XV xiv CONTENTS CONTENTS 276 135.The Long Cireular Cylinder·,··· 408 95.Torsion of Rectangular Bara................. 410 96.Additional Results. 278 136.The Sphere·,··· g7.Solution of Torsional Probleme by Energy Method,.·,··· 280 137.General Equations 、 421 98.Torsion of Rolled Profile Seetions. .287 138.Initial Stresses.. 425 99.The Uae of Soap Films in Solving Torsion Problems.. ··.289 139.Two-dimensional Problems with Steady Heat Flow 427 100.Hydrodynamical Analogies... 140.Solutions of the General Equations 44 433 10l.Torsion of Hol0 w Shafts:.,,··········,···· 294 102.Torsion of Thin Tubes . 298 CHAPTER 15. THE PROPAGATION OF WAVES IN ELASTIC SOLID MEDIA 103.Torsion of a Bar in which One Cross Section Remains Plane. 302 438 104.Torsion of Circular Shafta of Variable Dinmeter.........304 141..·· Problem···············。·,,313 142.Longitudinal Waves in Prismatical Bars. ···。38 143.Longitudinal Impact of Bars... 444 CHAPTER 12.BENDING OF PRISMATICAL BARS 144.Waves of Dilatation and Waves of Distortion in Isotropic Elastie Media.· 452 454 105.Bending of n Cantilever···,············316 145.Plane Waves....... ·,318 146.Propagation of Waves over the Surfnce of an Elnstie Solid Body... 456 106.Stress Funetion,.·.·, 107.Cireular Cross Section. 319 108.Elliptie Cross Seetion 321 APPENDIX. THE APPLICATION OF FINITE DIFFERENCE EQUATIONS 109.Rectangular Cross Section 323 IN ELASTICITY 110.Additional Results .. 329 l,Derivation of Finite Difference Equations,,·,,·····, 461 111.Nonsymmetrical Cross Sections......... ······831 2.Methods of8 uccessive Approximation,.·······.。,.. 465 1l2.8 henr Center,.....:,,·····,, 333 113.The Solution of Bending Problems by the Soap-film Method.... 336 3.Relaxation Method..... 468 4.Triangular and Hexagonal Nets 473 t 340 5.Block and Group Relaxation..... 477 115.Further Investigations of Bending. 341 6.Torsion of Bars with Multiply-conneeted Cross Sections. 479 7.Points Near the Boundary.... 480 CHAPTER 18.AXIALLY SYMMETRICAL STRESS DISTRIBUTION IN A 8.Biharmonic Equation,·· 483 g.Toraion of Cireular8 hafts of Variable Diameter,·+·,,··· 400 SOLID OF REVOLUTION 116.General Equation8,:,·············348 495 1l7.Solution by Polynomials.····,,。。·。。。,,。·..347 AUTHOR INDEX. 118.Bending of a Circular Plate. 349 499 119.The Rotating Disk as a Three-dimensional Problem. 352 120.Force at a Point of an Indefinitely Extended Solid........ 354 121.Spherical Container under Internal or External Uniform Pressure.. 356 122.Local Stresses around a Spherieal Cavity:··,·,····,,,359 l23.Force on Boundary of a Semi-infinite Body.,,,·。·. ,362 124.Load Distributed over a Part of the Boundary of a Semi-infinite Solid 366 125.Pressure between Two Spherieal Bodies in Contaet.. ,372 126.Preasure between Two Bodies in Contact.More General Cnse .377 127.mpact of8 pheres。·,,, ···383 128. Symmetrical Deformation of a Circular Cylinder......... 384 l29.The Circular Cylinder with a Band of Pressure,,.·.····- 388 l30.Twist of a Cireular Ring Sector,,,·.,.·.。··,,.+ 391 l31,Pure Bending of a Circular Ring8 ector.,.·····,··· 395 CHAPTER 14.THERMAL STRESS 132.The Simplest Cases of Thermal Streas Diatribution ·······898 133.Some Problems of Plane Thermal Stress... 404 134.The Thin Circular Disk:Tempersture Symmetrical about Center.. 406