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| Sokolnikoff I.S. — Mathematical Theory of Elasticity |
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| Предметный указатель |
Amne transformation 2 5 18
Analysis, of strain 1—34
Analysis, of stress 35—36
Anisotropic media 61 212 217 274 276
Arutinyan, N.C. 316
Avazashvili, D.Z. 253
Baes, L. 190
Basil, N.M. 328
Bautz, W. 191 209
Beams, anisotropic 212 217 276
Beams, bent by couples 100
Beams, bent by distributed loads 274
Beams, bent by terminal loads 217 228
Beams, cantilever 269 282 291 296 302 312 323
Beams, compound 270
Beams, curved 275
Beams, extension, torsion, and flexure of 97—276
Beams, flexural rigidity of 111
Beams, flexure of, cardioid 242
Beams, flexure of, circular 235 253
Beams, flexure of, elliptical 237 258
Beams, flexure of, rectangular 210 272
Beams, flexure of, triangular 252 255
Beams, initially twisted 274
Beams, of variable cross section 275 (see also “Extension” “Flexure” “Torsion”)
Beams, technical theory of 203
Beams, torsion of, anisotropic 212 274
Beams, torsion of, cardioid 245
Beams, torsion of, circular 119
Beams, torsion of, compound 270
Beams, torsion of, conical 208
Beams, torsion of, curved 275
Beams, torsion of, elliptical 134 190
Beams, torsion of, hollow 191 191 196
Beams, torsion of, initially twisted 274
Beams, torsion of, polygonal 186 187 275 316
Beams, torsion of, rectangular 143 308 317 318 320 333 338
Beams, torsion of, semicircular 181
Beams, torsion of, triangular 139 143
Beams, torsional rigidity of 125 141 175 189
Beltrami — Michell equations 78
Beltrami, E. 78
Bending of beams see “Beams” “Flexure”
Bending-moment diagram 268
Bergmann, S. 180
Bernoulli — Euler law 110 115 233 264 274
Bernstein, B. 18G
Betti and Rayleigh Theorem 297
Bicberbach, L. 170
Biczeno, C.B. 101 195 300 301 321 323
Biharmonic function 79
Biot, M.A. 33
Blinchikov, T.N. 204
Boundary-value problems in elasticity 73
Boundary-value problems in elasticity, dynamical 83
Boundary-value problems in elasticity, existence of solution of 92
Boundary-value problems in elasticity, mixed 93
Boundary-value problems in elasticity, uniqueness of solution of 92
Brillouin, I, . 91 204
Cantilever beam 269 282 291 296 302 312 323
Caratheodory, C. 168 170
Carslaw, H.S. 154
Cartesian tensors 13
Castigliano’s Theorem 301
Cauchy — Riemann equations 127
Cauchy, integral formula of 156
Cauchy, integral formula of, Integral Theorem of 155
Cauchy’s quadric 11 40
Center of flexure 224 227
Central line of a beam 108
Central line of a beam, curvature of 110 233
Cesaro, E. 27
Christoffell, M.B. 109
Christopherson, D.G. 314
Churchill, H.V. 154
Circular pipe, bending of 253
Circular pipe, bending of, torsion of 196
Collocation method 317
Collocation method, application, to torsion problem 317
Collocation method, estimates of errors in 323
Compatibility, equations of 24 27 34 77
Complete systems of functions 313
Complex variable theory 154
Conformal mapping 165
Conformal mapping, applications of 176
Conformal mapping, Riemann’s theorem on 168
Continuity of class  18
Coulomb, C.A. 12I
Courant, R. 288 311 313 322 328 331
Cranz, H. 191
Curvilinear coordinates 197
Curvilinear coordinates, cylindrical 202
Curvilinear coordinates, plane polar 201
Curvilinear coordinates, spherical 203
Deformation 1
Deformation, Eulerian components of 29
Deformation, finite 28
Deformation, homogeneous 4 8
Deformation, infinitesimal 5 18 28
Deformation, Lagrangian components of 29
Deformation, nonhomogeneous 19
Deformation, plane 22
Deformation, pure 2 8 19
Deformation, quadric of 11
Deimel, R.F. 212
Den Hartog, J.P. 190
Deutler, H. 190
Dilatation 17 19 20 32 117
Dilatation, strain energy of 118
Dilatation, uniform 21
Dirichlet, conditions of 151
Dirichlet, conditions of, problem of 128
Dirichlet, conditions of, problem of, for a circle 133 163
Dirichlet, conditions of, problem of, method of finite differences for 335
Dirichlet, conditions of, problem of, Poisson’s formula for 165
Dirichlet, conditions of, problem of, Schwartz’s formula for 165
Displacement, components of 18
Displacements, continuity of 27
Displacements, continuity of, neighboring 281
Divergence 20
Duncan, W.J. 312 315
Dynamical equations 82
D’Alembert, Principle of 82
Elastic coefficients 60 65 67
Elastic coefficients, symmetry of 63
Elastic limit 58
Elastic moduli 67
Elastic moduli, interpretation of 68
Elastic moduli, interpretation of, relations among 71 72
Energy, complementary 286
Energy, complementary, minimum principle of 278 313
Energy, complementary, of deformation 90 278
Energy, complementary, of strain 83 87 284
Energy, complementary, potential 90 280 282 306
Engelmann, F. 195
Equations, of Beltrami — Michell 78
Equations, of Cauchy — Riemann 127
Equations, of compatibility 24 27 34 77
Equations, of elasticity, in curvilinear coordinates 201
Equations, of equilibrium 41 72 201
Equilibrium equations 41 72
Equilibrium equations in curvilinear coordinates 201
Error functions 314 316 323
Eulerian strain components 30 63
Euler’s equation 287 289
Evans, G.C. 105
Extension 8 12 31
Extension, of beams 101 104
Finite deformations and strains 28 89
Finite differences, application of, to torsion 338
| Finite differences, application of, to torsion, method of 334
Finite differences, application of, to torsion, use of, in Poisson’s equation 345
Flexural rigidity 111
Flexure, center of 224 227 230 258
Flexure, function of 221 225 229 231 263
Flexure, of beams, anisotropic 274
Flexure, of beams, cardioid 242
Flexure, of beams, circular 235
Flexure, of beams, compound 276
Flexure, of beams, curved 275
Flexure, of beams, elliptical 237 258
Flexure, of beams, hollow 253
Flexure, of beams, initially twisted 274
Flexure, of beams, rectangular 240 272
Foppl, A. 80 81 118 212
Foppl, L. 190
Forces, body 35 73
Forces, surface 35
Forsyth, A.R. 170
Fourier series 150
Fried, B. 337 342 344
Friedrichs, K. 328
Galerkin, B.G. 149 150 314 323
Galerkin’s method 313 322
Galerkin’s method, application of, to torsion 315
Galerkin’s method, estimates of errors in 323
Galerkin’s method, modification of 315
Gauss’ Theorem 20
Geckeler, J.W. 142
Generalized Hooke’s law 59 tS8
Generalized Kronecker delta 10
Golusin, G. 169
Goodier, J.N. 96 101
Goursat, E. 163
Gradient 20
Grarnmel, R. 191 195 300 301 320
Graustein, W.C. 136
Green — Gauss Theorem 20
Green, S.L. 170
Greenhill, A.G. 182
Griffith, A.A. 187 262
Grooves, effect of 139 191
Hamack’s Theorem 100
Harmonic function 79
Hatamura, M. 190
Higgins, T.J. 184 275 345
Hilbert, D. 288 313
Holder’s condition 104
Homogeneous media 60 65
Homogeneous strain 4 8 33
Hooke, R. 57
Hooke’s law 57
Hooke’s law, connection of, with energy 83
Hooke’s law, for isotropic bodies 70 200
Hooke’s law, generalized 59 88
Hooke’s law, in curvilinear coordinates 200
Hooke’s law, symmetry of coefficients in 88
Infinitesimal deformation 5 18 28
Influence coefficients 300 302
Invariants 13 17 50 90 117
Invariants, equations satisfied by 79
Isotropic media 60 64 65
Jackson, D. 154
Jacobsen, L.S. 191 209
Janelidze, G. 274
Kantorovich, L. 169 315
Kappus, R. 33
Kellogg, O.D. 126 129 131 133 105
Kirchhoff, G. 40
Knopp, K. 154
Koch, J.J. 321 323
Kolossoff, G. 149
Kopf, E. 190
Korn, A. 92
Kronecker delta 2 10
Kryloff, V. 169
Kufarev, P.F. 186
Lagrangian strain components 29 30 63
Lame, G. 67
Lamp’s constants 67
Laurent’s series 157
Least-squares method 318
Least-squares method, application of, to torsion 318
Lechnitzky, S.G. 276
Lecornu, L. 33 64
Leibenson, L. 139
Lichtenstein, L. 92
Lipsehitz condition 104
Load, plane of 232
Load, point of 217
Local effects 209 273
Lourie, A.I. 274
Love, A.E.H. 17 23 24 28 33 41 45 54 59 64 71 83 91 95 96 107 116 127 133 142 150 182 191 201 203 212 217 231 274
MacMillan, W.D. 133
MacRobert, J.M. 210
March, H.W. 187 191 195 217
Matuyama, T. 190
Maxwell’s influence coefficients 300
McConnell, A.J. 203
McGivern, J.G. 190
Melentieff, P. 169
Membrane analogy 131 132 187 255 257 261 314 318
Membrane deflection 188
Membrane function 262
Membrane function, connection of, with flexure and torsion 263
Michell, J.H. 78
Minimum potential energy, theorem on 281 304
Minimum potential energy, theorem on, application of 291 312
Minimum principle of stress 286
Moduli of elasticity 67
Moduli of elasticity, bulk 70
Moduli of elasticity, compression 70
Moduli of elasticity, determination of 111
Moduli of elasticity, Poisson’s 68
Moduli of elasticity, relations among 71 72
Moduli of elasticity, rigidity 69
Moduli of elasticity, shear 69
Moduli of elasticity, values of 71
Moduli of elasticity, Young’s 68
Mooratoff, M. 169
Morris, R.M. 174 184 228 243
Moskovitz, D. 345
Murnaghan, F.D. 33 89
Muschelisvili, N.I. 97 160 171
Mushtari, N.M. 252 253
Navier, C.L.M.H. 121
Navier’s equations 74
Nemenyi, P. 195 263
Neuber, H. 209
Neumann’s problem 123 163
Neutral plane 111 115
Nonhomogencous deformation 19
Normal stresses 52
Odqvist, F. 203 204
Ollendorff, F. 170
Orthogonal transformation 12
Orthotropic medium 62 64
Osgood, W.F. 136 163 170
Palerino, D. 276
Panov, D.Y. 33 275
Pearson, K. 40
Picard, E. 159 163
Piccard, A. 190
Pippard, A.J.S. 302
Plane deformation 22
Plane strain 22
Plane stress 56
Plane, neutral 111 115 232
Plane, of bending 115 232
Plane, of load 232
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