Lai W.M., Rubin D., Krempl E. — Introduction to continuum mechanics :: Электронная библиотека попечительского совета мехмата МГУ

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Lai W.M., Rubin D., Krempl E. — Introduction to continuum mechanics

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Название: Introduction to continuum mechanics

Авторы: Lai W.M., Rubin D., Krempl E.

Аннотация:

New material has been added to this third edition text for a beginning course in continuum mechanics. Additions include anisotropic elastic solids, finite deformation theory, some solutions of classical elasticity problems, objective tensors and objective time derivatives of tensors, constitutive equations for viscoelastic fluids, and equations in cylindrical and spherical coordinates. Many examples and problems with selected answers are included.

Язык:

Рубрика: Физика/Классическая физика/Упругие среды/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: third edition

Год издания: 1999

Количество страниц: 556

Добавлена в каталог: 18.06.2005

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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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