弹性力学course.buaa.edu.cn/access/content/group/318f253c... · 3 s. p. timoshenko, j.n....
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弹性力学Theory of Elasticity
闫晓军，Xiaojun Yan, Ph.D.
School of Jet Propulsion
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About the course
The homework will take 20% of the overall score, the mid-term exam another 20%, while the final exam will take the rest 60%. ( 平时20% ，期中20% ，期末60% )
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The lectures will be given in Chinese, but will be written in English and Chinese ，and Chinese textbook is selected.（中文讲述，中英文课件，中文教材）
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About the course
References:
1 杨桂通，《弹性力学》，高等教育出版社，2002 12 徐芝纶， 《弹性力学简明教程》，高等教育出版社，19833 S. P. Timoshenko, J.N. Goodier, “Theory of Elasticity”, McGraw-Hill Book Company, 19704 Martin H. Sadd, “Elasticity”, Elsevier Butterworth–heinemann, 2005
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Content（内容）
1. Introduction（概述）2. Mathematical Preliminaries （数学基础）3. Stress and Equilibrium（应力与平衡）4. Displacements and Strains （位移与应变）5. Material Behavior- Linear Elastic Solids
（弹性应力应变关系)6. Formulation and Solution Strategies（弹性力学问题求解）7. Two-Dimensional Formulation （平面问题基本理论）8. Two-Dimensional Solution （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）10. Three-Dimensional Problems（三维空间问题）11. Bending of Thin Plates （薄板弯曲）12. Introduction to Finite Element Mechod（有限元方法介绍）13. Plastic deformation – Introduction（塑性力学基础）
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Introduction
• Why we study this course?• What is Elasticity （弹性力学？）
• History of Elasticity（历史）
• Applications of Elasticity （应用）
• Basic Assumptions（基本假设）
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Why we study this course?• From the view of art
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Nano Car A380
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Why we study this course?• From the view of art (History)
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First helicopter CH-47“支努干”(Chinook) 直升机
You understand deeply about essence of the real world
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Why we study this course?• From the view of practical life
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You have a power tool to change your life
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What is Elasticity
• Solid Mechanics: deals with the deformations set up in a solid as a result of a system of forces. 固体力学：研究固体在外力载荷作用下物体内部所产生的变形等。
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What is Elasticity固体：“A material is called solid rather than fluid if it can also support a substantial shearing force over the time scale of some natural process or technological application of interest.”
J. R. Rice
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Difference between solids and fluids Mechanics of Solids, The New Encyclopedia of Britannica, 15th edition, Vol. 23, pp. 734-747, 2002,
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What is Elasticity
Elasticity is an elegant and fascinating subject that deals with determination of the stress,strain, and displacement distribution in an elastic solid under the influence of external forces.
研究弹性体在外力载荷或者温度改变
（外界因素）时，物体内部所产生的位移、变形和应力分布等。
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What is Elasticity
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Elastic
F
DPerfectly Elastic
F
D
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History of Elasticity
• Newton• Galileo• Hooke• Bernoullis
• Navier
• Poisson
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G. I. TaylorGriffith , Irwin , RiceCourant ,CloughZiekiewitz, Feng Kang
CauchySaint-VenantKirchhoffLoveTimoshenkoTheodore Von Karman
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History(1600-1700)
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• Leonardo da Vinci• System for equalizing the release of a spring
the possible length dependence of the wire strength due to statistical defects distribution
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History (1600-1700)• Galileo
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Rods under tension: Independent of length , proportional to the cross section.
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History (1600-1700)•Galileo’ test•A deformable body ,First time•Geometric dependence : beam length, the bending resistance of cross-section.•stress distribution was wrong
d
L
W
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History(1600-1700)
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Isaac Newton
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History (1600-1700)• Robert Hooke (1635-1703)
Hooke memorial window, St. Helen's, Bishopsgate, City of London.
Willen ChurchThe only building in existence that Robert Hooke designed and that is in original condition.
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History (1600-1700)
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• Hooke Law
• 郑玄（公元127－200）tension is proportional to the stretch
Hooke’s law established the notion of (linear) elasticity but not yet in a way that was expressible in terms of stress and strain.
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每加物一石，则张一尺。
History (1700-1880)
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• Bernoullis(Concepts of stress and strain)
Daniel Bernoulli 1700-1782
Jacob Bernoulli 1654-1705
Johann Bernoulli1667-1748
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History (1700-1880)
• Leohard Euler
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Johann Bernoulli’s student, 1727
εσ E=
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History (1700-1880)
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• Clande-Louis-Marie-Henri Navier (1821)
“Equilibrium and motion of elastic solids”
( ) 02 ,2 =++∇ ikiki fuuC
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u: displacement vectorC a measure of elastic modulus f the body force vector.
History (1700-1880)
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• Simon Denis PoissonPoisson’s ratio （1829）
Longitudinal and transverse waves
Foam structures with a negative Poisson's ratio, Science, 235 1038-1040 (1987).
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History (1700-1880)
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• Augustin-Louis Cauchy
formalized the concept of stress in the context of a generalized three-dimensional theory (提出
了三维空间应力的概念)
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History (1700-1880)
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• Augustin-Louis Cauchy Concepts of princprincipal stresses and principal
strains（主应力和主应变）
Generalized Hooke’s law（广义虎克定律）
Equations of motion in terms of components of stress with their boundary conditions（以应力表示的运动方程）
Cauchy’s relation of elasticity tensor （弹性张量的关系式）
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History (1700-1880)
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• Adhemer Jean Claude Barre
de Saint-Venant (a student of Navier ) Saint-Venant Principle （圣维南原理）
Semi-inverse solution(1853) Beam Bending
Bending and torsion of a non-circular prismatic rod
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• Gustav Robert KirchhoffFounding master of electro-
magnetismKirchhoff plate theory
History (1700-1880)
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History (1880-1950)
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• Love the point source theory and
Love wave
A treatise on the
mathematical theory of
elasticity(1892-1893)
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History (1880-1950)
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• S.P.Timoshenko (work with Prandtl, the father of aerodynamics. )
Beams on elastic foundation
Timoshenko beam theory
Mechanics of plates and shells
Elastic vibrationa scientist and an engineer
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History (1880-1950)
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• Theodore Von Karman H. S. Tsien and W. Z. Chien Werner Heisenberg
• Large deflection and buckling
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• Theodore Von Karman
and G. I. TaylorEstablishing IUTAM
History (1950-)
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• Griffith (1921), Irwin (1957), Rice (1968)
• fracture mechanics (G, K, J)
History (1950-)
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• Courant (1943)• Clough, Ziekiewitz, Feng Kang, Finite Element
Method
History (1950-)
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Applications of Elasticity
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• Aeronautic Engineering
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Applications of Elasticity
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• Astronautic Engineering
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Applications of Elasticity
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Integrated CircuitElasticity plays a central role in estimating the integrity of ICs.
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Applications of Elasticity
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Computational Microscope
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Applications of Elasticity
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Biology and BiomechanicsThe wing of a dragonfly and topological optimization
Dragonfly wings - note the more reinforced structure in the leading third of each wing. The front wing beats approximately 1/4 of a cycle ahead of the rear wing.
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Basic Assumptions
• Continuous(连续性)• Homogeneous（均匀）
• Isotropic（各向同性）
• perfectly elastic（理想弹性）
• Small deformation（小变形）
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