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### Theory of Elasticity

Engineering Physics

Applications and Design

Beam Deflection, Stress Equation and Calculators

Theory of Elasticity, Book of Theorectical Physics

L.D. Landau

E.M. Lifshitz

177 pages

Open: Theory of Elasticity, Book of Theorectical Physics

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Preface

The present volume of our Theoretical Physics deals with the theory of elasticity.

Being written by physicists, and primarily for physicists, it naturally includes not only the ordinary theory of the deformation of solids, but also some topics not usually found in textbooks on the subject, such as thermal conduction and viscosity in solids, and various problems in the theory of elastic vibrations and waves. On the other hand, we have discussed only very briefly certain special matters, such as complex mathematical methods in the theory of elasticity and the theory of shells, which are outside the scope of this book.

Theory of Elasticity is the branch of ** Solid Mechanics ** which deals with the

**in**

*stress and displacements**elastic solids*produced by

*external forces*or

*changes in temperature*.

TOC

I. FUNDAMENTAL EQUATIONS

§1. The strain tensor 1

§2. The stress tensor 4

§3. The thermodynamics of deformation 8

§4. Hooke's law 10

§5. Homogeneous deformations 13

§6. Deformations with change of temperature 15

§7. The equations of equilibrium for isotropic bodies 17

§8. Equilibrium of an elastic medium bounded by a plane 25

§9. Solid bodies in contact 30

§10. The elastic properties of crystals 37

II. THE EQUILIBRIUM OF RODS AND PLATES

§11. The energy of a bent plate 44

§12. The equation of equilibrium for a plate 46

§13. Longitudinal deformations of plates 53

§14. Large deflections of plates 58

§15. Deformations of shells 62

§16. Torsion of rods 68

§17. Bending of rods 75

§18. The energy of a deformed rod 78

§19. The equations of equilibrium of rods 82

§20. Small deflections of rods 89

§21. The stability of elastic systems 97

III. ELASTIC WAVES

§22. Elastic waves in an isotropic medium 101

§23. Elastic waves in crystals 106

§24. Surface waves 109

§25. Vibration of rods and plates 113

§26. Anharmonic vibrations 118

IV. DISLOCATIONS

§27. Elastic deformations in the presence of a dislocation 123

§28. The action of a stress field on a dislocation 131

§29. A continuous distribution of dislocations 134

§30. Distribution of interacting dislocations 139

§31. Equilibrium of a crack in an elastic medium 144

V. THERMAL CONDUCTION AND VISCOSITY IN SOLIDS

Page

§32. The equation of thermal conduction in solids 150

§33. Thermal conduction in crystals 152

§34. Viscosity of solids 153

§35. The absorption of sound in solids 155

§36. Highly viscous fluids 161

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