应力和平衡方程.ppt

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1、Theory of ElasticityChapter 3Stress and Equilibrium(应力和平衡方程)Chapter Page Content（内容）（内容）1.Introduction（概述）（概述）2.Mathematical Preliminaries（数学基础）（数学基础）3.Stress and Equilibrium（应力与平衡）（应力与平衡）4.Displacements and Strains（位移与应变）（位移与应变）5.Material Behavior-Linear Elastic Solids（弹性应力应变关系（弹性应力应变关系)6.Formulati

2、on and Solution Strategies（弹性力学问题求解）（弹性力学问题求解）7.Two-Dimensional Formulation（平面问题基本理论）（平面问题基本理论）8.Two-Dimensional Solution（平面问题的直角坐标求解）（平面问题的直角坐标求解）9.Two-Dimensional Solution（平面问题的极坐标求解）（平面问题的极坐标求解）10.Three-Dimensional Problems（三维空间问题）（三维空间问题）11.Bending of Thin Plates（薄板弯曲）（薄板弯曲）12.Plastic deformatio

3、n Introduction（塑性力学基础）（塑性力学基础）13.Introduction to Finite Element Mechod（有限元方法介绍）（有限元方法介绍）31Chapter 3(第三章第三章)3.1 Body and Surface Forces（体力和面力）（体力和面力）3.2 Stress Vector（应力）（应力）3.3 Stress Tensor(应力张量应力张量)3.4 State of stress at a point(一点应力状态一点应力状态)3.5 Principal stress(主应力主应力)3.6 Octahedral strains(八面体应力

4、八面体应力)3.7 Spherical and Deviatoric Stresses（应力球张（应力球张量和应力偏张量）量和应力偏张量）3.8 Equilibrium Equations（平衡方程）（平衡方程）Chapter Page 323.1 Body and Surface Forces（体力和面力）Chapter Page 3External loadings（外力）Body forces（体力）Surface forces.（面力）Notation and Sign3xyzOChapter Page 3Surface forces（面力）：Notation and Sign4xyz

5、O3.1 Body and Surface Forces（体力和面力）3.2 Stress Vector（应力矢量）Chapter Page 3Stress Vector（应力矢量）（应力矢量）5AppPn(法线法线)Chapter Page 3.2 Stress Vector（应力矢量）ApPn(法线法线)(1)The intensity of internal force at point P(内力集度内力集度)(2)Stress vector(应力矢量应力矢量)63(3)Normal and shearing stress(正应力、剪应力正应力、剪应力)Chapter Page 3Str

6、ess Tensor at a point(一点的应力张量)73.3 Stress Tensor(应力张量)The stress on x plane x面的应力The stress on y plane y面的应力The stress on z plane z面的应力Chapter Page 383.3 Stress Tensor(应力张量)ij:stress tensor(应力张量应力张量)Von Karman NotationsPositive DirectionsNotation and SignChapter Page 3.4 State of stress at a point(一

7、点应力状态)Stress Vector（矢量）（矢量）stress tensor(张量张量)?93Chapter Page 3103.4 State of stress at a point(一点应力状态)(2-D)Mechanics of Materials(材料力学材料力学)Chapter Page 1133D:through equation condition:(由平衡条件得如下公式由平衡条件得如下公式)3.4 State of stress at a point(一点应力状态的描述)Chapter Page 1233.4 State of stress at a point(一点应力

8、状态的描述)Normal and shearing stress(由平衡条件得如下公式)Chapter Page 133 Through the Indicial Notation（由指标记法）：（由指标记法）：3.4 State of stress at a point(一点应力状态的描述)Coordinate Transformations（坐标变换）（坐标变换）x y zx y zChapter Page 143 is a two order tensor (是一个二阶张量是一个二阶张量)The state of stress at point P can be successfully

9、 described by(P点的应力状态可以由点的应力状态可以由 完整的描述完整的描述)3.4 State of stress at a point(一点应力状态的描述)Chapter Page 315In two dimensional coordinate（在二维坐标系）（在二维坐标系）3.4 State of stress at a point(一点应力状态的描述)Chapter Page 316Three dimensional(三维)：3.4 State of stress at a point(一点应力状态的描述)Chapter Page 3173.5 Principal str

10、ess(主应力)Chapter Page 3.5 Principal stress(主应力)183Chapter Page 3.5 Principal stress(主应力)The general characteristic equation for the stress tensor（应力张量特征方程）（应力张量特征方程）Invariants of the stress tensor193Chapter Page principal stress s s 1,s s 2,s s 3Octahedral plane（八面体平面）（八面体平面）其中其中 为第四强度理论的等效应为第四强度理论的等

11、效应力力3.6 Octahedral strains(八面体应力)203Chapter Page 3213.7 Spherical and Deviatoric Stresses（应力球张量和应力偏张量）Chapter Page 3spherical stress（球应力）（球应力）while the deviatoric stress becomes（应力偏张量）（应力偏张量）223.7 Spherical and Deviatoric Stresses（应力球张量和应力偏张量）Chapter Page 323 3.8 Equilibrium Equations（平衡方程）Chapter P

12、age 2433.8 Equilibrium Equations（平衡方程）Chapter Page 3-D2533.8 Equilibrium Equations（平衡方程）Chapter Page 2633.8 Equilibrium Equations（平衡方程）Chapter Page equilibrium equation in cylindrical coordinates.（柱坐标系下的平衡方程）（柱坐标系下的平衡方程）2733.8 Equilibrium Equations（平衡方程）Chapter Page 2833.8 Equilibrium Equations（平衡方程）Chapter Page 329 Vocabularies（常用词汇）body force 体力体力surface force面力面力state of stress应力状态应力状态principal stress 主应力主应力octahedral 八面体八面体spherical stresses 球应力球应力deviatoric stresses 偏应力偏应力equilibrium equations 平衡方程平衡方程Chapter Page Homework2-12-32-4303