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| Borodich F. — Theory of Elasticity |
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| Предметный указатель |
Airy, G. B. 156
Airy’s function 156 162 164 270 308
Amplitude of vibration 105
Analogy, Prandtl’s 252
Anisotropy 73; see Bodies
Areas, octahedral 39
Areas, principal 31
Axisymmetrical three-dimensional stress 273
Bars, bending of 44
Bars, buckling of 138
Bars, pure 211 163
Bars, torsion of 71 116 231
Beams, bending of, built-in at ends 176
Beams, of rectangular cross section 131 152
Beams, supported at ends 171
Beizeno, C. B. 229
Beltrami — Mitchell equations 138 251 278 282
Beltrami, E. 139
Bending moment 323
Bending of beam, built-in at ends 176
Bending of cantilever 163
Bending of plate 316
Bending of plate, pure 327
Bending of prismatical bar 44
Bending of prismatical bar, pure 126 163
Bending of rectangular cross section 131 152
Bending of rectangular cross section, supported at ends 171
Bending of rod 44
Bending of rod, of circular cross section 262
Bending of rod, pure 71
Bending of rod, transverse 258
Bending of strip 181 189
Bending of wedge 219
Bernoulli, J. 9 126
Biharmonic function 162 273 282
Blokh, V. I. 269
Bodies, anisotropic 73
Bodies, homogeneous 73
Bodies, isotropic 73
Bodies, nonhomogeneous 73
Body forces 17
Bolle, L 331
boundary conditions 24 96
Boussinesq, J. 211 278 284 290
Boussinesq’s problem 290
Bredt, R. 256
Bredt’s theorem 256
Buckling of bar 138
bulk modulus 81
Cantilever, bending of 163
Castigliano, A. 273 364
Castigliano’s variational equation 364
Cauchy — Riemann conditions 235 238
Cauchy, A. L. 10 29 48 235
Cauchy’s equations 48 97
Cauchy’s quadric 30 39
Clapeyron, B. P. E. 10 143
Clapeyron’s theorem 143 352
Closeness of system of functions 381
Co-ordinates, cylindrical 200
Co-ordinates, polar 200
Coefficients of Lam 78 94
Coker, E. G. 188
Compatibility, conditions of 55 97 151 203
Compendium of basic equations 96
Completeness of system of functions 381
Components, of displacement 19 45
Components, of rotation 51
Components, of strain 49
Components, of stress 28 84
Compression of wedge 219
Condition, Lvy’s 155
Conditions, Cauchy — Riemann 235 238 307
Conditions, Dirichlet’s 198
Conditions, of compatibility (continuity) of strain components 55 97 151 203
Conditions, on surface 24 96
Constants, elastic 88
Contact problem 143 189
Continuity 12
Coulomb, C. A. 9 116 238
Coulomb’s theory of torsion 116 238
Criterion, Lejeune — Dirichlet’s 355
Curved bar, pure bending of 210
Cylindrical co-ordinates 201
density 17
Diagrams, stress-strain 73
Dilatation, cubical 64
Dilatation, waves of 311
Dilatation, waves of, irrotational 313
Dirichlet, P. G. L. 198 235
Dirichlet’s conditions 198
Displacements 19 45
Displacements, virtual, principle of 354
Distortion, waves of 311
Divergence, of displacement vector 311
D’Alembert, J. le R., Ill 313 354
d’Alembert’s principle 354
Effect of load on medium bounded by plane 290
Ellipsoid, stress 36 37
Elongations 45
Elongations, principal 63
End plate of cylindrical reservoir 347
Equation, biharmonic 278
Equation, biharmonic, Lvy’s 151 155
Equation, biharmonic, Laplace’s 232 273
Equation, biharmonic, of transverse vibration of string 111
Equation, Sophie Germain’s 322
Equation, Sophie Germain’s, variational, of Castigliano 364
Equation, Sophie Germain’s, variational, of Lagrange 352
Equation, Sophie Germain’s, wave 310
Equations, Beltrami — Mitchell 139 251 278 282
Equations, canonical 363
Equations, Cauchy’s 48 97
Equations, differential, of Navier 21 96 110 202 270
Equations, for plane problem in polar co-ordinates 200
Equations, geometrical 97
Equations, Lam’s 99 141 278 282
Equations, of bending for plates 319
Equations, of compatibility 55 97 151 203
Equations, of equilibrium in statics 18
Equations, of torsion for plates 316 319 326
Equilibrium, general equations of 18 265
Equilibrium, of elastic sphere 284
Euler, L. 9 87 126 193 297
Euler’s substitution 297
Euler’s theorem on homogeneous functions 87
Expansion, volume 312
Extension 48
F ppl, A. 256 387
Fppl, L. 256 387
Field of function 274
Filon, L. N. G. 181 188—189 303
Filonenko-Boroditch, M. M. 189 271 380 385 386
Flexural rigidity of plate 322
Forces, body 10—12 16
Forces, external 11
Forces, Internal 10
Forces, shearing 324
Formula, Fourier’s 198
Formula, Green — Ostogradsky’s 25
Formulas, Love’s for displacements 300
Fourier, J. B. J. 111
Fourier’s series 111
Function, analytic 238
Function, biharmonic 162 273 278
Function, force 355
Function, harmonic 232 273
Function, stress, of Airy 156 162 164 270 308
Function, stress, of Prandtl 236 250
Function, torsion 231 250
| Functions, stress of Maxwell 266
Functions, stress of Morera 268
Galerkin, B. G. 301 338 344
Galilei, G. 9
Germain, Sophie 9 322
Germain’s equation 322
Gradient of Prandtl’s stress function 254
Grammel, R. 229
Green — Ostrogradsky formula 25
Green, G. 10
Harmonic function 232 273
Hertz, H. 300
Hertz’s problem of two bodies in compression 300
Homogeneity 73 74
Homogeneous deformation 52
Homogeneous stress 162
Hooke, R. 9 73
Hooke’s law 74 85
Hooke’s law, generalised 76 94 97 149 205
Hooke’s law, in shear 74 117
Hypothesis, of continuous structure of solids 12
Hypothesis, of linear elements, Kirchhoff’s 318
Hypothesis, of natural state 87 137
Identities, Saint-Venant’s 55
Initial stress 86
Integrals, Mohr’s 378
Invariants of strain deviator 65
Invariants of strain tensor 65
Invariants of stress deviator 40
Invariants of stress tensor 34
Ionov, V. N. 386
Isotropy 73 89
Jasinsky, F. S. 10
Jastrz§bski, N. F. 10
Kelvin, Lord 10 328
Kirchhoff, G. 143 318 328
Kirchhoff’s hypothesis of linear elements 318
Kochin, N. E. 312
Kolosoff, G. V. 10 303 387
Kononenko, E. S. 385
Krutkov, Ju. A. 269
Krylov, A. N. 387
Lvy, M. 155 199 339
Lvy’s condition (equation) 155
Lagrange, J. L. 9 352
Lagrange, principle of 354
Lagrange, variational equation of 352
Lam, coefficients of 78 94
Lam, ellipsoid of 35—38
Lam, equations of 99 141 277 282
Lam, G. 10 29 79 99 209 379
Lamb, H. 328
Laplace, P. S. 100 250
Laplacian operator 100 203
Laplacian potential 274
Law, Hooke’s 74 85
Law, of shearing stresses 21 42
Least work, principle of 375
Leibenzon, L. S. 300 316 368 373 387
Lejeune — Dirichlet’s criterion 355
Level lines of function 242
Limit of proportionality 74
Liubimov, V. M. 386
Love waves 316
Love, A. E. H. 299 303 316 387
Marcus, H 347
Mariotte, E. 9
Maslov, G. N. 187
Mathieu, E 10 387
Maxwell, J. C. 10 265
Maxwell’s stress functions 266
Mean hydrostatic stress 42
Membrane 252
Method of sections 11
Method of sections, photoelastic 156
Method of sections, Ritz — Timoshenko 358
Minimum elastic energy, theorems of 355 373
Miroshnichenko, E. R. 386
Mitchell, J. H. 10 139 229
Modulus, in shear 74
Modulus, in tension 74
Modulus, of rigidly 75
Modulus, of volume expansion 81
Modulus, Young’s 74
Mohr, O. 378
Mohr’s integrals 378
Molecular theory of structure of bodies 10
Morera, G 265
Morera’s stress functions 268
Muskhelishvili, N. I. 10 29 56 303 309 387
Navier, C. L. M. H. 10 333 387
Navier’s equations 21 96 110 202 270
Netrebko, V. P. 385
Neumann, K. G. 234
Neumann’s problem 234
Neutral axis 127
Nonhomogeneity 73
Novozhilov, V. V. 342
Number, Poisson’s 74
Oblique planes 326
Octahedral areas 39
Operator, Laplacian 74 203—204
Ostrogradsky, M, V. 10
Papkovitch, P. F. 187—188 375 387
Paraboloid 241 326 327
Period of vibration 105
Pfeiffer, P. 387
Photoelastic method 156
Plamant 211
Plane problem, equations for, in polar co-ordinates 200
Plane problem, solution of, in terms of stresses 158
Plane strain 147 151
Plane stress 27
Plane stress, generalised 151
Planes, oblique 326
Planes, principal 128
Plates, bent by couples 327
Plates, boundary conditions for 328—331
Plates, flexural rigidity of 322
Plates, of special forms, circular 344
Plates, of special forms, elliptic 331
Plates, of special forms, rectangular 328 333
Plates, theory of moderately thick 318
Poisson, S. D. 10 74 328
Poisson’s number 74
Poisson’s ratio 74
Polar co-ordinates 200
Ponomarev, S D. 42
Potential elastic energy 145 356
Potential elastic energy, minimum of 355 373
Potential, displacement 53
Potential, elastic forces having 83
Potential, Laplacian 274
Prandtl, L. 236 250—252
Prandtl’s analogy 252
Prandtl’s function 236 250
Principal areas 31
Principal elongations 63
Principal of D’Alembert 354
Principal of Lagrange 354
Principal of least work 375
Principal of Saint — Venant 119
Principal of superposition 72 137
Principal of virtual displacements 354
Principal planes 128
Principal strain 66
Principal stress 31
Prism, rectangular, elastic 379
Prism, stretched of its own weight 132
Problem, Boussinesq’s 290
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