英汉双语弹性力学.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,*,Chapter 1 Introduction,Elasticity,1,第一章 绪 论,2,Chapter 1 Introduction,1-1 The Modeling of the Engineering Mechanics Problem,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,1-2 The Basic Contents of the Elasticity,Exercises Lesson,Introduction,3,第一章 绪 论,1-1 工程力学问题的建模,1-3 弹性力学问题的基本假设,1-4 弹性力学中的几个基本概念,1-5 弹性力学的学习方法,1-2 弹性力学的基本内容,习题课,绪 论,4,Introduction,The elasticity is a branch of the solid mechanics,the task of it is to research the elasticity objects stress,deformation and displacement due to external force or change of temperature.,The elasticity is the foundation of studying plasticity,fracture mechanics and finite element method.,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.,5,绪 论,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。,弹性力学是学习塑性力学、断裂力学、有限元方法的基础。,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。,6,Introduction,Through the process of establishing the mechanics model in the engineering mechanics problem,generally three parts should be simplified:,Suffering Force Simplification,Material Simplification,Construction Simplification,1、The Modeling Process of the Engineering Mechanics Problem,1-1 The Modeling of the,Engineering Mechanics Problem,7,绪 论,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：,受力简化,材料简化,结构简化,一、工程力学问题的建模过程,1-1 工程力学问题的建模,图1-1,8,Introduction,Material is simplified according to these hypothesises of the same kind,consecution and uniformity in each direction.,（3）Material simplification,According to the Saint-Venants principle,the complex force system is simplified to an equivalent force system.,（2）Suffering Force Simplification,Such as space problem is simplified to flat surface problem and symmetry problem in axis,and entity construction is simplified to plate construction,（1）Construction Simplification,9,绪论,根据各向同性、连续、均匀等假设进行简化。,（3）材料简化,根据圣维南原理，复杂力系简化为等效力系。,（2）受力简化,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。,（1）结构简化,10,Introduction,Proceed to handle to the small quantity in high level.Proceed the linearization that may be linearized.,2、Advertent Problem in Modeling Process,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.,（2）Experiment Verification,（1）Linearization,11,绪论,对高阶小量进行处理，能进行线性化的，进行线性化。,二、建模过程中注意的问题,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。,（2）实验验证,（1）线性化,12,Introduction,The elasticity is a branch of the solid mechanics,the task of it is to research the elasticity objects stress,deformation and displacement due to external force or change of temperature.,1-2 The Basic Contents of the Elasticity,1、Investigative task,The research object of the elasticity is general and complicated shape structure piece,entity structure,plate shell etc.,2、Investigative object,13,绪论,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。,1-2 弹性力学的基本内容,一、研究任务,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。,二、研究对象,14,Introduction,Plasticity:plasticity analysis and design of the structure.,3、The relation about the other course：,Material mechanics:research stress and displacement of the bar structure piece that is pulled,pressed,sheared,bent or turned.,Theoretical mechanics:Study statics and dynamics of the rigid body(constraint force,velocity,acceleration).,Structual mechanics:research internal force and displacement of the bar structure.,Elasticity:stress and displacement analysis of general plane problem,plate,shell and entity structure etc.,15,绪论,塑性力学：结构的塑性分析、设计；,三、与其他学科的关系：,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；,理论力学：研究刚体的静、动力学（约束力、速度、加速度）。,结构力学：研究杆系结构的内力与位移；,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,Introduction,1-3 The Basic Assumption of the Elasticity,In elasticity,doing some necessary assumptions under the premise that can satisfy the practical needing precision and making the problem solved.,（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 Hookes law-the stress becomes the direct proportation with homologous deformation.And the elasticity constant doesnt 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 change along with position coordinates change.,The basic assumption of the elasticity：,17,绪论,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。,（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。,弹性力学的基本假设为：,18,Introduction,（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,绪论,（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,（2）Ideal elasticity assumption:supposing that the object is a ideal elastic body,then the elastic body obey the Hookes law-the stress becomes the direct proportation with homologous deformation.,Introduction,2、Advertent Problem in Modeling Process,物体内任意一点的位移，用它在 、轴上的投影 、来表示，以沿坐标轴正向为正，沿坐标轴负向为负。,Plus sign and negative sign are separately determined by the direction of components,and then isForceLength-3。,（1）整个物体象一个刚体一样进行的运动所引起的位移，一般包括平移和转动。,如图16所示的 、。,练习3什么是小变形假设？小变形假设带来那些简化？,Definition：The object bears the external force function.,练习3什么是小变形假设？小变形假设带来那些简化？,理论力学：研究刚体的静、动力学（约束力、速度、加速度）。,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.,在学习中，不要过分拘泥于细节，应着眼于推导的主要过程，公式的推导和记忆，最好通过矩阵形式和张量。,P点所受面力的集度为：,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。,（五）各物理量之间的关系,练习2弹性力学中基本假设是什么？,According to the Saint-Venants principle,the complex force system is simplified to an equivalent force system.,Introduction,1-4 The Several Basic Concepts of the Elasticity,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.,（2）Property：volumetric force is different from the different location in a point;the volumetric force is continuous in distribution.,1.External stress,1.Volumetric force,（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.,z,x,y,V,O,P,Fig.1-2,21,绪论,1-4 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。,（2）性质：体力随点的位置不同而不同；体力是连续分布的。,（一）外力,（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12所示 。,图1-2,z,x,y,V,O,P,22,Introduction,（3）Gather degree：,（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:,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 isForceLength-3。,The average gather degree of volumetric force:,The gather degree of volumetric force at point P:,The direction of F is the limited one of,23,绪论,（3）集度：,（4）体力分量：,将,F,沿三个坐标轴分解，可得到三个正交的分力：,X,、,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,。,体力的平均集度为：,P点所受体力的集度为：,的方向就是 的极限方向。,24,Introduction,2.Surface force,(3)Gather degree of surface force:the average gather degree of the surface force above :,The gather degree of the surface force at,P,:,(4)The components of surface force:,The components of surface force are ,and then are ForceLength-2,x,y,z,P,S,(2)Property:In general,surface force is the function of located coordinates at point in the surface of the object.,(1)Definition:surface force is distributed one in the surface of the object.For instance,liquid stress and contact stress .,It is shown in Fig.1-3.,25,绪 论,2.面力,上面力的平均集度为：,（3）面力集度：,P点所受面力的集度为：,（4）面力分量：,P点的面力分量为 、，因次是力长度,-2,。,x,y,z,P,S,图1-3,（2）性质：面力一般是物体表面点的位置坐标的函数。,（1）定义：分布在物体表面上的力。如流体压力和接触力,。如图13所示。,26,Introduction,3.Stress gather degree：,The average gather degree of internal force above :,The stress at point,P,:,-Positive stress,-Shearing strength,And then areForceLength-2,The stress component at point P is ,.,：The same point in the object,whose stress of different cross sections is different.,1.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.,x,y,z,A,B,P,o,A,Fig.1-4,27,绪论,（二）应力,3.应力集度：,上的内力的平均集度为：,P,点的应力为：,-正应力,-切应力,因次是力长度,-2,。,P,点的应力分量为 、,2.性质：,在物体内的同一点，不同截面上的应力是不同的。,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14所示 。,x,y,z,A,B,P,o,A,图1-4,28,Introduction,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.,The component of the stress on the plane is equal in size but contrary in direction at the meaning of omitting the small quantity in high level.,(1)For analyzing the state of one point,one small positive parallel hexahedron is taken out from the point.The component of the stress of each section along with coordinates axis that is called the component of the stress.,x,y,z,o,29,绪 论,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。,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。,（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。,x,y,z,o,图1-5,30,Introduction,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.,The positive stress is recorded,y,the positive direction along y axis is positive,whose suffix means the direction along coordinates axis.,（2）Symbol provision：,y,x,y,z,o,Fig.1-6,The stress paralleling the surface of the unit is called the slicing stress,which is showed by ,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.,is showed in Fig.1-6.,31,绪 论,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。,正应力记为,y,沿,y,轴的正向为正,其下标表示所沿坐标轴的方向。,y,x,y,z,o,图1-6,（2）符号规定：,平行于单元体面的应力称为切应力，用 、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。如图16所示的 、。,32,Introduction,The components of the stress on other,x,z,positive surface is shown in Fig.1-7.,The stress on positive surface is positive along the positive direction of coordinates,and is negative athwart the positive direction of coordinates.,33,绪论,其它,x、z,正面上的应力分量的表示如图17所示。,凡正面上的应力沿坐标正向为正，逆坐标正向为负。,图1-7,34,Introduction,The stress that paralleling the surface of the unit is shown like,yx,、,yz,in Fig.1-8,which is positive along the negative direction of x axis and z axis.,Fig.1-8 shows that the normal of the surface of the unit is the negative direction of y,the positive stress is recorded ,which is positive along the negative direction of y axis.,35,绪论,平行于单元体面的应力如图示的,yx,、,yz,，沿,x,轴、,z,轴的负向为正。,图1-8,图18所示单元体面的法线为,y,的负向，正应力记为,沿,y,轴负向为正。,36,Introduction,Elasticity,（3）Noticing the slicing stress sign of elasticity is distinguishing with material mechanics.Generally the slicing stress is positive in elasticity,such as the Fig.1-9shows.However,the sign closing both sides is different in material mechanics.,Material,Mechanics,We should draw stress circle according to the sign provision of material mechanics.,37,绪论,弹性力学,材料力学,（3）注意弹性力学切应力符号和材料力学是有区别的，图19中，弹性力学里，切应力都为正，而材料力学中相邻两面的的符号是不同的。,在画应力圆时，应按材料力学的符号规定。,图1-9,38,Introduction,2.Shearing stress：In Fig.1-5,the orthogonal changes of the line segment,PA,PB,PC,are means with the radian,which is called shearing stress.Shearing stress is shown respectively by ,.,The strain,is the changes of the shape.The strain of the object may come down to the changes of the length and the angle.,1.Positive strain：In Fig.1-5 the flex of the line segment PA,PB,PC per-unit length,namely unit flexible or opposite flex,which is called positive strain,positive strain is shown respectively by ,.,P,Fig.1-5,39,绪论,2.切应变：图1-5中线段,PA,、,PB,、,PC,之间的直角的改变，用弧度表示，称为切应变。分别用 、表示。,（三）形变（应变）,形变,就是形状的改变。物体的形变可以归结为长度的改变和角度的改变。,1.正应变：图1-5中线段,PA,、,PB,、,PC,每单位长度的伸缩，即单位伸缩或相对伸缩，称为正应变。分别用 、表示。,P,图1-5,40,Introduction,（2）Among all points of the object have the opposite displacement,so the object produce distortion.In the elasticity,studying primarily the displacement that the distortion of the object causes.,（1）The displacement that the movement of the whole object like a rigid body proceeding causes,generally which includes the translation and the rotation.In this way the displacement do not make the opposite distance of the shape and particle of the object change.(Object only contain outside effect but have no inside effect),1.When the positions of all point of the object change,thinking generally it is constituted by the displacement of two kinds of property：,Displacement：,When the object transform,the amount of changes of the all point position calls the displacement.,2.The expressing method of the displacement,The displacement of random point in object,whose projection of,u,v,w,in the axis of x,y,z are used to mean it.Positive direction along coordinates axis is positive,negative direction along coordinates axis is negative.These three projections are called the component of the displacement of the point.,41,绪论,（2）物体的各点间有相对位移，因而物体产生了变形。弹性力学中主要研究物体由变形而引起的位移。,（1）整