[工学]弹性力学 第二章ding07-xin.ppt

Chapter 2 Theory of Plane Problems 第二章：平面问题的理论 2.1 Plane stress and plane strain 平面应力问题与平面应变问题 2.2 Differential equations of equilibrium 平衡微分方程 2.3 Stress at a point. Principal stresses 斜截面上的应力。主应力 2.4 Geometrical equations. Rigid-body displacements 几何方程。刚体位移 2.5 Physical equations. 物理方程 2.6 Boundary conditions 边界条件 2.7 Saint-venant`s principle-1 圣维南原理 2.8 solution of plane problem in terms of displacements 按位移求解平面问题 2.9 solution of plane problem in terms of stresses 按应力求解平面问题 2.10 Case of constant body forces 常体力情况下的简化 2.11 Airy`s stress function. Inverse method and semi-inverse method 艾瑞应力函数。逆解法与半 逆解法 学习指导： 系统介绍平面问题的基本理论（基本方程和边界条件），及两种解法。 2.1 Plane stress and plane strain  2.1 平面应力问题与平面应变问题 A spatial problem becomes a plane problem when the body has a particular shape and particular external forces. Plane problems: plane stress problems and plane strain problems 当物体的形状特殊，外力分布特殊，空间问题转化为平面问题。 平面问题: 平面应力问题与平面应变问题 1. Conditions for plane stress problem平面应力问题的条件 Body--a very thin plate of uniform thickness t. External forces— 1. The surface forces act on the edges only. 2. The surface forces and body forces are parallel to the faces of the plate and distributed uniformly over the thickness. Body—很薄的等厚度薄板 External forces— 1. 面力仅作用板周边 2. 面力体力平行于板面 且沿 厚度无变化。 2. Coordinate system for plane stress problem平面应力问题的坐标系 x and y axes are in the middle plane and z axis is perpendicular to the middle plane. x，y轴放在薄板的中面内，z垂直于中面。 平面应力问题示意图 3. Stresses for plane stress problem平面应力问题的应力 Noting the absence of surface forces on the faces of the plate, we have (?z ?zx ?zy)z=?t/2=0 since stress gradients through plate are small, (?z ?zx ?zy)z=any ≈ 0 (?x ?y ?xy)≠0 ,They are functions of x and y only. the plate is said to be in a plane stress condition 板 面无面力作用故: (?z ?zx ?zy)z=?t/2=0 通过板的应力梯度小 (?z ?zx ?zy)z=any ≈ 0 (?x ?y ?xy)≠0 , 板为处于平面应力