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| Sokolnikoff I.S. — Mathematical Theory of Elasticity |
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| Предметный указатель |
Affine transformation 2 5 18
Analysis, of strain 1—34
Analysis, of stress 35—36
Anisotropic media 61 212 217 274 276
Beams see also "Extension" "Flexure" "Torsion"
Beams, anisotropic 212 217 276
Beams, bent by couples 106
Beams, bent by distributed loads 274
Beams, bent by terminal loads 217 228
Beams, cantilever 269 282 291 296 302 312 323
Beams, compound 276
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, technical theory of 263
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 134 196
Beams, torsion of, hollow 191 191 196
Beams, torsion of, initially twisted 274
Beams, torsion of, of variable cross section 275
Beams, torsion of, polygonal 186 187 275 316
Beams, torsion of, rectangular 143 308 317 318 320 333 33S
Beams, torsion of, semicircular 181
Beams, torsion of, torsional rigidity of 125 141 175 189
Beams, torsion of, triangular 139 143
Beltrami — Michell equations 78
Bending of beams see "Beams" "Flexure"
Bending-moment diagram 268
Bernoulli — Euler law 110 115 233 264 274
Betti and Rayleigh Theorem 297
Biharmonic function 79
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
Cantilever beam 269 282 291 296 302 312 323
Cartesian tensors 13
Castigliano's Theorem 301
Cauchy — Riemann equations 127
Cauchy's quadric 11 40
Cauchy, integral formula of 156
Cauchy, Integral Theorem of 155
Center of flexure 224 227
Central line of a beam 108
Central line of a beam, curvature, of 110 233
Circular pipe, bending of 253
Circular pipe, 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
Curvilinear coordinates 197
Curvilinear coordinates, cylindrical 202
Curvilinear coordinates, plane polar 201
Curvilinear coordinates, spherical 203
D'Alembert, principle of 82
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
Dilatation 17 19 20 32 117
Dilatation, strain energy of 118
Dilatation, uniform 21
Dirichlet, conditions of 151
Dirichlet, problem of 128
Dirichlet, problem of, for a circle 133 163
Dirichlet, problem of, method of finite differences for 335
Dirichlet, problem of, Poisson's formula for 165
Dirichlet, problem of, Schwartz's formula for 165
Displacement, components of 18
Displacements, continuity of 27
Displacements, neighboring 281
Divergence 20
Dynamical equations 82
Elastic coefficients 60 65 67
Elastic coefficients, symmetry of 63
Elastic limit 58
Elastic moduli 67
Elastic moduli, interpretation of 68
Elastic moduli, relations among 71 72
Energy of deformation 90 278
Energy of strain 83 87 284
Energy, complementary 286
Energy, minimum principle of 278 313
Energy, potential 90 280 282 306
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
Euler's equation 287 289
Eulerian strain components 30 63
Extension 8 12 31
Extension of beams 101 104
Finite deformations and strains 28 89
Finite differences, application of, to torsion 338
Finite differences, method of 334
Finite differences, 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 see also "Beams"
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
Forces, body 35 73
Forces, surface 35
Fourier series 150
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
Generalized Hooke's law 59 88
Generalized Kroneeker delta 10
Gradient 20
Green — Gauss Theorem 20
| Grooves, effect of 139 191
Harmonic function 79
Harnack's theorem 100
Hoelder's condition 164
Homogeneous media 60 65
Homogeneous strain 4 8 33
Hooke's law 57
Hooke's law for isotropic bodies 70 200
Hooke's law in curvilinear coordinates 200
Hooke's law, connection of, with energy 83
Hooke's law, generalized 59 88
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
Kroneeker delta 2 10
Lagrangian strain components 29 30 63
Lamp's constants 67
Laurent's series 157
Least-squares method 318
Least-squares method, application of, to torsion 318
Lipschitz condition 164
Load, point of 217
Load, point of, plane of 232
Local effects 209 273
Maxwell's influence coefficients 300
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
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
Navier's equations 74
Neumann's problem 123 163
Neutral plane 111 115
Nonhomogeneous deformation 19
Normal stresses 52
Orthogonal transformation 12
Orthotropic medium 62 64
Plane deformation 22
Plane stress 56
Plane, neutral 111 115 232
Plane, of bending 115 232
Plane, of load 232
Plane, strain 22
Poisson's ratio 68
Poisson's ratio, measurement of 111
Poisson, integral of 165
potential energy 90 280
Potential energy of twisted shaft 282
Potential energy, minimum principle of 278 313
Principal strain 13 15
Principal strain, axes of 67
Principle, of D'Alembert 82
Principle, of minimum energy 278 312
Principle, of minimum stress 286
Principle, of Saint-Venant 95
Principle, of superposition 5 28 79
Proportional limit 58
Pure deformation 2 18 19
Pure shear 11
Quadric, of deformation 11
Quadric, of stress 46
Rayleigh — Betti Theorem 297
Rayleigh — Ritz method 304
Rayleigh — Ritz method, applications of 305 308
Rayleigh — Ritz method, estimates of error in 324
Reciprocal theorems 297 302 303
Relaxation of boundary conditions 329
Residues 157
Riemann's theorem 168
Rigid body motion 2 5 19
Rigid body motion, conditions for 6
Rigidity, flexural 111
Rigidity, modulus of 69
Rigidity, torsional 125
Ritz's method 304
Ritz's method, applications of 305 308
Ritz's method, estimates of errors in 324
Rotation, components of 7 19 20 21 23
Saint-Venant, principle of 95 99 209
Saint-Venant, semi-inverse method of 100
Schwarz — Christoffel transformation 169
Schwarz's formula 163 165
Section modulus 268
Shear 10 38
Shear, maximum 52 54
Shear, modulus of 69
Shearing, force 266
Shearing, lines of 130
Shearing, strain 22
Shearing, stress 10 38 52 54
Simply connected regions 25
Skew symmetry 6
Statically determinate systems 270 273
Strain energy 83 87 278 284
Strain energy in a bent beam 118 292
Strain energy of deviation 117
Strain energy of dilatation 118
Strain energy of distortion 118
Strain energy of twisted beam 282
Strain, analysis of 1—34
Strain, components of 20 29 30
Strain, description of 29
Strain, deviations in 117
Strain, finite 28 89
Strain, homogeneous 4 8 33
Strain, infinitesimal 28
Strain, invariants of 17
Strain, notations for 23
Strain, plane 22
Strain, principal 13
Strain, quadric of 11
Strain, shearing 21 200
Strain, tensor 8 19 20 31 199
Stress, actual 57
Stress, analysis of 35-56
Stress, concentration of 189 191
Stress, deviations in 117
Stress, examples of 54
Stress, function in torsion 127 129
Stress, invariants of 45 50
Stress, maximum 52 54
Stress, nominal 57
Stress, normal 38 52 55
Stress, notations for 40
Stress, plane 56
Stress, principal 49
Stress, quadric of 46
Stress, shearing 38 55
Stress, tensor 37 50
Stress, tensor, symmetry of 43
Stress, tensor, transformation of 44
Stress, ultimate 58
Stress, units for 49
Stress-strain relations 57—96
Stress-strain relations, for isotropic bodies 70 72 191
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