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Sokolnikoff I.S. — Mathematical Theory of Elasticity
Sokolnikoff I.S. — Mathematical Theory of Elasticity

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Название: Mathematical Theory of Elasticity

Автор: Sokolnikoff I.S.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1946

Количество страниц: 382

Добавлена в каталог: 03.12.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $C^{(n)}$      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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