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| Авторизация |
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| Амензаде Ю.А. — Теория упругости |
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| Предметный указатель |
 -tensor 37
Absolute derivative, of tensors 34
Absolute derivative, of vectors 33
Addition of tensors 19
Affine transformations 16
Airy's formulas 116
Airy's stress function 116
Airy's stress function in polar co-ordinates 120
Airy's stress function, boundary conditions for 116
Airy's stress function, complex representation of 130
Analogies, hydrodynamic 196
Analogies, membrane 191
Analytic continuation 162
Angle, between co-ordinate lines 25
Angle, between directions in space 27
Anisotropic body 75
Associated tensors 25
Base vectors 23
Beltrami — Michell relations 91 92
Beltrami — Michell relations for generalized plane stress 115
Beltrami — Michell relations for plane strain 110
Bending, of circular plates 249 274
Bending, of circular plates, under symmetrical loading 251 276
Bending, of prismatic bodies 206
Bending, of prismatic bodies by couples 105
Bending, of prismatic bodies of elliptical cross section 216
Bending, of thin plates 268
Bending, of thin plates by couples 252
Bending, of thin plates by transverse force 268
Bessel functions 247
Betti's identity 82
Betti's reciprocal theorem 219
Biharmonic equation 116
Biharmonic equation in spherical co-ordinates 249
Biharmonic function, complex representation of 130
Body forces 40
Body of revolution, loaded symmetrically 246
Body of revolution, torsion of 253
Boundary conditions, for Airy's stress function 116
Boundary conditions, for bending of plates 271
Boundary conditions, in generalized plane stress 114
Boundary conditions, in heat conduction problems 87
Boundary conditions, in non-linear elasticity 230
Boundary conditions, in plane strain 110
Boundary conditions, in thermoelastic problems 94
Boundary value problems in elastodynamics 95
Boundary value problems in elastostatics 93
Boundary value problems, fundamental, first 93 138
Boundary value problems, fundamental, mixed 93 139
Boundary value problems, fundamental, second 93 139
Boundary value problems, fundamental, two-dimensional 110 138
Boundary value problems, reduction of, to functional equations 154
Boundary value problems, uniqueness of solution 95
BOUSSINESQ's formulas 239
Boussinesq's hydrodynamic analogy 196
Bredt's formulas 196
bulk modulus 79
Castigliano's formula 74
Castigliano's principle 222
Cauchy principal value 147
Cauchy type integral 146
Cauchy type integral, limiting values of 149
Cauchy — Riemann relations 111
Cauchy's formula 146
Cauchy's integral 145
Centre of flexure 213
Christoffel symbols 28
Circular cylinder, hollow, under uniform pressure 121 156
Circular cylinder, hollow, under uniformly distributed tangential forces 155
Circular cylinder, solid, loaded symmetrically 247
Circular disk, rotating 123
Circular plate, bending of 249 274
Circular plate, symmetrical bending of 251 276
Clapeyron's formula 73
Clapeyron's theorem 82
Co-ordinate lines 16 25
Co-ordinate lines, angle between 25
Co-ordinates, transformation of 15
Coefficient of linear thermal expansion 80
Cofactors of determinant 23
Compatibility equations for strains (Saint Venant's) 60
Compatibility equations for strains (Saint Venant's) in Cartesian co-ordinates 65
Compatibility equations for strains (Saint Venant's) in Cartesian co-ordinates, for plane strain 109
Compatibility equations for strains (Saint Venant's) in cylindrical co-ordinates 66 92
Compatibility equations for strains (Saint Venant's) in cylindrical co-ordinates, for axially symmetric problems 92
Complementary work 224
Complementary work, principle of minimum 224
Complex potentials 162
Complex representation, of Airy's stress function 130
Complex representation, of biharmonic function 130
Complex representation, of displacements 129 164
Complex representation, of harmonic function 128
Complex representation, of resultant moment 132
Complex representation, of resultant vector 131
Complex representation, of stress tensor 129 163
Complex torsion function 196
Complex variable theory 138
Components, of strain, in terms of displacements 61
Components, of stress, complex representation of 129 163
Components, of vectors and tensors 16 17
Components, physical, of vectors and tensors 27
Compression of spheres 244
Conformal mapping 142
Conservation of energy 82
Contact pressure 244
Contact problems 240
Contraction of tensors 19
Contravariant tensor 17
Contravariant vector 16
Convolution of functions 171 174
Couple-stress vector 42
Covariant derivative, of tensors 35
Covariant derivative, of vectors 34
Covariant tensor 17
Covariant vector 17
Cylinder, circular, hollow, under uniform pressure 121 156
Cylinder, circular, hollow, under uniformly distributed tangential forces 155
Cylinder, circular, solid, loaded symmetrically 247
D'Alembert's principle 43
Diffusivity 86
Direct methods of solution 98
Dirichlet conditions 170
Disk, circular, rotating 123
Displacement vector 57 85
Displacements in terms of strains 66
Displacements, complex representation of 129 164
Displacements, principle of virtual 220
Duhamel — Neumann equations 86
Elastic coefficients 70
Elastic coefficients, relations between 75
Elastic constants, Lame's 77 79 86
Elastic potential 74 75
Energy integral for equations of motion 80
Energy, complementary 224
Energy, complementary, principle of minimum 224
Energy, integral of 80
Energy, potential 222
Energy, potential, principle of minimum 222
Energy, strain 79 82
Equality, theorem of, for shearing stresses 48
Equations, of compatibility 60 65 66 92 109
Equations, of equilibrium, for generalized plane stress 114
Equations, of equilibrium, for non-linear body 230
Equations, of equilibrium, for plane problem, in polar coordinates 120
Equations, of equilibrium, for plane strain 109
Equations, of equilibrium, for plane stress 111
Equations, of equilibrium, in Cartesian co-ordinates 48
Equations, of equilibrium, in cylindrical co-ordinates 49
Equations, of equilibrium, in spherical co-ordinates 49
Equations, of equilibrium, in terms of displacements 84
| Equations, of equilibrium, in terms of stresses 44 90
Equations, of equilibrium, variational 228
Equations, of equilibrium, vector 232
Equations, of motion, in Cartesian co-ordinates 48
Equations, of motion, in Cartesian co-ordinates, in cylindrical co-ordinates 49
Equations, of motion, in Cartesian co-ordinates, in spherical co-ordinates 49
Equations, of motion, in Cartesian co-ordinates, in terms of displacements 84
Equations, of motion, in Cartesian co-ordinates, in terms of displacements, in cylindrical co-ordinates 88 89
Equations, of motion, in Cartesian co-ordinates, in terms of displacements, in spherical co-ordinates 88 90
Equations, of motion, in Cartesian co-ordinates, in terms of stresses 44
Extension, of line element 56
Extension, of prismatic rods 100
Extension, of prismatic rods, by gravitational force 101
Extensions, principal 64
External forces 39
Finite strain tensor 55
Finite strain tensor in Cartesian co-ordinates 61
Finite strain tensor, components of, in terms of displacements 57
Flexural rigidity of plate 270
Flexure function 209
Flexure, centre of 213
Forces, body 40
Forces, surface 39
Formulas of transformation of co-ordinates 15
Fourier heat conduction equation 86
Fourier integral transformation 170
Fourier inversion formula 170 173
Fourier multiple transforms 172
Fourier transform 170
Functional equations, reduction of boundary value problems to 154
Fundamental equations of elasticity 84
Gauss — Ostrogradsky formula 37
Generalized heat conduction equation 87
Generalized Hooke's law 69
Generalized Hooke's law for generalized plane stress 114
Generalized Hooke's law for isotropic body 77 80
Generalized Hooke's law for plane strain 108
Generalized Hooke's law for plane stress 112
Generalized Hooke's law in complex form 129
Generalized plane stress 113
Generalized plane stress, equations of equilibrium for 114
Generalized plane stress, generalized Hooke's law for 114
Half-plane with concentrated force applied to its boundary 180
Half-plane with distributed force applied to its boundary 179
Half-plane, first boundary value problem for 165
Half-plane, mixed boundary value problem for 167
Half-plane, second boundary value problem for 166
Half-plane, solution of boundary value problems for 161
Half-plane, weightless, solution of biharmonic equation for 177
Half-space under concentrated load 238
Half-space under distributed load 238
Half-space, indentation by sphere 245
Half-space, vibrations of 262
Hamiltonian operator 221
Harmonic function, complex representation of 128
Harnack's theorem 151
Helmholtz free energy 72
Hertz contact problem 240
Hoelder condition 147
Homogeneous body 75
Hydrodynamic analogy 196
Hydrostatic pressure 99
Identical relations between strain components 60; see "Compatibility equations"
Improper integral 147
Indentation problems 245
Initial conditions, in elastodynamics 95
Initial conditions, in heat conduction problems 87
Inner multiplication 20
Invariant 16
Invariants of stress and strain 54
Inverse methods of solution 98
Isotropic body 75
Kirchhoff's boundary conditions 272
Kronecker symbols 18
Lame's elastic constants 77 79 86
Lame's equations 85
Lame's equations for generalized plane stress 115
Lame's equations for plane strain 109
Lame's equations for plane stress 112
Lame's problem 120
Laplace's equation 87
Laplace's equation in spherical co-ordinates 249
Laplacian 121
Lateral contraction 78
Levy's equation 110
Levy's theorem 111 141
Limiting values of Cauchy type integral 149
Line element, extension of 56
Lines of shearing stress 187
Lipschitz condition 147
Mass forces 40
Membrane 191
Membrane analogy 191
Method of sections 41
Middle plane 268
Minimum principles, complementary energy 224
Minimum principles, potential energy 222
Modulus of elasticity in tension 70 78
Multiplication of tensors 19
Newton's law of cooling 87
Non-homogeneous body 75
Non-linear elasticity 230
Orthotropic body 76
Parallel vector fields 30
Physical components of vectors and tensors 27
Plane problem 108
Plane problem, equations of equilibrium for, in polar co-ordinates 120
Plane strain 63 108
Plane strain, compatibility equations for 109
Plane strain, equations of equilibrium for 109
Plane strain, generalized Hooke's law for 108
Plane stress 111
Plane stress, equations of equilibrium for 111
Plane stress, generalized 113
Plane stress, generalized Hooke's law for 112
Plane stress, generalized, equations of equilibrium for 114
Plane stress, generalized, generalized Hooke's law for 114
Plane, absolutely rigid, indentation by sphere 245
Plane, infinite, under body forces 174
Plane, infinite, under concentrated force 176
Plates, bent by couples 252
Plates, boundary conditions for 271
Plates, circular, bending of 249 274
Plates, circular, symmetrical bending of 251 276
Plates, flexural rigidity of 270
Plates, infinite, with circular hole 157
Plates, infinite, with elliptic hole 159
Plates, middle plane of 268
Plates, thin 268
Plates, thin, bending equation for 268
Plates, thin, bending equation for, in polar co-ordinates 274
Plates, thin, theory of 268
Plates, under transverse loading 268
Poisson's boundary conditions 272
Poisson's equation 86
Poisson's ratio 70 78
potential energy 222
Potential energy, principle of minimum 222
Potential, complex 162
Potential, elastic 74 75
Potential, strain tensor 74
Potential, stress tensor 71
Prandtl's formula 187
Prandtl's stress function 186
Pressure, between bodies in contact 244
Pressure, hydrostatic 99
Pressure, over surface of half-space 238
Principal directions, of strain 64 78
Principal directions, of stress 52 78
Principal extensions 64
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