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1、2 . 应 变 状 态 分 析,Analysis of strians,正应变:,(1) 应变的定义（Difinition of strains),2.1 一点应变状态概念,Concept of strain state at one point,线应变以拉长为正，缩短为负；,切应变:,角应变以直角的减小量为负，增加量为正。,(2) 应变状态矩阵 (strain state matrix ),If the linear strains along any direction and the shearing strains between any two vertical directions
2、 at one point are all known , we say the state of strain at this point is determined .,结构一点处应变情况的总和称为一点应变状态.,如果一点处沿任何方向的线应变以及任意两个相互垂直方向间的切应变都已知,则说该点的应变状态是确定的.,Like the state of stress at one point , the state of strain can be determined by a matrix . It is called strain state matrix .,类似一点应力状态的描述,一点
3、应变状态可以用一个矩阵确定,该矩阵称为应变状态矩阵.,Strain state matrix,Strain state matrix is a symmetrical matrix too . That is :,应变状态矩阵,In Mechanics of Materials all the problems ordinary are plane state of stress , so their state of strain ordinary is three-dimensional state .,材料力学的问题一般是平面应力问题,所以其应变状态通常是三向应变状态.,(1) 斜方向上
4、的应变,考察倾斜微元线段的伸长率时，无须考虑可能存在的局部的刚体平移。,也无须考虑可能存在的局部的刚体转动。,Normal strain along the slope directions,2.2 平面（双向）应变状态分析,Two-dimentional analysis of strain,x 方向的线应变将影响倾斜微元线段的伸长率。,y 方向的线应变将影响倾斜微元线段的伸长率。,角应变也将影响倾斜微元线段的伸长率。,斜方向上的应变 :,拉为正压为负,直角增大为正减小为负,(2) 主应变与应变主方向,Principal strains and principal strain direct
5、ions,At one point if there are three directions vertical to each other and the shearing strains between them are all equal to zero , these directions are called pricipal strain directions and the normal strains along these directions are called principal strains .,Principal strain directions,Princip
6、al strains,(a) 概念 ( Concepts),For the plane stress state , the principal strains are :,For the isotropic materials , the principal stress directions and principal strain directions are just same .,Directions 1 , 2 , 3 are the principal strain directions too .,对线弹性各向同性材料来说,主应力方向和主应变方向是一致的.,2.4 应变的测量,应变片( strain gage ),分析和讨论: 应变片可以直接测量切应变吗？,k 灵敏度系数,Measurements of strain,应变片的测量结果常用 微应变 来表示，记为 。,直角应变花 ( rectangular rosette ),等角应变花 ( equiangular rosette ),在主轴坐标系下,忽略二阶微量,故有,(2) 体积变化率,习 题,8-14 8-16 8-17,本节内容结束,谢谢大家,
