弹性理论（第3版·影印版） (2009 年度畅销榜NO.23108 )

本书是弹性理论世界名著和经典教材。全书14章，包括绪论、平面应力和平 面应变、直角坐标中的二维问题、极坐标中的二维问题、光弹性与云纹实验方 法、曲线坐标中的二维问题、三维应力和应变问题、一般定理、 简单的三维弹 性问题、扭转、杆的弯曲、回转体中的轴对称应力和变形、热应力、弹性固体 介质中波的传播。最后有一附录，讲述差分方程在弹性理论中的应用。书中附 有习题供读者练习，还附有大量注释文献引导读者对相关问题作更为深入的研究。
本书可作为高等学校弹性力学课程的英文教科书或教学参考书，也是科研与工程技术人员值得珍藏的世界名著。

本书特色
·是弹性理论世界名著和经典教材。
·作者的宗旨是：把弹性理论中必要的基本知识以简明易懂的方式传授给工程师们。
·叙述浅入深，物理概念清晰，数学推导力求浅显。
·重视工程应用，汇集了不少实际应用中极为弹性理论典型解例。
·附有习题供读者练习，还附有大量注释文献引导读者对相关问题作更深入的研究。

Preface to the Third Edition ix
Preface to the Second Edition xi
Preface to the First Edition xiii
Notation xxv

Chapter 1 Introduction 1
1. Elasticity 1
2. Stress 2
3. Notation for Forces and Stresses
4. Components of Stress 4
5. Components of Strain 6
6. Hooke's Law 8
7. Index Notation 12
Problems 14

Chapter 2 Plane Stress and Plane Strain 15
8. Plane Stress 15
9. Plane Strain 15
10. Stress at a Point 17
11. Strain at a Point 23
12. Measurement of Surface Strains 24
13. Construction of Mohr Strain Circle for Strain Rosette 26
14. Differential Equations of Equilibrium 26
15. Boundary Conditions 28
16. Compatibility Equations 29
17. Stress Function 31
Problems 33

Chapter 3 Two-dimensional Problems in Rectangular Coordinates 35
18. Solution by Polynomials 35
19. End Effects. Saint-Venant's Principle 39
20. Determination of Displacements 40
21. Bending of a Cantilever Loaded at the End 41
22. Bending of a Beam by Uniform Load 46
23. Other Cases of Continuously Loaded Beams 50
24. Solution of the Two-dimensional Problem in the Form of a Fourier Series 53
25. Other Applications of Fourier Series. Gravity Loading 60
26. End Effects. Eigensolutions 61
Problems 63

Chapter 4 Two-dimensional Problems in Polar Coordinates 65
27. General Equations in Polar Coordinates 65
28. Stress Distribution Symmetrical about an Axis 68
29. Pure Bending of Curved Bars 71
30. Strain Components in Polar Coordinates 75
31. Displacements for Symmetrical Stress Distributions 77
32. Rotating Disks 80
33. Bending of a Curved Bar by a Force at the End 83
34. Edge Dislocation 88
35. The Effect of Circular Holes on Stress Distributions in Plates 90
36. Concentrated Force at a Point of a Straight Boundary 97
37. Any Vertical Loading of a Straight Boundary 104
38. Force Acting on the End of a Wedge 109
39. Bending Couple Acting on the End of a Wedge 112
40. Concentrated Force Acting on a Beam 113
41. Stresses in a Circular Disk 122
42. Force at a Point of an Infinite Plate 127
43. Generalized Solution of the Two-dimensional Problem in Polar Coordinates 132
44. Applications of the Generalized Solution in Polar Coordinates 136
45. A Wedge Loaded along the Faces 139
46. Eigensolutions for Wedges and Notches 141
Problems 144

Chapter 5 Photoelastic and Moire Experimental Methods 150
47. Experimental Methods and Verifications 150
48. Photoelastic Stress Measurement 150
49. Circular Polariscope 155
50. Examples of Photoelastic Stress Determination 157
51. Determination of the Principal Stresses 168
52. Three-dimensional Photoelasticity 162
53. The Moire Method 164

Chapter 6 Two-dimensional Problems in Curvilinear Coordinates 168
54. Functions of a Complex Variable 168
55. Analytic Functions and Laplace's Equation 170
Problems 171
56. Stress Functions in Terms of Harmonic and Complex Functions 172
57. Displacement Corresponding to a Given Stress Function 175
58. Stress and Displacement in Terms of Complex Potentials 176
59. Resultant of Stress on a Curve. Boundary Conditions 179
60. Curvilinear Coordinates 181
61. Stress Components in Curvilinear Coordinates 185
Problems 187
62. Solutions in Elliptic Coordinates. Elliptic H01e in Uniformly Stressed Plate 187
63. Elliptic Hole in a Plate under Simple Tension 191
64. Hyperbolic Boundaries. Notches 194
65. Bipolar Coordinates 196
66. Solutions in Bipolar Coordinates 198
Other Curvilinear Coordinates 202
Assignable Shapes 203
67. Determination of the Complex Potentials from Given Boundary Conditions. Methods Of Muskhelishvili 203
68. Formulas for the Complex Potentials 206
69. Properties of Stress and Deformation Corresponding to Complex Potentials Analytic in the Material Region around a Hole 207
70. Theorems on Boundary Integrals 209
71. A Mapping Function ( ) for the Elliptic Hole. The Second Boundary Integral 212
72. The Elliptic Hole. Formula for ( ) 213
73. The Elliptic Hole. Particular Problems 214
Problems 211

Chapter 7 Analysis of Stress and Strain in Three Dimensions 219
74. Introduction 219
75. Principal Stresses 221
76. Stress Ellipsoid and Stress-director Surface 222
77. Determination of the Principal Stresses 223
78. Stress Invariants 224
79. Determination of the Maximum Shearing Stress 224
80. Homogeneous Deformation 226
81. Strain at a Point 228
82. Principal Axes of Strain 231
83. Rotation 232
Problems 234

Chapter 8 General Theorems 235
84. Differential Equations of Equilibrium 235
85. Conditions of Compatibility 237
86. Determination of Displacements 240
87. Equations of Equilibrium in Terms of Displacements 240
88. General Solution for the Displacements 242
89. The Principal of Superposition 243
90. Strain Energy 244
91. Strain Energy of an Edge Dislocation 249
92. Principle of Virtual Work 250
93. Castigliano's Theorem 254
94. Applications of the Principle of Least Work Rectangular Plates 258
95. Effective Width of Wide Beam Flanges 262
Problems 268
96. Uniqueness of Solution 269
97. The Reciprocal Theorem 271
98. Approximate Character of the Plane Stress Solutions 274
Problems 277

Chapter 9 Elementary Problems of Elasticity in Three Dimensions 278
99. Uniform Stress 278
100. Stretching of a Prismatical Bar by Its Own Weight 279
101. Twist of Circular Shafts of Constant Cross Section 282
102. Pure Bending of Prismatical Bars 284
103. Pure Bending of Plates 288

Chapter l0 Torsion 291
104. Torsion of Straight Bars 291
105. Elliptic Cross Section 297
106. Other Elementary Solutions 299
107. Membrane Analogy 303
108. Torsion of a Bar of Narrow Rectangular Cross Section 307
109. Torsion of Rectangular Bars 309
110. Additional Results 313
111. Solution of Torsional Problems by Energy Method 315
112. Torsion of Rolled Profile Sections 321
113. Experimental Analogies 324
114. Hydrodynamical Analogies 325
115. Torsion of Hollow Shafts 328
116. Torsion of Thin Tubes 332
117. Screw Dislocations 336
118. Torsion of a Bar in Which One Cross Section Remains Plane 338
119. Torsion of Circular Shafts of Variable Diameter 341
Problems 349

Chapter 11 Bending of Bars 354
120. Bending of a Cantilever 354
121. Stress Function 356
122. Circular Cross Section 358
123. Elliptic Cross Section 359
124. Rectangular Cross Section 361
125. Additional Results 366
126. Nonsymmetrical Cross Sections 369
127. Shear Center 371
128. The Solution of Bending Problems by the Soap-film Method 374
129. Displacements 378
130. Further Investigations of Bending 378

Chapter 12 Axisymmetric Stress and Deformation in a Solid of Revolution 380
131. General Equations 380
132. Solution by Polynomials 383
133. Bending of a Circular Plate 385
134. The Rotating Disk as a Three-dimensional Problem 388
135. Force at a Point in an Infinite Solid 390
136. Spherical Container under Internal or External Uniform Pressure 392
137. Local Stresses around a Spherical Cavity 396
138. Force on Boundary of a Senti-infinite Body 398
139. Load Distributed over a Part of the Boundary of a Semi-infinite Solid 403
140. Pressure between Two Spherical Bodies in Contact 409
141. Pressure between Two Bodies in Contact. More General Case 414
142. Impact of Spheres 420
143. Symmetrical Deformation of a Circular Cylinder 422
144. The Circular Cylinder with a Band of Pressure 425
145. Boussinesq's Solution in Two Harmonic Functions 428
146. The Helical Spring under Tension (Screw Dislocation in a Ring) 429
147. Pure Bending of an Incomplete Ring 432

Chapter 13 Thermal Stress 433
148. The Simplest Cases of Thermal Stress Distribution. Method of Strain Suppression 433
Problems 438
149. Longitudinal Temperature Variation in a Strip 439
150. The Thin Circular Disk: Temperature Symmetrical about Center 441
151. The Long Circular Cylinder 443
Problems 452
152. The Sphere 452
153. General Equations 456
154. Thermoelastic Reciprocal Theorem 459
155. Overall Thermoelastic Deformations. Arbitrary Temperature Distribution 460
156. Thermoelastic Displacement. Maisel's Integral Solution 463
Problems 466
157. Initial Stress 466
158. Total Volume Change Associated with Initial Stress 468
159. Plane Strain and Plane Stress. Method of Strain Suppression 469
160. Two-dimensional Problems with Steady Heat Flow 470
161. Thermal Plane Stress Due to Disturbance of Uniform Heat Flow by an Insulated Hole 475
162. Solutions of the General Equations. Thermoelastic Displacement Potential 476
163. The General Two-dimensional Problem for Circular Regions 481
164. The General Two-dimensional Problem in Complex Potentials 482

Chapter 14 The Propagation of Waves in Elastic Solid Media 485
165. Introduction 485
166. Waves of Dilatation and Waves of Distortion in Isotropic Elastic Media 486
167. Plane Waves 487
168. Longitudinal Waves in Uniform Bars. Elementary Theory 492
169. Longitudinal Impact of Bars 497
170. Rayleigh Surface Waves 505
171. Spherically Symmetric Waves in the Infinite Medium 508
172. Explosive Pressure in a Spherical Cavity 510

Appendix The Application of Finite-difference Equations in Elasticity 515
1. Derivation of Finite Difference Equations 515
2. Methods of Successive Approximation 520
3. Relaxation Method 522
4. Triangular and Hexagonal Nets 527
5. Block and Group Relaxation 532
6. Torsion of Bars with Multiply-connected Cross Sections 534
7. Points Near the Boundary 536
8. Biharmonic Equation 538
9. Torsion of Circular Shafts of Variable Diameter 545
10. Solutions by Digital Computer 549
Name Index 553
Subject index 559

本书是弹性理论世界名著和经典教材。作者编写本书的宗旨是：把弹性理论中必要的基本知识以简明易懂的方式传授给工程师们。叙述由浅入深，物理概念清晰，数学推导力求浅显。选材时十分重视工程应用，汇集了不少实际应用中极为重要的弹性理论典型解例。 本书的第一、第二版分别出版于1934年和1951年。1970年出版的第三版又进行了审查、删减、增补和调整，反映了自第二版问世后应用弹性理论领域的最新进展。因第一作者铁摩辛柯教授于1972年5月逝世，此后再无出版新版。如今到了公元21世纪，美国土木工程、矿山治金与石油工程、机械工程、电工电子工程和化学工程等五个国家级工程协会联合精选了一套10本高水平的经典著作作为“工程科学专著”出版，其中唯有铁摩辛柯一人有3本著作(本书及其姐妹篇“弹性稳定理论”、“板壳理论”)被列选，可见作者及本书影响之深远。 本书在我国的影响也很大。其第二版由徐芝纶和吴永桢翻译成中文，于1964年由高等教育出版社出版。在第二版译文的基础上徐芝纶又完成了第三版的翻译工作，由高等教育出版社于1990年出版。我国工科院校广泛采用的弹性力学教材，例如徐芝纶教授编著的“弹性力学”，大多继承了本书的体系和风格，因此本书是我国弹性力学课程首选的英文教材或参考书。 全书共分14章：第1章绪论，第2章平面应力和平面应变，第3章直角坐标中的二维问题，第4章极坐标中的二维问题，第5章光弹性与云纹实验方法，第6章曲线坐标中的二维问题，第7章三维应力和应变问题，第8章一般定理，第9章简单的三维弹性问题，第10章扭转，第11章杆的变曲，第12章回转体中的轴对称应力和变形，第13章热应力，第14章弹性固体介质中波的传播。最后有一附录，讲述差分方程在弹性理论中的应用。书中附有习题供读者练习，还附有大量参考文献引导读者对相关问题作更为深入的研究。 本书可作为高等学校弹性力学课程的英文教科书或教学参考书，也是科研与工程技术人员值得珍藏的世界名著。

Preface to the Third Edition In the revision of this book for a third edition, the primary intention and plan of the first edition have been preserved--to provide for engineers, in as simple a form as the subject allows, the essential fundamental knowledge of the theory of elasticity together with a compilation of solutions of special problems that are important in engineering practice and design. The numerous footnote references indicate how the several topics may be pursued further. Since these are now readily supplemented by means of Applied Mechanics Reviews, new footnotes have been added sparingly with this in mind. Small print again indicates sections that can be omitted from a first reading. The whole text has been reexamined, and many minor improvements have been made throughout by elimination and rearrangement as well as addition. The major additions reflect developments and extensions of interest and practical applicability that have occurred since the appearance of the second edition in 1951. End effects and eigensolutions associated with the principle of Saint-Venant are treated in Chapters 3 and 4. In view of the rapid growth of the applications of dislocational elastic solutions in materials science, these discontinuous displacement solutions have been given more explicit treatment as edge dislocations and screw dislocations in Chapters 4, 8, 9, and 12. An introduction to the moire method with a practical illustration has been added to Chapter 5. The treatment of strain energy and variational principles has been recast in three-dimensional form and embodied in Chapter 8, which now provides a basis for new sections on thermoelasticity in Chapter 13. The discussion of the use of complex potentials for two-dimensional problems has been extended by a group of new articles based on the now wellknown methods of Muskhelishvili. Moreover, the approach is somewhat different, in that advantage has been taken of solutions previously developed in order to deal with analytic functions only. Further solutions for the elliptic hole, important in current fracture mechanics (cracks), are given explicit treatment. The discussion of axisymmetric stress in Chapter 12 has been simplified; and new sections have been added that replace the approximate analysis by a more exact one for the cut ring, as one turn of a helical spring. In view of its greatly increased applications, as in nuclear energy equipment, Chapter 13, on thermal stress, has been extended by inclusion of a thermoelastic reciprocal theorem and several useful results obtained from it; and by an introduction to thermal stress concentrations due to disturbance of heat flow by cavities and inclusions has also been added. In addition, treatment of two-dimensional problems has been supplemented by the two final articles, the last bringing the two-dimensional thermoelastic problems into connection with the complex potentials and Muskhelishvili procedures of Chapter 6. In Chapter 14, on wave propagation, a rearrangement gives prominence to the basic three-dimensional theory. A solution for explosive pressure in a spherical cavity has been added. The Appendix on numerical finite difference methods includes an example of the use of a digital computer to cope with a large number of unknowns. Some of these changes offer simplifications of analysis arrived at in the experience of giving courses at Stanford University over the past twenty years. Many valuable suggestions, corrections, and even completely formulated problems with solutions, have come from numerous students and correspondents, to whom a blanket but most cordial acknowledgment is both unavoidable and inadequate. Almost all the "Problems" are from examinations set and given at Stanford University. The reader may see roughly from these what parts of the book correspond to a course sequence occupying somewhat less than three hours per week for the academic year. J. N. Goodier Preface to the Second Edition The many developments and clarifications in the theory of elasticity and its applications which have occurred since the first edition was written are reflected in numerous additions and emendations in the present edition. The arrangement of the book remains the same for the most part. The treatments of the photoelastic method, two-dimensional problems in curvilinear coordinates, and thermal stress have been rewritten and enlarged into separate new chapters which present many methods and solutions not given in the former edition. An appendix on the method of finite differences and its applications, including the relaxation method, has been added. New articles and paragraphs incorporated in the other chapters deal with the theory of the strain gauge rosette, gravity stresses, Saint-Venant's principle, the components of rotation, the reciprocal theorem, general solutions, the approximate character of the plane stress solutions, center of twist and center of shear, torsional stress concentration at fillets, the approximate treatment of slender (e.g., solid airfoil) sections in torsion and bending, and the circular cylinder with a band of pressure. Problems for the student have been added covering the text as far as the end of the chapter on torsion. It is a pleasure to make grateful acknowledgment of the many helpful suggestions which have been contributed by readers of the book. S. P. Timoshenko J. N. Goodier Preface to the First Edition During recent years the theory of elasticity has found considerable application in the solution of engineering problems. There are many cases in which the elementary methods of strength of materials are inadequate to furnish satisfactory information regarding stress distribution in engineering structures, and recourse must be made to the more powerful methods of the theory of elasticity. The elementary theory is insufficient to give information regarding local stresses near the loads and near the supports of beams. It fails also in the cases when the stress distribution in bodies, all the dimensions of which are of the same order, has to be investigated. The stresses in rollers and in balls of bearings can be found only by using the methods of the theory of elasticity. The elementary theory gives no means of investigating stresses in regions of sharp variation in cross section of beams or shafts. It is known that at reentrant corners a high stress concentration occurs and as a result of this cracks are likely to start at such corners, especially if the structure is submitted to a reversal of stresses. The majority of fractures of machine parts in service can be attributed to such cracks. During recent years considerable progress has been made in solving such practically important problems, In cases where a rigorous solution cannot be readily obtained, approximate methods have been developed. In some cases solutions have been obtained by using experimental methods. As an example of this the photoelastic method of solving two-dimensional problems of elasticity may be mentioned. The photoelastic equipment may be found now at universities and also in many industrial research laboratories. The results of photoelastie experiments have proved especially useful in studying various cases of stress concentration at points of sharp variation of cross-sectional dimensions and at sharp fillets of reentrant corners. Without any doubt these results have considerably influenced the modern design of machine parts and helped in many cases to improve the construction by eliminating weak spots from which cracks may start. Another example of the successful application of experiments in the solution of elasticity problems is the soap-film method for determining stresses in torsion and bending of prismatical bars. The difficult problems of the solution of partial differential equations with given boundary conditions are replaced in this case by measurements of slopes and deflections of a properly stretched and loaded soap film. The experiments show that in this way not only a visual picture of the stress distribution but also the necessary information regarding magnitude of stresses can be obtained with an accuracy sufficient for practical application. Again, the electrical analogy which gives a means of investigating torsional stresses in shafts of variable diameter at the fillets and grooves is interesting. The analogy between the problem of bending of plates and the two-dimensional problem of elasticity has also been successfully applied in the solution of important engineering problems. In the preparation of this book the intention was to give to engineers, in a simple form, the necessary fundamental knowledge of the theory of elasticity. It was also intended to bring together solutions of special problems which may be of practical importance and to describe approximate and experimental methods of the solution of elasticity problems. Having in mind practical applications of the theory of elasticity, matters of more theoretical interest and those which have not at present any direct applications in engineering have been omitted in favor of the discussion of specific cases. Only by studying such cases with all the details and by comparing the results of exact investigations with the approximate solutions usually given in the elementary books on strength of materials can a designer acquire a thorough understanding of stress distribution in engineering structures, and learn to use, to his advantage, the more rigorous methods of stress analysis. In the discussion of special problems in most cases the method of direct determination of stresses and the use of the compatibility equations in terms of stress components has been applied. This method is more familiar to engineers who are usually interested in the magnitude of stresses. By a suitable introduction of stress functions this method is also often simpler than that in which equations of equilibrium in terms of displacements are used. In many cases the energy method of solution of elasticity problems has been used. In this way the integration of differential equations is replaced by the investigation of minimum conditions of certain integrals. Using Ritz's method this problem of variational calculus is reduced to a simple problem of finding a minimum of a function. In this manner useful approximate solutions can be obtained in many practically important cases. To simplify the presentation, the book begins with the discussion of two-dimensional problems and only later, when the reader has familiarized himself with the various methods used in the solution of problems of the theory of elasticity, are three-dimensional problems discussed. The portions of the book that, although of practical importance, are such that they can be omitted during the first reading are put in small type. The reader may return to the study of such problems after finishing with the most essential portions of the book. The mathematical derivations are put in all elementary form and usually do not require more mathematical knowledge than is given in engineering schools. In the cases of more complicated problems all necessary explanations and intermediate calculations are given so that the reader can follow without difficulty through all the derivations. Only in a few cases are final results given without complete derivations. Then the necessary references to the papers in which the derivations can be found are always given. In numerous footnotes references to papers and books on the theory of elasticity which may be of practical importance are given. These references may be of interest to engineers who wish to study Some special problems in more detail. They give also a picture of the modern development of the theory of elasticity and may be of some use to graduate students who are planning to take their work in this field. In the preparation of the book the contents of a previous book ("Theory of Elasticity," vol. I, St. Petersburg, Russia, 1914) on the same subject, which represented a course of lectures on the theory of elasticity given in several Russian engineering schools, were used to a large extent. The author was assisted in his work by Dr. L. H. Donnell and Dr. J. N. Goodier, who read over the complete manuscript and to whom he is indebted for many corrections and suggestions. The author takes this opportunity to thank also Prof. G. H. MacCullough, Dr. E. E. Weibel, Prof. M. Sadowsky, and Mr. D. H. Young, who assisted in the final preparation of the book by reading some portions of the manuscript. He is indebted also to Mr. L. S. Veenstra for the preparation of drawings and to Mrs. E. D. Webster for the typing of the manuscript.