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弹性力学 Theory of Elasticity

弹性力学 Theory of Elasticity. 闫晓军， Xiaojun Yan, Ph.D. Associate Professor School of Jet Propulsion. Theory of Elasticity. Chapter. Page. 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）

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弹性力学 Theory of Elasticity

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  1. 弹性力学Theory of Elasticity 闫晓军，Xiaojun Yan, Ph.D. Associate Professor School of Jet Propulsion

  2. Theory of Elasticity Chapter Page 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 Formulation （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） 1 1

  3. Theory of Elasticity Chapter Page About the course The lectures will be given in Chinese, but the lecture 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） 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% ) 1 2

  4. Theory of Elasticity Chapter Page About the course References: 1 杨桂通，《弹性力学》，高等教育出版社，2002 1 2 徐芝纶， 《弹性力学简明教程》，高等教育出版社，1983 3 S. P. Timoshenko, J.N. Goodier, “Theory of Elasticity”, McGraw-Hill Book Company, 1970 4 Martin H. Sadd, “Elasticity”, Elsevier Butterworth–heinemann, 2005 1 3

  5. Theory of Elasticity Chapter Page Introduction • What is Elasticity （弹性力学？） • History of Elasticity（历史） • Applications of Elasticity（应用） • Basic Assumptions（基本假设） 1 4

  6. Theory of Elasticity Chapter Page 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。 5

  7. Theory of Elasticity Chapter Page 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 Difference between solids and fluids Mechanics of Solids, The New Encyclopedia of Britannica, 15th edition, Vol. 23, pp. 734-747, 2002, 6

  8. Theory of Elasticity Chapter Page 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。 1 7

  9. F F Theory of Elasticity D D Chapter Page What is Elasticity Elastic Perfectly Elastic 8

  10. Theory of Elasticity Chapter Page History of Elasticity Cauchy Saint-Venant Kirchhoff Love Timoshenko Theodore Von Karman • Newton • Galileo • Hooke • Bernoullis • Navier • Poisson G. I. Taylor Griffith , Irwin , Rice Courant ,Clough Ziekiewitz, Feng Kang 9

  11. Leonardo da Vinci System for equalizing the release of a spring Theory of Elasticity Chapter Page History(1600-1700) the possible length dependence of the wire strength due to statistical defects distribution 10

  12. Galileo Theory of Elasticity Chapter Page History (1600-1700) Rods under tension: Independent of length , proportional to the cross section. 1 11

  13. Theory of Elasticity Chapter Page History (1600-1700) • Galileo’ test • A deformable body ,First time • Geometric dependence : beam length,the bending resistance of cross-section. • stress distribution was wrong 1 12

  14. Isaac Newton Theory of Elasticity Chapter Page History(1600-1700) 1 13

  15. Robert Hooke (1635-1703) Willen Church The only building in existence that Robert Hooke designed and that is in original condition. Theory of Elasticity Hooke memorial window, St. Helen's, Bishopsgate, City of London. Chapter Page History (1600-1700) 1 14

  16. Theory of Elasticity Chapter Page History (1600-1700) • 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. 每加物一石，则张一尺。 1 15

  17. Bernoullis Theory of Elasticity Jacob Bernoulli 1654-1705 Johann Bernoulli 1667-1748 Daniel Bernoulli 1700-1782 Leohard Euler, Johann Bernoulli’s student, 1727 Chapter Page History (1700-1880) 1 16

  18. Clande-Louis-Marie-Henri Navier (1821) • “Equilibrium and motion of elastic solids” Theory of Elasticity Chapter Page History (1700-1880) u: displacement vector C a measure of elastic modulus f the body force vector. 1 17

  19. Simon Denis Poisson • Poisson’s ratio（1829） • Longitudinal and • transverse waves Theory of Elasticity Foam structures with a negative Poisson's ratio, Science, 235 1038-1040 (1987). Chapter Page History (1700-1880) 1 18

  20. 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) Theory of Elasticity Chapter Page History (1700-1880) 1 19

  21. Theory of Elasticity Chapter Page History (1700-1880) • 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） 1 20

  22. Theory of Elasticity Chapter Page History (1700-1880) • 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 1 21

  23. Gustav Robert Kirchhoff • Founding master of electro-magnetism • Kirchhoff plate theory Theory of Elasticity Chapter Page History (1700-1880) 1 22

  24. Love • the point source theory and Love wave • A treatise on the mathematical theory of elasticity(1892-1893) Theory of Elasticity Chapter Page History (1880-1950) 1 23

  25. S.P.Timoshenko (work with Prandtl, the father of aerodynamics. ) • Beams on elastic foundation • Timoshenko beam theory • Mechanics of plates and shells • Elastic vibration a scientist and an engineer Theory of Elasticity Chapter Page History (1880-1950) 1 24

  26. Theodore Von Karman • H. S. Tsien and • W. Z. Chien • Werner Heisenberg • Large deflection and buckling Theory of Elasticity Chapter Page History (1880-1950) 1 25

  27. Theodore Von Karman • and G. I. Taylor • Establishing IUTAM Theory of Elasticity Chapter Page History (1950-) 1 26

  28. Griffith (1921), Irwin (1957), Rice (1968) • fracture mechanics (G, K, J) Theory of Elasticity Chapter Page History (1950-) 1 27

  29. Fracture mechanics Theory of Elasticity Chapter Page History (1950-) 1 28

  30. Courant (1943) • Clough, Ziekiewitz, Feng Kang, Finite Element Method Theory of Elasticity Chapter Page History (1950-) 1 29

  31. Theory of Elasticity Chapter Page Applications of Elasticity • Construction 1 30

  32. Aeronautic Engineering Theory of Elasticity Chapter Page Applications of Elasticity 1 31

  33. Astronautic Engineering Theory of Elasticity Chapter Page Applications of Elasticity 1 32

  34. Integrated Circuit Elasticity plays a central role in estimating the integrity of ICs. Theory of Elasticity Chapter Page Applications of Elasticity 1 33

  35. Nanotechnology Theory of Elasticity Chapter Page Applications of Elasticity 1 34

  36. Computational Microscope Theory of Elasticity Chapter Page Applications of Elasticity 1 35

  37. Biology and Biomechanics The wing of a dragonfly and topological optimization Theory of Elasticity 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. Chapter Page Applications of Elasticity 1 36

  38. Sports • Archery Theory of Elasticity Chapter Page Applications of Elasticity 1 37

  39. Theory of Elasticity Chapter Page 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） 38

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