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Quoc N.S. — Stability and nonlinear solid mechanics |
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Предметный указатель |
Acoustic tensor 240
Assumption, fundamental curve 133
Assumption, proportional loading 151
Assumption, simple eigenvalue 109
Assumption, small deformation 16
Assumption, small pre-deformation 151
Assumption, small strain-finite rotation 16 149
Assumption, state-independent potential 213
Assumption, transversality 119 136
Asymptotic expansion 135 219
Bifurcation, angular 108 137
Bifurcation, diagram 116—117
Bifurcation, dynamic 107
Bifurcation, Hopf 119
Bifurcation, static 107
Bifurcation, tangent 108 137 226
Boundary condition, implied 45
Boundary condition, natural 45
Buckling 149
Buckling, elastic 149
Buckling, plastic 185 191
Catastrophe theory 174
Centre manifold 115 125
Coefficient, elastic 34 56
Coefficient, Poisson 56
Condition, co-P-positivity 52
Condition, co-positivity 51 319
Condition, P-positivity 51 345 354
Condition, positivity 51 319 345 354
Condition, Signorini 65
Condition, strong ellipticity 240
Configuration, reference 6
Configuration, relaxed 236
Constitutive law 4
Constraint, bilateral 180
Constraint, perfect 180
Constraint, unilateral 180
Contact, effective 340
Contact, loose 340
Continuity of the solution 271
contour 315
Crack, curved 308
Crack, delamination 329
Crack, driving force 317 329
Crack, linear 308
Crack, plane 315
Criterion, Griffith 289
Criterion, maximum release rate 311
Criterion, Mises 69
Criterion, mode-1 311
Criterion, non-bifurcation 319
Criterion, plastic 68
Criterion, second variation 47 99 164 284
Criterion, second variation, Lagrangian 182
Criterion, stability 319
Criterion, Tresca 69
Critical load, Euler 137
Critical load, reduced 188 198
Critical load, tangent 188 194 217
Curve, bifurcated 133
Curve, fundamental 133
Cyclic plasticity 83
Derivative, Frechet 42
Derivative, Gateaux 42
Derivative, material 12
Derivative, objective 235
Derivative, with respect to domain 295 317
Description, Euler 7 233
Description, Lagrange 5 233
Description, updated Lagrange 233
Displacement 5
Dissipation, intrinsic 31
Dissipation, thermal 31
Eigenvalue 53 375
Eigenvalue problem 52 133
Eigenvector 53 375
Elasticity, linear 56
Elasticity, nonlinear 56
Energy, balance 11
Energy, complementary 57
Energy, cost 209 224
Energy, internal 18
Energy, kinetic 18
Energy, surface 317
Energy, total potential 5 60
Equation, Biot 254
Equation, continuity 12
Equation, differential, autonomous 91
Equation, differential, non-autonomous 274
Equation, dynamic 58
Equation, energy 30
Equation, Euler 45
Equation, Hamilton 5
Equation, local 45
Equation, reduced 113 125 135 170
Equation, state 33
Equation, static 59
Equation, thermal 40
Equation, variation 44
Equilibrium, mechanical 17
Equilibrium, thermal 17
Equilibrium, thermo-elastic 163
Equilibrium, thermodynamic 17
Evolution, plastic 68
Evolution, thermo-mechanical 304
Existence 63 271
Flux 25
Force, dissipation 31
Force, generalized 3
Force, state 24
Force, thermodynamic 24—25
Formula, Lagrange 4
Friction 335
Friction, Coulomb 335
Function, convex 47
Function, dual 48
Functional 44
Functional, Liapunov 93
Fundamental law of dynamics 2
Gradient, deformation 6
Hardening, isotropic 75
Hardening, kinematic 76
Hardening, parameter 72
Imperfection 167
Imperfection, geometry 167
Imperfection, load 167 173
Imperfection, sensitivity 173
Inequality, Clausius — Duhem 30
Inequality, Drucker 88
Inequality, Korn 63
Instability, configurational 323
Instability, divergence 96
| Instability, flutter 96
Integral, J 294
Integral, path-independent 294 299
Internal entropy production 19
Law, conduction 32
Law, evolution 68
Law, Mooney — Rivlin 158
Law, Ogden 159
Law, propagation, brittle 289 318
Law, viscous 325
Lemma, Gronwall 95
Local state postulate 29
Localization, strain 239
Matrix, mass 2
Matrix, stiffness 360
Method, asymptotic expansion 110
Method, continuation 360
Method, explicit 364
Method, implicit 364
Method, incremental 360
Method, inverse power 375
Method, large time-increment 369
Method, Liapunov — Schmidt 112 134
Method, linearization 93
Method, Newton — Raphson 360
Method, visco-plastic regularization 268
Minimum principle, complementary energy 59
Minimum principle, Greenberg 89
Minimum principle, Hodge — Prager 90
Minimum principle, potential energy 59
Minimum, global 46
Minimum, local 46
Minimum, strict 46
Mode, diffuse 240
Mode, localized 240
Mode, multiple 141
Mode, simple 141
Model, generalized standard 37 73
Model, Shanley, elastic-plastic 185
Model, Shanley, three-dimension 227
Model, Shanley, visco-elastic 276
Modulus, elastic 71 188
Modulus, limit 285
Modulus, plastic 71
Modulus, reduced 188
Modulus, tangent 188
Modulus, Young 56
Multiplier, Lagrange 180
Multiplier, plastic 70 265
Obstacle, fixed 335
Obstacle, moving 335
Parameter, free 2
Parameter, load 96
Parameter, restrained 2
Parameter, time-independent 2
Plasticity, hardening 36 72
Plasticity, perfect 36
Point, bifurcation 108
Point, critical 119
Point, limit 109
Point, regular 109
Point, singular 109 134 215 359 361
Point, stationary 44
Potential 5
Potential, dissipation 26 37 70 257 336—337
Potential, energy 37 257 337
Potential, plastic, multiple 265
Potential, plastic, simple 265
Potential, rate 71
Principle, first 18
Principle, maximum dissipation 74 258
Principle, maximum plastic work 258
Principle, mixed 61
Principle, second 21
Principle, virtual work 2
Problem, eigenvalue 375
Problem, linear complementarity 50 345
Problem, rate 87 89 339
Rate, deformation 7
Rate, displacement 13
Rate, energy release 289
Rate, strain 13
Rate, transversality 136
Response, dynamic 80
Response, static 80
Response, steady 371
Saddle point 61
Second derivative of energy 295
Shake-down 83
SHAPE 315
Solid, elastic 360
Solid, elastic-plastic 365
Solution, steady state 371
Space, Sobolev 43
Stability 91
Stability, asymptotic 92 280
Stability, configurational 323
Stability, directional 211
Stability, dynamic 211
Stability, evolution 273
Stability, numerical 368
Stability, of a equilibrium 354
Stability, static 211
Strain, elastic 68
Strain, Green — Lagrange 6
Strain, plastic 68
Stress, Boussinesq 14
Stress, nominal 14
Stress, Piola — Kirchhoff 14
Stress, Piola — Lagrange 14
Stress, tensor 8
Stress, vector 8
Symmetry, major 238
System, conservative 5 97 133
System, discrete 1
System, Hamilton 4
System, perfect 168
System, simple dissipation 317
System, standard dissipative 253
Theorem, Hopf 119
Theorem, implicit function 53 112 134
Theorem, Lejeune — Dirichlet 98 182
Theorem, Melan — Koiter 84
Thermal effects 17 37
Thermodynamics 17 304
Transform, Legendre — Fenchel 5 23 57
Transformation, reversible 18
Unilateral contact 64 335
Uniqueness 63 271
Variable, dual 23
Variable, normal 22
Variable, state 22
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