应力和平衡方程.ppt

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1、Theory of Elasticity,Chapter 3Stress and Equilibrium(应力和平衡方程),Content（内容）,Introduction（概述）Mathematical Preliminaries（数学基础）Stress and Equilibrium（应力与平衡）Displacements and Strains（位移与应变）Material Behavior-Linear Elastic Solids（弹性应力应变关系)Formulation and Solution Strategies（弹性力学问题求解）Two-Dimensional Formula

2、tion（平面问题基本理论）Two-Dimensional Solution（平面问题的直角坐标求解）Two-Dimensional Solution（平面问题的极坐标求解）Three-Dimensional Problems（三维空间问题）Bending of Thin Plates（薄板弯曲）Plastic deformation Introduction（塑性力学基础）Introduction to Finite Element Mechod（有限元方法介绍）,3,1,Chapter 3(第三章),3.1 Body and Surface Forces（体力和面力）3.2 Stress

3、Vector（应力）3.3 Stress Tensor(应力张量)3.4 State of stress at a point(一点应力状态)3.5 Principal stress(主应力)3.6 Octahedral strains(八面体应力)3.7 Spherical and Deviatoric Stresses（应力球张量和应力偏张量）3.8 Equilibrium Equations（平衡方程）,3,2,3.1 Body and Surface Forces（体力和面力）,3,External loadings（外力）,Notation and Sign,3,3,Surface

4、forces（面力）：,Notation and Sign,4,3.1 Body and Surface Forces（体力和面力）,3.2 Stress Vector（应力矢量）,3,Stress Vector（应力矢量）,5,3.2 Stress Vector（应力矢量）,The intensity of internal force at point P(内力集度),(2)Stress vector(应力矢量),6,3,(3)Normal and shearing stress(正应力、剪应力),3,Stress Tensor at a point(一点的应力张量),7,3.3 Stre

5、ss 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,3,8,3.3 Stress Tensor(应力张量),ij:stress tensor(应力张量),Von Karman Notations,Positive Directions,Notation and Sign,3.4 State of stress at a point(一点应力状态),9,3,3,10,3.4 State of stress at a point(一点应力状态),(2-

6、D)Mechanics of Materials(材料力学),11,3,3D:through equation condition:(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),12,3,3.4 State of stress at a point(一点应力状态的描述),Normal and shearing stress(由平衡条件得如下公式),13,3,Through the Indicial Notation（由指标记法）：,3.4 State of stress at a point(一点应力状态的描述),Coordina

7、te Transformations（坐标变换）,x y z,x y z,14,3,is a two order tensor(是一个二阶张量),The state of stress at point P can be successfully described by(P点的应力状态可以由 完整的描述),3.4 State of stress at a point(一点应力状态的描述),3,15,In two dimensional coordinate（在二维坐标系）,3.4 State of stress at a point(一点应力状态的描述),3,16,Three dimensi

8、onal(三维)：,3.4 State of stress at a point(一点应力状态的描述),3,17,3.5 Principal stress(主应力),3.5 Principal stress(主应力),18,3,3.5 Principal stress(主应力),The general characteristic equation for the stress tensor（应力张量特征方程）,Invariants of the stress tensor,19,3,其中 为第四强度理论的等效应力,3.6 Octahedral strains(八面体应力),20,3,3,21

9、,3.7 Spherical and Deviatoric Stresses（应力球张量和应力偏张量）,3,spherical stress（球应力）,while the deviatoric stress becomes（应力偏张量）,22,3.7 Spherical and Deviatoric Stresses（应力球张量和应力偏张量）,3,23,3.8 Equilibrium Equations（平衡方程）,24,3,3.8 Equilibrium Equations（平衡方程）,3-D,25,3,3.8 Equilibrium Equations（平衡方程）,26,3,3.8 Equ

10、ilibrium Equations（平衡方程）,equilibrium equation in cylindrical coordinates.（柱坐标系下的平衡方程）,27,3,3.8 Equilibrium Equations（平衡方程）,28,3,3.8 Equilibrium Equations（平衡方程）,3,29,Vocabularies（常用词汇）,body force 体力surface force面力state of stress应力状态principal stress 主应力octahedral 八面体spherical stresses 球应力deviatoric stresses 偏应力equilibrium equations 平衡方程,Homework,2-12-32-4,30,3,