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 徐汉忠第二版2001/10 弹性力学第二章
徐汉忠第二版2001/10 弹性力学第二章 1 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
Spatial problems and plane problems 空间问题转化为平面问题。 a spatial problem- a plane problem the body has a particular shape particular external forces. 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 Plane problems: plane stress problems and plane strain problems 平面问题:平面应力问题与平面应变问题 徐汉忠第二版2001/10 弹性力学第二章 2
徐汉忠第二版2001/10 弹性力学第二章 2 Spatial problems and plane problems 空间问题转化为平面问题。 • a spatial problem a plane problem the body has a particular shape. particular external forces. • 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。 • Plane problems: plane stress problems and plane strain problems 平面问题: 平面应力问题与平面应变问题
A conditions for plane stress problem 平面应力问题的条件 Body-a very thin plate of uniform thickness t 很薄的等厚度薄板 External forces 1. The surface forces act on the edges only 面力仅作用板周边 2. The surface forces and body forces are parallel to the faces of the plate and distributed uniformly over the thickness 面力体力平行于板面且沿厚度无变化 徐汉忠第二版2001/10 弹性力学第二章
徐汉忠第二版2001/10 弹性力学第二章 3 A. conditions for plane stress problem 平面应力问题的条件 • Body--a very thin plate of uniform thickness t. 很薄的等厚度薄板 • External forces-- 1. The surface forces act on the edges only. 面力仅作用板周边 2. The surface forces and body forces are parallel to the faces of the plate and distributed uniformly over the thickness. 面力体力平行于板面且沿厚度无变化
t/2 t/2 z Fig 2.1.1 徐汉忠第二版2001/10 弹性力学第二章
徐汉忠第二版2001/10 弹性力学第二章 4
B 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 pla ane x,y轴放在薄板的中面内,z垂直于中面 徐汉忠第二版2001/10 弹性力学第二章
徐汉忠第二版2001/10 弹性力学第二章 5 B. 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