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| Авторизация |
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| Поиск по указателям |
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| Lai W.M., Rubin D., Krempl E. — Introduction to continuum mechanics |
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| Предметный указатель |
Acceleration of a particle in cylindrical coordinates 88
Acceleration of a particle in rectangular coordinates 87
Acceleration of a particle in spherical coordinates 89
Acoustic wave 404
Airy’s stress function 276 282
Anisotropic elastic solid 219 293
Anisotropic elastic solid, monoclinic 299 312
Anisotropic elastic solid, orthotropic 301 311
Anisotropic elastic solid, plane of material symmetry 296
Anisotropic elastic solid, transversely isotropic 303 308
Antisymmetric tensor 35
Apparent viscosity 513 515—516
Axial vector 36 94
Barotropic flow 409
Bernoulli’s equations 392
BKZ fluid 503
Body force 187
Boundary layer 399
bulk modulus 220 228
Bulk viscosity 358
Cauchy stress tensor 202 319 321
Cauchy stress vector 174
Cauchy’s equations of motion 189
Cauchy’s stress principle 173—174
Cayley — Hamilton theorem 323
Channel flow 371—372 523
Characteristic equation 39
Choked flow 417
Co-rotational derivatives 508
Compatibility conditions for finite deformation 144
Compatibility conditions for infinitesimal strain 114
Compatibility conditions for rate of deformation 119
Complex shear modulus 470
Compliance matrix 294
Compressible flow, converging nozzle 414
Compressible flow, converging-diverging nozzle 416
Compressible flow, one-dimensional 412
Compressible Newtonian fluid 401
Compressive stresses 177
Conjugate pairs 207
Conservation of mass 112 147 349 437
Continuum mechanics 79
Contraction of indices 9
Control volume 433—434
Convected Maxwell fluid 512
Conversion of elastic constants 230
Corotational Jeffrey fluid 514
Couette flow 380 389 526
Creep experiment 465
Creep function 466
Current configuration as reference configuration 476
Deformation gradient 120 126 317
Differential type constitutive equations, incompressible fluids 503
Dilatation 105 220
Dilatational wave 240
Displacement field 92
Displacement gradient 95
Dissipation functions 383
Divergence theorem 430
Dual vector 36 94
Dummy index 3
Dyadic product 21
Eigenvalues of a tensor 38
Eigenvectors of a tensor 38
Einstein’s summation convention 4
Elastic constants, table of 231
Elastic medium under large deformation 319
Elasticity 217
Elasticity tensor 221
Elasticity tensor, components of 225
energy equation 208 402
Energy equation, Newtonian fluid 384
Enthalpy 402
Entropy inequality 209
Equations of hydrostatics 350
Equations of motion 187
Equations of motion in cylindrical coordinates 190
Equations of motion in reference configuration 201
Equations of motion in spherical coordinates 190
Equilibrium equations 189
Equivoluminal wave 242
Eulerian description 84
Eulerian strain tensor 141 319
Euler’s equation of motion 391
Extra stress 464
Finger deformation tensor 138
Finite deformation 121
Finite deformation tensor 121 128 134 136 138 141 151 153 155—156 206 318—321
Finite deformation tensor in other coordinates 149
Finite deformation, area change 145
Finite deformation, isotropic elastic material 322
Finite deformation, volume change 146
Finite elastic deformation, bending of a bar 327
Finite elastic deformation, extension of incompressible solid 324
Finite elastic deformation, simple shear of an isotropic material 325
Finite elastic deformation, torsion-tension 331
First coefficient of viscosity 357
First Jaumann derivative 508
First Piola Kirchhoff stress tensor 202
Flow, channel flow 372 523
Flow, Couette 380 389 526
Flow, Hagen — Poiseuille 374
Flow, irrotational 390
Flow, oscillating plate 381
Flow, parallel 361
Flow, plane Couette flow 371
Flow, plane Couette of two layers 377
Flow, simple shearing 82
Flow, uni-directional 361
Fluid flow, boundary conditions 365
Fluid pressure 357
Fluids, definition of 348
Frame, change of frame 314 317 496
Frame, frame-indifferent quantities 315
Frame, principle of material frame indifference 319
Free index 5
Gauss’s theorem 431
Generalized linear Maxwell fluid, continuous spectrum 474
Generalized linear Maxwell fluid, discrete relaxation spectra 471
Generalized linear Maxwell fluid, integral form 473
Global principle 427
Green’s deformation tensor 129
Green’s Theorem 427
Hagen — Poiseuiile flow 374
History of relative deformation tensor 486
Homogeneous media 219
Hookean elastic solid, linear 220
Hookean elastic solid, nonlinear 322
Hugoniot equation 413
Hydrostatic pressure 349
Hydrostatic stress 179 230
Identity tensor 23
Incompressible elastic material 232
Incompressible material 113 147
Incompressible Newtonian fluid 359
Incompressible simple fluid 497
Indeterminate pressure 359
Infinitesimal deformations 94
Infinitesimal rotation tensor 106
Infinitesimal strain tensor 98
Inhomogeneous media 219
Integral type constitutive equation, linear 473
Integral type constitutive equation, nonlinear 498 503
Irrotational flow as solution of Navier — Stokes equation 394
Irrotational flow, inviscid compressible fluid 408
Irrotational flow, inviscid fluid 391
Irrotational wave 240
Isentropic pressure density relation 406
Isochoric condition 324
Isotropic elastic solid 219 225 306
| Isotropic function 322 502
Isotropic function(al) 497
Isotropic tensor 225
Jaumann derivative of stress 507
Kelvin’s problem 190
Kinematic equations of motion 80
Kinematic viscosity 396
Kronecker delta 6
Lagrange multiplier 184
Lagrange stress tensor 196
Lagrangian description 84
Lagrangian strain tensor 134 136 206 319
Lame’s constants 226
Laminar flow 370
Left Cauchy — Green tensor 138 151 155—156 318 321
Linear anisotropic elastic solid 293
Linear elastic solid 220
Linear isotropic elastic solid 225 306—307
Linear Maxwell fluid 464 469 475
Linear transformation 11
Linearly viscous fluid 356
Local principle 427
Longitudinal wave 239
Loss modulus 471
Mach number 411
Material coordinates 80 83
Material derivative 85
Material description 83
Material volume 433
Maximum shearing stress 182
Maxwell element 464
Mean normal compressive stress 357
Memory function 475
Modulus of elasticity 218 228
Monoclinic elastic solid 299—300 312
Moving control volume 449
Moving frames of reference 447
Navier — Stokes equations, cylindrical coordinates 364
Navier — Stokes equations, incompressible fluid 360
Navier — Stokes equations, spherical coordinates 365
Navier’s equations, cartesian coordinates 235
Navier’s equations, cylindrical coordinates 236
Navier’s equations, spherical coordinates 236
Newtonian fluid 355
Non-Newtonian fluid 462
Normal strains 100
Normal stress differences 505—506
Normal stress functions 500 514—516 522
Nth Jaumann derivative 508
Objective quantities 315
Objective rate of stress 506
Objective scalar, vector, tensor 316
Oldroyd 3-constant fluid 515
Oldroyd 4-constant fluid 516
Oldroyd fluid A 515
Oldroyd lower convected derivative 508
Oldroyd upper convected derivative 510
Orthogonal tensor 24
Orthotropic elastic solid 301 311
Particle in a continuum 79
Pathline 80 367
Permutation symbol 7
Phase angle 471
phase velocity 239
Piezometric head 362 374
Piola Kirchhoff stress tensor 195 319
Piola Kirchhoff stress tensor, first Piola Kirchhoff 196 201
Piola Kirchhoff stress tensor, second Piola Kirchhoff 197 206 320
Plane equivoluminal wave 242
Plane irrotational wave 238
Plane of material symmetry 296 299
Plane Poiseuille flow 372
Plane strain 275
Plane strain in polar coordinates 281
Plane stress 281
Poisson’s ratio 219 228
Polar decomposition theorem 124 478
Principal directions, strain 105
Principal directions, tensor 43
Principal planes, of stress 182
Principal Scalar invariants 45
Principal strain 105
Principal stresses 182
Principal stretch 122
Principal values 43
Principle of conservation of energy 454
Principle of conservation of mass 112 147 349 437
Principle of linear momentum 187 440
Principle of material frame indifference 319
Principle of moment of momentum 178 451
Principle of superposition 238
Pure bending of a beam 269
Pure bending of a curved beam 285
Pure stretch 121
Quotient rule 34
Rate of change of a material element 106
Rate of deformation tensor 108
Rate of extension 109
Rate of heat flow 207
Rate of shear 110
Rate type constitutive equations 511
Recursive formulas for Rivlin — Ericksen tensor 491
Reference configuration 158
Reference description 84
Reference time 79
Reflection of plane elastic waves 248
Refraction index 250
Relative deformation gradient 159 477
Relative deformation tensor 478
Relative deformation tensor, cylindrical coordinates 482
Relative deformation tensor, rectangular coordinates 480
Relative deformation tensor, spherical coordinates 485
Relative deformation tensor, transformation law in a change of frame 494
Relative Finger deformation tensor 479
Relative left Cauchy — Green tensor 159 479
Relative left stretch tensor 478
Relative Piola deformation tensor 479
Relative right Cauchy — Green tensor 159 479 499
Relative right stretch tensor 478
Relative rotation tensor 478
Relaxation function 466
Reynolds number 370
Reynolds transport theorem 435
Right Cauchy — Green tensor 128 153 155 318 320
Rigid body motion 93
Rivlin — Ericksen fluid, incompressible of complexity n 503
Rivlin — Ericksen tensor 486 488—490
Rivlin — Ericksen tensor in terms of velocity gradient 491
Rivlin — Ericksen tensor, transformation laws 496
Rivlin’s universal relation 334
Second order fluid 504
Second Piola Kirchhoff stress tensor 197 206 320
Second-order tensor 11
shear modulus 220 228
Shear strain 100
Shear stress function 506 513 522
Shear wave 242
Shearings 110
Simple bending 269
Simple extension 254
Simple shear stress state 229
Simple shearing motion 82
Simply-connected region 116
Snell’s law 251
Spatial coordinates 84
Spatial description 83
Speed of sound 406
Spherical pressure vessel 291
Spin tensor 108 111
St. Venant’s principle 256 262
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