken out from the point.The component of the stress of each section along with coordinates B axis that is called the component of P the stress. z A The component of the stress on the plane is equal in size but o y contrary in direction at the meaning x of omitting the small quantity in Fig.1-5 29 high level.4.应力分量 4.应力分量应力不仅和点的位置有关,和截面的方位也有关,不是 一般的矢量,而是二阶张量.CPBz o xAy图1 - 5(1)为了分析一点的应力状 态,在这一点从物体内取出一个 微小的正平行六面体,各面上的 应力沿坐标轴的分量称为应力分 量. 相对平面上的应力分量在略 去高阶小量的意义上大小相等, 方向相反.30(2)Symbol provision: ) :The drawing shows that the normal of the surface of the unit is y,it is called surface y.The stress that the stress component plumbs the surface of the unit is called the positive stress.z o x yThe positive stress is recorded σy,the positive direction along y axis is positive,whose suffix means the direction along coordinates axis. The stress paralleling the surface of the unit is called the slicing stress,which is showed by τ yx ,τ yz and whose the first suffix y means the flat surface of the place and the second suffix x,z mean respectively along the direction of the coordinates axis. τ yx, τ yz is showed in Fig.1-6.31τ yz τ yxσyFig.1-6(2)符号规定: 符号规定: 图示单元体面的法线为y,称 为y面,应力分量垂直于单元体 面的应力称为正应力.z o x y正应力记为σy,沿y轴的正 向为正,其下标表示所沿坐标轴 τ 的方向.yzτ yzτ yxσy图1 - 6平行于单元体面的应力称为 切应力,用 τ yx ,τ yz 表示,其第 一下标y表示所在的平面,第二下 标x,z分别表示沿坐标轴的方向. τ τ 如图1-6所示的 , yx. yz32The components of the stress on other x,z positive surface is shown in Fig.17.τ xyFig.1-7The stress on positive surface is positive along the positive direction of coordinates, and is negative athwart the positiv包含各类专业文献、外语学习资料、文学作品欣赏、行业资料、各类资格考试、生活休闲娱乐、幼儿教育、小学教育、高等教育、38英汉双语弹性力学1等内容。　
　五个基本假设在建立弹性力学基本方程时有什么用途? 1-3 五个基本假设在建立...弹性力学 第1章――绪论 54页 免费 英汉双语弹性力学1 52页 免费 弹性力学第... 　1《英汉双语高等数学电子教程》_专业资料。1《英汉双语高等数学电子教程》 2《英汉...力学电子教程》 29《弹性力学电子教程》 30《流体力学电子教程》 31《理论力学... 　? 并在边界上满足应力边界条件(1 分) 。对于多连体,有时还必须考虑位移单值...英汉双语弹性力学11 62页 免费 弹性力学-11 暂无评价 122页 1下载券 ... 　1《英汉双语高等数学电子教程》 2《英汉双语大学物理电子教程》 3《英汉双语大学...力学电子教程》 29《弹性力学电子教程》 30《流体力学电子教程》 31《理论力学... 　1《英汉双语高等数学电子教程》_专业资料。1《英汉双语高等数学电子教程》 2《英汉...力学电子教程》 29《弹性力学电子教程》 30《流体力学电子教程》 31《理论力学... 　弹性力学主要内容_物理_自然科学_专业资料。1、弹性力学的研究对象、内容及范围 弹性力学是研究在外界因素(外力、温度变化)的影响下,处于弹性阶段的物 体所产生的... 　1《英汉双语高等数学电子教程》_专业资料。1《英汉双语高等数学电子教程》 2《英汉...力学电子教程》 29《弹性力学电子教程》 30《流体力学电子教程》 31《理论力学... 　弹性力学复习题1_高等教育_教育专区。弹性力学复习题 C 2015 年春 一、 名词解释 1. 弹性力学: 研究弹性体由于受外力作用或者温度改变等原因而发生的应力、应变... 　第1 章 弹性力学基础第 1 节 材料力学和弹性力学一、 弹性力学的基本假设 大量的工程问题都涉及到应力、应变及位移的分析计算,弹性力学(又称弹性理论)就 是研究...同一项的高阶无穷小相减还等于那个项的高阶无穷小吗?比如o(x^3)-o(x^3)=o(x^3)?_百度作业帮
同一项的高阶无穷小相减还等于那个项的高阶无穷小吗?比如o(x^3)-o(x^3)=o(x^3)?
同一项的高阶无穷小相减还等于那个项的高阶无穷小吗?比如o(x^3)-o(x^3)=o(x^3)?
这个就不一定了比如 2x ,x 是同阶的无穷小量 2x-x =x 还是同阶的但是 x sinx 也是同阶的,但是 X-sinx 就是 o(x^3)了
啊，自己想高中物理竞赛用到的“微元法”,为什么可以略去高阶无穷小量?比如：x=vt+1/2at^2,如果t是微元,则可略去1/2at^2,只保留x=vt.这是为什么啊?依据是什么啊?现在还没搞明白._百度作业帮
高中物理竞赛用到的“微元法”,为什么可以略去高阶无穷小量?比如：x=vt+1/2at^2,如果t是微元,则可略去1/2at^2,只保留x=vt.这是为什么啊?依据是什么啊?现在还没搞明白.
高中物理竞赛用到的“微元法”,为什么可以略去高阶无穷小量?比如：x=vt+1/2at^2,如果t是微元,则可略去1/2at^2,只保留x=vt.这是为什么啊?依据是什么啊?现在还没搞明白.
能略去的原因就是有vt存在,t->0的时候vt要比 t^2大得多,后面一项可忽略.如果有个式子是x=10+t ,t是小量.那么即使这里t是一阶小量,t也可以忽略,因为跟前面的10比太小了.我能体会你心情,刚开始都有些“放不下”,扔了不放心.你可以看一些微积分的书,极限的章节,可能会解决你的问题可以说这不是粗略值,是绝对科学严谨的.在小量运算（也就是取极限t->0）的前提下就得这么算.
无穷细分后的t已经很小了再平方后可以忽略依据是什么啊？一个数无穷小就可以认为为0如果1、2、3次项都有，那么可略去哪项？是略去2、3次项，还是3次项？无穷小量有下列性质：
1、有限个无穷小量代数和仍是无穷小量。
2、有限个无穷小量之积仍是无穷小量。
3、有界函数与无穷小量之积为无穷小量。最小的可以省我是高中生，对高等数学不太了解，解释通俗点行吗？不是一...
一个数无穷小就可以认为为0
如果1、2、3次项都有，那么可略去哪项？是略去2、3次项，还是3次项？
无穷小量有下列性质：
1、有限个无穷小量代数和仍是无穷小量。
2、有限个无穷小量之积仍是无穷小量。
3、有界函数与无穷小量之积为无穷小量。最小的可以省
我是高中生，对高等数学不太了解，解释通俗点行吗？
不是一开始就讲了么。。。。两个小数的积比这两个小数还小
略去后得到的结果是不是粗略值？
用微元法的基本都是曲线，肯定是粗略值精确值人不好算常用近似X很小时有sinx=tanx=x(1+x)的n次方=1+nx举个例子我们把原子的质量视为原子核的质量，因为电子的质量远小于1个质子/中子的质量远小于,物理上实验误差要求小于0.1%,所以当a<0.1% b时可以认为a<<b,