弹性力学双语讲义(chapter1)

1.2 some important concepts in theory of elasticity 1.2 弹性力学中的几个重要概念 A. External Forces 外力 B. Stress 应力 C. Deformation(Strain) 形变 应变 形变(应变 应变) D. Displacement 位移
Comparison among the three courses in solid mechanics 固体力学三门学科的比较
• Three branches have the same purpose and do differ from one another both in objects studied and the methods of analysis used. • 1. Objects studied 研究对象 2. Methods of analysis 研究方法
A. external forces 外力
1. Body forces 2. Surface forces
体积力，体力 体积力， 表面力， 表面力，面力
1. Body forces
体力。 体力。
External forces or the loads,distributed over the volume of the body,are called body forces. 分布在物体体内的外力叫体力 E.g. gravitational forces, or inertia forces in the case of a body in motion. 例如： 重力， 例如： 重力， 惯性力
• Elasticity deals with the stresses and displacements of the structural elements such as blocks, plates and shells, which are not in the form of a bar. • 弹性力学研究块体、板和壳体的应力和位移。 弹性力学研究块体、板和壳体的应力和位移。
•A prismatical tension member with a small hole •It is assumed in mechanics of materials that the tensile stresses are uniformly distributed across the net section of the member. •The analysis in elasticity shows that the stresses are by no means uniform, but are concentrated near the hole.
1. objects studied:--研究对象 研究对象: 研究对象 (1) Similarity---------相同点 相同点
to deal with the elastic solids 都是研究弹性体
(2)objects studied--difference研究对象 不同点 研究对象--不同点 研究对象 Mechanics of materials : bar element 材料力学 单根杆件 Structural bar systems:-Mechanics : truss, rigid frame 杆件系统： 桁架，刚架。 结构力学 杆件系统： 桁架，刚架。 Elasticity: 1. plates and shells 板，壳 2.blocks: 块体 弹性力学 e.g. dams,foundations 坝，基础 3.analyze bar element precisely 对杆件作精确分析
(2) methods of analysis:------ difference 研究方法-------- 不同点 不同点: 研究方法
Mechanics of materials: some assumptions on the strain condition or the stress condition are made 材料力学： 材料力学： 对应变或应力情况作某些假定 Elasticity：no assumptions on the strain condition ： or the stress condition are made. 弹性力学 : 对应变或应力情况不作假定
• Elasticity also analyze a bar element thoroughly and precisely. • 弹性力学对杆件作更精确分析
2. methods of analysis:研究方法 研究方法
(1) Similarity--- 相同点 :
equilibrium aspects geometrical aspects physical aspects
1.1 Contents of Theory of Elasticity 1.1 弹性力学的内容 • NAME Theory of elasticity is often called elasticity for short. It is a branch of solid mechanics. 弹性力学的理论简称为弹性理论或弹性力学. 弹性力学的理论简称为弹性理论或弹性力学. 它是固体力学的一个分枝
Body force components 体力分量 • F=X i+Y j+Z k=(X,Y,Z) • The projections of F on the x,y,and z axes are called the body force components at P. 体力在坐标轴上的投影叫体力分量。 体力在坐标轴上的投影叫体力分量。 • The body force components will be denoted by X,Y and Z 体力分量用X,Y,Z表示 体力分量用 表示
Mechanics of materials: some assumptions on the strain condition or the stress condition are made The assumptions simplify the mathematical derivation to a certain extent. The assumptions inevitably reduce the degree of accuracy of the results obtained..
Three branches of solid mechanics 固体力学的三个分枝 固体力学的三个分枝
• Mechanics of materials 材料力学, 材料力学, Structural Mechanics 结构力学 Elasticity 弹性力学
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What does the Elasticity deal with? It deals with the stresses, deformations and displacements in elastic solids produced by external forces or changes in temperature. 研究弹性体由于外力和温度改变而引起的应力， 由于外力和温度改变而引起的应力 研究弹性体由于外力和温度改变而引起的应力， 形变和位移。 形变和位移。 It analyzes the stresses, deformations and displacements of structural elements within the elastic range and thereby to check the sufficiency of their strength, stiffness and stability. 分析结构的应力，形变和位移， 分析结构的应力，形变和位移，检查是否满足强 刚度和稳定性条件。 度，刚度和稳定性条件。
• Structural Mechanics deals with the stresses and displacements of a structural in the form of a bar system, such as a truss or a rigid frame. • 结构力学研究杆件系统（例：桁架或刚架）的应力 结构力学研究杆件系统（ 桁架或刚架） 和位移
静力学方面 几何学方面 物理学方面
•equilibrium aspects --equilibrium of forces of an isolated body 静力学方面--脱离体力的平衡 静力学方面 脱离体力的平衡 • geometrical aspects --the relations between displacements and strains. 几何学方面--位移和应变的关系 几何学方面--位移和应变的关系 • physical aspects-- -the relations between stresses and strains 物理学方面--应力和应变的关系 物理学方面 应力和应变的关系
•The problem of bending of a straight beam under transverse loads. •It is assumed in mechanics of materials that a plane section of the beam remains plane after bending, which leads to the linear distribution of bending stresses. •No assumption, that a plane section of the beam remains plane after bending, is made in Elasticity.
Body force Fig.
体力定义图。 体力定义图。
F=lim ∆Q/ ∆V
∆v 0
F--body force vector at p, The vector quantity F is the intensity of body force at P F-- P点的体力矢量 点的体力矢量 ∆V--an elementary volume of the body around point p 包含P点的小体积 ∆V--包含 点的小体积 包含 ∆Q--body force acting on ∆ V 作用在∆ 上的体力的合力 ∆Q--作用在∆ V上的体力的合力 作用在
• Mechanics of materials deals essentially with the stresses and displacements of structural element in the shape of a bar, straight or curved, which is subjected to tension, compression, shear, bending, or torsion. 材料力学研究受到拉、 材料力学研究受到拉、压、剪、弯或扭的直杆 或曲杆的应力和位移。 或曲杆的应力和位移。
Elasticity： ： no assumptions on the strain condition or the stress condition are made. The results obtained in elasticity are more accurate and may be used to check the approximate results obtained in Mechanics of materials.
弹性力学 Elasticity The lectures will be given both in English and Chinese 采用中英文双语讲授
Textbook: Applied Elasticity 徐芝纶 中文教材： 中文教材： 弹性力学简明教程 徐芝纶
Chapter 1. Introduction 第一章 绪论