《THE mathematical theory of ferfectly elastic solods》

CHAPTER Ⅰ. PROPERTIES OF ELASTIC SOLIDS1

1-17 Solid Matter as it really is1

18-34 Real Matter with ideally perfect Elasticity6

35-46 Ideal Continuous Matter with perfect Elasticity14

CHAPTER Ⅱ. ANALYSIS OF STRAINS19

47-50 Preliminary19

51-58 Theory of Small Strains in general20

59-66 General properties of Homogeneous Strain24

67-80 Analytical investigation27

81-84 Pure Homogeneous Strain32

85,86 Rotational Homogeneous Strain35

87,88 Principle of Superposition36

89-105 Components of Pure Strain37

106-110 Standard Components, or Types of Reference46

111-120 Specification of Strains48

121 Change of Axes of Reference54

122,123 Heterogeneous Strain in general55

124-128 Irrotational Strain in general56

129 Strain in Two Dimensions59

EXAMPLES ON CHAPTER Ⅱ62

APPENDIX Ⅰ.—GEOMETRY OF STRAINS65

APPENDIX Ⅱ.—FINITE SHEARS69

CHAPTER Ⅲ. ANALYSIS OF STRESSES75

130-137 Preliminary75

138-147 Equations of Equilibrium and Motion, and Boundary Conditions79

148-152 Standard Types of Reference89

153-155 Principle of Superposition93

156-158 Type of Stress, Homogeneous Stress95

159-173 Graphic properties of Stress in Three Dimensions96

174 Hydrostatic Pressure, etc104

175-184 Stress in Two Dimensions106

185,186 Stress in One Dimension114

187 Heterogeneous Stress in general115

EXAMPLES ON CHAPTER Ⅲ115

CHAPTER Ⅳ. POTENTIAL ENERGY OF STRAIN118

188 Introductory118

189-192 Work done by Stress119

193 Work done by Applied Forces and Surface Tractions122

194,195 Identity of these Expressions123

196-201 Potential Energy of Strain125

202-206 Crystalline Symmetry (?olotropy)129

207-209 Isotropy132

210-214 Elastic Moduli of Isotropic Solids134

215 Principal Axes of Strain and Stress139

216 Principal Surfaces of Strain, Lines of Stress140

217,218 Equations of Motion and Equilibrium, and Boundary Conditions143

219,220 Deduction of these from the Principle of Virtual Work145

221 Absolute Moduli, Weight Moduli, Length Moduli149

222 Resilience, Strength, Tenacity, Modulus of Rupture150

223-229 Possible forms of Discontinuity in Strain and Stress152

APPENDIX Ⅲ.—HOOKE'S LAW162

APPENDIX Ⅳ.—ELASTIC PROPERTIES OF NATURAL MATERIALS169

(A) Plastic Solids and Viscous Fluids169

(B) Ductile Metals181

(C) Brittle Solids196

(D) Timber198

NUMERICAL TABLES OF ELASTIC CONSTANTS, ETC199

(A) Factors for reduction from one system of units to another199

(B) Compressibility of Liquids200

(C) Weight Moduli of Solids in C.G.S. units201

(C big) Practical Table in English measure202

(D) Ultimate and Working Strength203

(E) Variation of Young's Modulus with temperature204

(F) Variation of Rigidity with temperature204

CHAPTER Ⅴ. CURVILINEAR CO?RDINATES205

230 Definitions and Notation205

231 Formul? of differentiation208

232 Principal Curvatures of the Co?rdinate Surfaces210

233 Surfaces in general215

234-236 Strain and Stress216

237-239 Equations of Motion and Equilibrium, and Boundary Conditions224

240-242 Special applications of Curvilinears230

243-252 Various systems of Curvilinears233

EXAMPLES ON CHAPTER Ⅴ257

CHAPTER Ⅵ. GENERAL SOLUTIONS AND EXAMPLES262

253 Recapitulation of the General Problem262

254-259 Preliminary Theorems265

260-263 Problem of Free Vibrations II279

264 Forced Vibrations under Surface Tractions only284

265,266 Sir William Thomson's method285

267-274 The Irrotational Solution288

275-277 The Rotational Solution299

278 Poisson's Integrals302

279-284 Forced Vibrations under Surface Tractions and Applied Forces derivable from a Potential305

285-294 Equilibrium under Surface Tractions only312

295-300 Spherical Harmonic Solution328

301 Solution in terms of Potentials, by Sir William Thomson's method339

302 Sir G. B. Airy's Solution341

303 Equilibrium under Conservative Applied Forces342

304-306 Spherical Harmonic Solution343

307-309 307 bis Sir G. B. Airy's Solution350

310-321 Boussinesq's Potential Solutions360

EXAMPLES ON CHAPTER Ⅵ375

CHAPTER Ⅶ. BEAMS AND WIRES385

322,323 Introductory385

324-328 St. Venant's Problem386

329 Extension394

330-342 Torsion395

343-355 Flexion410

356-358 Recomposition of Solutions421

359,360 Equilibrium and Motion of naturally Straight Wires423

361 The Linea Elastica429

362,363 The Helix of Equilibrium432

364 Simplified form of the Equations when the transverse deflection is small433

365,366 Small Vibrations of Wires435

367-370 Deflection from the Horizontal under Gravity437

371-376 Greenhill's Problems on Stability of Beams439

377-383 Naturally Curved Wires, and Circular Hoops444

EXAMPLES ON CHAPTER Ⅶ449

APPENDIX Ⅴ.—STRENGTH UNDER TORSION AND FLEX- ION.—NACHWIRKUNG454

CHAPTER Ⅷ. PLATES AND SHELLS458

384,385 Introductory458

386,387 Clebsch' Problem459

388-393 Flexion by Couples only462

394 Straining without Flexion Couple467

395-398 Equilibrium of Thin Plates under Impressed Forces and Edge Tractions, such that their components parallel to their Faces of the Plate are evanescent or reducible to couples468

399-403 Solution by the Energy Method473

405-407 Normal Vibrations of Thin Shells under Normal Forces478

EXAMPLES ON CHAPTER Ⅷ483

CHAPTER Ⅸ. IMPACT486

408 Definitions and Fundamental Principles486

409 Example of Sudden Release487

410 Example of Direct Collision489

EXAMPLES ON CHAPTER Ⅸ492

CHAPTER Ⅹ. VISCOSITY494

411 Analytical Expression of the effects of Viscosity494

412 Equations of Motion and Boundary Conditions for Viscous Solids494

413,414 Torsional Vibrations of a Viscous Cylinder495

415-417 Viscous L iquids497

APPENDIX Ⅵ.—ECONOMY OF MATERIAL IN NATURE500

ADDITIONAL NOTES504

NOTE Ⅰ. (3, page2).—Sphere of Action of the Intermolecular Forces504

NOTE Ⅱ. (123, page56).—Expressions for the Component Strains and Rotations to the second power of small quantities504

NOTE Ⅲ. (235, page222).—Transformation of the Component Rotations to Curvilinears506

NOTE Ⅳ. (239, page229).—Lamé’s transformation of the Equa- tions of Motion507

NOTE Ⅴ. (241, page231).—Differential Equations of Lines of Stress, in Curvilinears508

NOTE Ⅵ. (401, page477).—A Theorem in Conjugate Functions508

INDEX510