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| Sadd M.H. — Elasticity: theory, applications, and numerics |
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| Предметный указатель |
Airy stress function 132 253 326
Alternating symbol 6
Analytic function 247
Angle of twist 204
Anisotropic elasticity 72 283
Anti-plane stain 131
Antisymmetric tensors 6
Approximate solution methods 97
Axisymmetric problems, plane case 159 252
Axisymmetric problems, three-dimensional case 350—353 356 358
Beam problems, pure bending 143
Beam problems, sinusoidal transverse loading 150
Beam problems, uniform axial loading 141
Beam problems, uniform transverse loading 145
Beltrami stress function 363
Beltrami — Michell compatibility equations, general equations 88
Beltrami — Michell compatibility equations, plane strain 125
Beltrami — Michell compatibility equations, plane stress 128
Bending of curved beams 182
Betti / Rayleigh reciprocal theorem 110
Biharmonic equation 133 139
Biharmonic functions 133 139 348—350
Biharmonic solutions 133 139
Biharmonic vectors 350 366
Body couple 389
Body force vector in finite element theory 420
Body forces 49
boundary conditions 84
Boundary element method 98 413 429
Boussinesq potentials 356
Boussinesq problem 353 356
Brazilian test 185
bulk modulus 76 77
Burgers vector 373
Calculus of variations 117
Cartesian tensor notation 9
Castigiliano's theorem 117
Cauchy — Riemann equations 248
Cauchy's integral formula 249
Cauchy's integral theorem 248
Center of dilatation 361 368 382
Center of flexure 233
Center of rotation 383
Cerruti's problem 354
Characteristic equation (principal value problem) 12
Clapeyron's theorem 110
Coefficient of thermal expansion 78 320
Comma notation 16
Compatibility equations see Saint — Venant and/or Beltrami — Michell compatibility equations
Complementary energy 114
Completeness 347 354
Complex conjugate 246
complex derivative 247
Complex displacements 253
Complex Fourier series 260 308
Complex potential functions 254
Complex stresses 254
Complex temperature 334
Complex variable 245
Complex variable methods, anisotropic plane problem 301
Complex variable methods, anisotropic torsion problem 296
Complex variable methods, plane problem 252
Complex variable methods, thermoelastic plane problem 334
Complex variable methods, torsion problem 213
Compliance tensor 284
COMPOSITES 283 292
Concentrated force problem, plane problem 170 265 266 304 305
Concentrated force problem, three-dimensional problem 353 356
Conformal mapping or transformations 251 269 307
Conjugate functions 248
Conservation of angular momentum 60
Conservation of energy 320
Conservation of linear momentum 59
Constitutive relations 69
Contact problems 177
Continuum mechanics 3
Contraction of tensors 5
Conversion between plane strain and plane stress, isothermal case 129
Conversion between plane strain and plane stress, thermoelastic case 324
Convex region 355
Coordinate systems: Cartesian 7 437
Coordinate systems: cylindrical 19 437
Coordinate systems: general orthogonal curvilinear 20
Coordinate systems: polar 23
Coordinate systems: spherical 20 437
Coordinate transformation 7
Cosserat continuum 389
Couple stress tensor 389
Couple stress theory 50 388 390
Coupling term (thermoelastic energy equation) 320
Crack density parameter 385
Crack problems 179 273 312 341
Curl operation 17 22
Curved beams 182
Cyclic functions 258 336 338
Cylindrical coordinates 19
Deformation 27
Degrees of freedom 418
Del operator 17
Determinant 7
Dilatation 36 46
Dirac delta function 261
Direct solution method 93
Dislocations, edge 372—374
Dislocations, screw 47 372 375
Displacement formulation 89
Displacement gradient tensor 29
Displacement potentials 347
Displacement vector 28
Divergence operation 17 22
Divergence theorem 18
Doublet mechanics 371 403
Dual vector 26
Duhamel — Neumann thermoelastic law 78 320
Dyadic notation 10
Eigenvalue problem 12
Elastic limit 70
Elastic material 70
Elastic moduli 72 77
Elasticity with distributed cracks 371 385
Elasticity with voids 371 397
Elliptical hole problem 272 307
energy equation 319
Energy methods: minimum complementary energy 114
Energy methods: minimum potential energy 114
Engineering strains 32
Equilibrated body force 398
Equilibrated force 398
Equilibrated stress vector 398
Equilibrium equations 59
Equilibrium equations, Cartesian 60 438
Equilibrium equations, cylindrical 62 439
Equilibrium equations, polar 67
Equilibrium equations, spherical 63 439
Euler — Bernoulli beam theory 116
Eulerian description 28
Even functions 154
Extension of cylinders 202
Failure criteria (distortional slrain energy) 107
Finile difference method 98 413
Finite element method 98 413 414
Flamant solution 170 266
Flamant's paradox 406
Flexure of cylinders, circular section 233
Flexure of cylinders, general formulation 229
Flexure of cylinders, rectangular section 235
Force doublet 360 367 380 381
Fourier law of heat conduction 319
Fourier methods 96 149 219
Fourier series 153
| Fracture mechanics 181 274 312 341
Functionally graded materials 72 100 137
Fundamental solution 111
Galerkin vector 347 349 366
Generalized plane stress 129
Global reference system 422
Gradient operation 17 22
Granular materials 198 403
Green's function 111 431
Green's theorem in the plane 19
Half Space problems 169 266 305
Harmonic functions 232 248 348 350
Heat conduction 319
Heat flux vector 319
Helmholtz representation theorem 347
Holomorphic functions 247
Homogeneous materials 71
Hooke's law 71 73 439 440
Hyperelastic materials 107
Incompressibility 76
Index notation 4
Indirect tension test 185
Induced mappings 308
Infinite space problems 265 304 351
Infinitesimal (small) deformations 28 31
Inner product 5
Integral transform methods 97
Internal energy 320
Interpolation functions 417
Invariants of a tensor 12
Inverse solution method 94 139
Irrotational vector field 347
Isochromatic fringe patterns 179 188 197 198
Isotropic materials 71
Isotropic tensors 9 73
Kelvin problem 111 351 367 377
Kolosov — Muskhelishvili potentials 254 257
Kronecker delta 6
Lagrange interpolation functions 417
Lagrangian description 28
Lame's constant 73 77
Lame's strain potential 348
Lamellar vector field 347
Laplace equation 96 131 208 248
Laplacian operation 17 22
Laurent series 249
Legendre differential equation 359
Legendre functions and polynomials 359
Length scales 371 392 394 403
Line integrals 18 248
Line of dilatation 384 410
Loading vector in finite element theory 420
Local coordinates 422
Love strain potential 351
Maclaurin series 249
Material symmetry 72 283
Material symmetry group 285
MATLAB 445
Matrix notation 3
Matrix products 16
Maximum shear stress 57 65 177 188 197
Maxwell stress function 347 364
Membrane analogy 211
Michell solution 157
Micro-polar stress theory 50 371 388
Micromechanics 371
Modulus of elasticity 74 77
Mohr's circle 57
Monoclinic materials 286
Morera stress function 347 364
Multiply connected regions 40 250
Multivaluedness 41 47 250 373
Navier equations, anti-plane strain case 131
Navier equations, general equations 90 440 441
Navier equations, plane strain case 125
Navier equations, plane stress case 128
Neumann principle 283
Nodal displacements 418
Nodal forces 420 421
Nodal points 414 417
Nonhomogeneous materials 72 100 137
Octahedral plane 65
Octahedral stress 65
Odd functions 128 154
Orthogonality conditions 9 286
Orthotropic materials 287 292
Papkovich — Neuber solution 347 354 376
Permutation symbol 6
Photoelastic results, contact loadings 178
Photoelastic results, crack problem 197
Photoelastic results, disk under compression 188
Photoelastic results, granular media 198
Physical components 21
Piola — Kirchhoff stress 53
Plane strain 123 299
Plane stress 126 299
Poisson equation 205
Poisson's ratio 74 77
Polar coordinate formulation, isothermal 133
Polar coordinate formulation, thermoelastic 329
Polar coordinates 23
Polynomial solutions 139
Poroelasticity 372
Positive definite strain energy form 106 291
Potential theory 209 325 376
Power series method for Airy function 96 139
Prandtl stress function 205
Pressure 76
Principal value problem, principal directions 12
Principal value problem, principal values 12
Proportional limit 70
Quadratic form of strain energy 106
Rayleigh — Ritz method 97 118
Reference temperature 320
Reissner's principle 117 120
Residues 250
Restrictions on elastic moduli 291
Rigid body motion 27 30 33
Rosette strain gage 44
Rotating disk problem 189 199
Rotation tensor 29
Saint — Venant compatibility equations 38
Saint — Venant theory for deformation of cylinders, bending / flexure 201 229
Saint — Venant theory for deformation of cylinders, extension 201 202
Saint — Venant theory for deformation of cylinders, torsion 201 203
Saint — Venant's principle 92 141 201
Scalar notation 3
Scale factors 20
Self-equilibrated forms 363
Semi-inverse solution method 95 201
Shear center 233
shear modulus 73 77
Shear strains 31
Simply-connected regions 40 248
Single-valued displacements 37
Singular stress states 376
Singularities, branch points and cuts 250
Singularities, general definition 247
Singularities, poles 249
Solenoidal vector field 348
Somigliana's identity 111 430
Specific heat capacity 320
spherical 43 438
Spherical cavity 360
Spherical coordinate solutions 343 358
Spherical coordinates 20
Spherical harmonics 359
Spherical strains 36
Stationary potential energy 114
Steady state thermal conditions 320
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