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Амензаде Ю.А. — Теория упругости
Амензаде Ю.А. — Теория упругости



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Название: Теория упругости

Автор: Амензаде Ю.А.

Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 285

Добавлена в каталог: 28.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\varepsilon$-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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