Theory of Elasticity – Filonenko-Borodich

In this post we will see Theory of Elasticity by M. Filonenko-Borodich.

the theory of elasticty filoneko borodich

The book was translated from the Russian by Marina Konyaeva and was first puublished by  PEACE PUBLISHERS MOSCOW in 1963.

All credits to original uploader.

You can get the book here.

Introduction 9

Chapter I.
Theory of Stress 13

1. State of Stress in a Body 13
2. Differential Equations of Equilibrium 16
3. Stresses on Areas Inclined to the Co-ordinate Planes. Surface Conditions 22
4. Analysis of the State of Stress at a Given Point in Principal Areas and Principal Stresses 25
5. Stress Distribution at a Given Point. Cauchy’s Stress Surface; Invariants of the Stress Tensor. Lame’s Ellipsoid 29
6. Maximum Shearing Stresses 35
7. Octahedral Areas and Octahedral Stresses 39
8. Spherical Tensor and Stress Deviator 39
9. Generalisation of the Law of Reciprocity of Stresses. Examples 42

Chapter II.
Geometrical Theory of Strain 45

10. Displacement Components and Strain Components, and Relation Between Them 45
11. Compatibility Equations 53
12. Tensor Character of the Strain at a Given Point in a Body 58
13. Dilatational Strain. Invariants of the Strain Tensor 6
14. Strain Deviator and Its Invariants 65
15. Finite Strain 67

Chapter III.
Generalised Hooke’s Law 72

16. General 72
17. Strains Expressed in Terms of Stresses 75
18. Stresses Expressed in Terms of Strains 78
19. Work Done by Elastic Forces in a Solid 82
20. Potential of Elastic Forces 83
21. Stress-strain Relations; Hypothesis of the Natural State of a Body 84
22. Elastic Constants; Reduction in Their Number Due to the Existence of the Potential of Elastic Forces 88
23. Isotropic Body 89


Chapter IV.
Solution of the Elasticity Problem in Terms of Displacements 96

24. Compendium of Basic Equations of the Theory of Elasticity 96
25. Lame’s Equations 99
26. Longitudinal and Transverse Vibrations in an Unbounded Elastic Medium 102
27. General Solution of the Equation of Vibrations 106
28. Longitudinal Vibrations of a Bar. Fourier’s Method 109

Chapter V.
Solution of the Elasticity Problem in Terms of Stresses 115

29. The Simplest Problems 115
30. Torsion of a Circular Bar 116
31. Saint-Venant’s Principle 118
32. The Problem of Torsion of a Circular Bar (Continued) 122
33. Pure Bending of a Prismatical Bar 126
34. Prism Stretched by Its Own Weight 132
35. Uniqueness of Solution of Elasticity Equations 136
36. Beltrami-Michell Equations 139
37. Three Kinds of Problems of the Theory of Elasticity. Uniqueness Theorem 142

Chapter VI.
Plane Problem in Cartesian Co-ordinates 147

38. Plane Strain 147
39. Generalised Plane Stress. Maurice Levy’s Equation. Stress Function 151
40. Solution of the Plane Problem by Means of Polynomials 162
41. Bending of a Cantilever 163
42. Beam on Two Supports 171
43. Triangular and Rectangular Retaining Walls (M. Levy’s Solutions) 177
44. Bending of a Rectangular Strip; Filon’s and Ribiere’s Solutions 181
45. One Modification of Filon’s Method 189
46. Strip of Infinite Length 196

Chapter VII.
Plane Problem in Polar Co-ordinates 200

47. General Equations of the Plane Problem in Polar Co-ordinates 200
48. Problems in Which Stresses Are Independent of the Polar Angle 205
49. Effect of a Concentrated Force (Flamant-Boussinesq Problem) 211
50. Wedge Loaded at the Vertex 217
51. General Solution of the Plane Problem in Polar Co-ordinates 222

Chapter VIII.
Torsion of Prismatical Bars and Bending 231

52. Torsion of Prismatical Bars 231
53. Saint-Venant’s Method. Special Cases 238
54. Solution of the Torsion Problem in Terms of Stresses. Prandtl’s Analogy 250
55. Case of Transverse Bending 258

Chapter IX.
More General Methods of Solving Elasticity Problems 265

56. General Solution of Differential Equations of Equilibrium in Terms of Stresses. Stress Functions 265
57. Equations of Equilibrium in Cylindrical Co-ordinates. Their General Solution 270
58. Harmonic and Biharmomc Functions 273
59. Biharmonic Equation 278
60. Reduction of Lame’s and Beltrami’s Equations to Biharmonic Equations 282
61. Boussinesq’s Method; Application of Harmonic Functions to Seeking of Particular Solutions of Lame’s Equations 284
62. Effect of a Load on a Medium Bounded by a Plane (Boussinesq’s Problem) 290
63. Effect of a Concentrated Force Normal to the Boundary and Applied at the Origin 294
64. Solution of the Plane Problem of Elasticity by Means of Functions of a Complex Variable 301
65. Filon’s Method 303
66. Wave Equations 310
67. Some Particular Solutions of the Wave Equation 313

Chapter X.
Bending of a Plate 317

68. General 317
69. Basic Equations of Bending and Torsion of a Plate 319
70. Analysis of the Results Obtained 323
71. Boundary Conditions for a Plate 328
72. Elliptic Plate Clamped at the Edge 331
73. Rectangular Plate. Navier’s Solution 333
74. Rectangular Plate. Levy’s Solution 339
75. Circular Plate 344
76. Membrane Analogy. Marcus’s Method 347

Chapter XI.
Variational Methods of the Theory of Elasticity 350

77. Variational Principles of the Theory of Elasticity. Fundamental Integral Identity 350
78. Lagrange’s Variational Equation 352
79. Ritz-Timoshenko Method 358
80. Castigliano’s Variational Equation 364
81. Application of Castigliano’s Variational Equation Problem of to the Torsion of a Prismatical Rod 368
82. First Problem of the Theory Elasticity; Second Theorem of Minimum Energy 373
83. Approximate Method Based on Variational Equation (11.61) 375
84. Lame’s Problem for an Elastic Rectangular Prism 379
References 387

Name Index 388
Subject Index 390

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5 Responses to Theory of Elasticity – Filonenko-Borodich

  1. Tarun says:

    Who is alternative of MIR publishers in Russia at present? I guess all books in Russia would be published in Russian only. Still Russia have great writers or they just follow American books?

  2. SM says:

    Dear Mitr,
    Thanks for your dedicated effort to bring the numerous Russian physics book to physics book lovers.Waiting for these books too from you.
    1. Fundamentals of Physics – Ivanov
    2. A Text Book of Elementary Physics, Vol-3 – Landsberg
    3. Questions and problems in General Physics – Savelyev
    4. Problems in School Physics – Savelyev
    5. Physics problems and questions – Gladkova & Landau
    6. Physics problems and questions – Goldfarb
    7. Collection of problems in General Physics – Sivukhin
    8. Selected Problems in Elementary Physics – Saraeva

  3. Eric says:

    I just got a new book its called Collected Problems in Physics by S.Kozel, E. Rashba, and S. Slavatinskii 1986 181 pages. Let me know if anyone knows anything about this book.

    • Neethiman Visvanthan says:

      Hi there, are you the same Eric from three years ago? Did you by any chance upload Vygodsky’s higher mathematics?

  4. SM says:

    Thanks for the news. It’s a good book. It will be better if you can upload Collected Problems of Physics by Kozel, Rashba, Slavatinskii or give the link.

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