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Ding H., Chen W., Zhang L. — Elasticity of Transversely Isotropic Materials
Ding H., Chen W., Zhang L. — Elasticity of Transversely Isotropic Materials

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Название: Elasticity of Transversely Isotropic Materials

Авторы: Ding H., Chen W., Zhang L.

Аннотация:

This book presents a comprehensive and systematic analysis of problems of transversely isotropic materials that have wide applications in civil, mechanical, aerospace, materials processing and manufacturing engineering. Various efficient methods based on three-dimensional elasticity are developed under a unified framework, including the displacement method, the stress method, and the state-space method. In particular, a three-dimensional general solution is derived to solve practical problems such as the infinite space, half-space, bimaterial space, layered medium, bodies of revolution, thermal stresses and three-dimensional contact. Exact and analytical solutions are also derived for static and dynamic problems of plates and shells, which may be used as the benchmarks for numerical or approximate analysis. Coupling effects of inner/outer fluids and surrounding elastic media on the free vibration cylindrical and spherical shells are discussed in detail. New state-space formulations are established for the analysis of rectangular plates and spherical shells, from which two independent classes of vibrations can be easily clarified.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2006

Количество страниц: 435

Добавлена в каталог: 16.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Added-mass-effect      320 351 352
Almansi's theorem      46 61 193
Anisotropic elasticity      1 29 54 364
Anisotropic material      11 13 118 376 379
Annular plate      147 148 151 154 155 280 381
Associated Legendre function      103 169 178 328 331 389 390
Associated Legendre's equation      389
Asymmetric vibration      283 301
Asymptotic expansions      287 289 294 336 337
Axis of symmetry      16
Axisymmetric deformation      53 54 275 374 379
Axisymmetric problem      46 54 60 61 94 108 154 189 373 374 382
Axisymmetric torsional vibration      283 285
Barium titanate ceramic      98
Basic equations      1 4 23 25 29 30 33 283 327 329 373 384
Basic variables      30 33 142 268
Bending      147 150 152 162 170 173 177 178 247 249 251 252 255 258 260 261 264-266 270 274 275 306 312 377 381 384
Bernoulli equation      317 346
Bessel function      100 189 258 277 286-288 290 294 303 304 307 329 336 345 382 383 391-396
Bessel's equation      286 303 388 389 391 393-395
Body force      7 39 43 54 63 64 132 142 143 155 165 183 190 247 271 275 284 310 327 365
boundary conditions      23-25 30 36 80 86 93 102 103 109 114 119 122 123 130-133 142 143 145 146 149 151 153 156 163 165 167 170 172 175-179 187 188 196 197 202 203 217 249 251 256 258 260 261 264-266 278 279 306 311 316 318 319 331 332 334 346-348 360 369 376 381
Boundary element method      283
Boundary element solution      78
Boussinesq solution      111
Breathing mode      283 284 292 296 301 343 344 349 351-353 355 356 360-362
Cartesian coordinate system      1 3-6 33 107 167 205
Cartesian coordinates      2-4 7 8 10 31 38 51 71 310 364
Cayley - Hamilton theorem      272 314 368
Cerruti solution      117
Characteristic roots      100 103
Circular frequency      249 258 271 277 285 312 322 328 330 354 387 395
Circular plate      148 150 152 154 157 158 247 257 258 260 264 275 278 280 281 310 381
Circumferential stress      97 99
Classical thin shell theory      344 345 350 354 355
Coefficient determinant      173 253 305 306 309 319 326 334
Coefficient of friction      224 228
Coefficient of heat radiation      187
Coefficients of thermal conduction      186
Compatibility conditions      6
Compatibility equations      56
Complex frequency      350 351 353
Compressible fluid      316 319 345 350-352 355 384
Compression of a cone      158
Concentrated force      71 83 158 159 161 162 164 167 168 214 215 217 222 231 244 374-376
Concentrated moment      167 173
Concentrated normal force      225 237
Concentrated tangential force      118 228 233 239
Cone      147 158 160-162 164 165 168 170 173 175 177 230 236 243 377 379
Conical shell      159 162 164 167 176 377
Conjugate operator      216
Constitutive equations      4 8 11 21 23 29 48
Constitutive relations      17 19 34 157 189 194 250 259 283 321 364
Contact area      209 212-214 216-218 222 224 225 227 228 231-233 237 239 241 242
Contact interface      214 233 243
Contact problem      205 216 224 241 242 244 378-380
Contact region      209 232 242 244
Contact sliding      217 222 224 230 236 241
Continuity conditions      94 96 309 314 332 333 336 368 369
Convergence rate      316 371
Coordinate transformation      4 206
Coulomb friction      217 222 224 230 237 241 244
Cylinder      147 214 283-286 288 292-294 296-298 301 305 306 318 380 382
Cylinder function      392
Cylindrical anisotropy      14
Cylindrical coordinate system      1 54 158
Cylindrical coordinates      2 4 6 7 14 18 21 31 39 51 52 147 148 158 185 191 192 194 197 214 257 283 316 382 387 388 395
Cylindrical panel      309 311 312 315
Cylindrical punch      224 225 236 241 244 379
Cylindrical shell      283-286 289 290-292 294 296 297 299 301 302 305-308 310 313 316 318 319 321 322 325 326 382
Cylindrical surface      149 151 286 289 293 294 298 299 305 324
Cylindrically orthotropic material      14
Damping component      350 351 353 354
Direction cosines      2-4 12 17 20 24 94
Displacement components      6 30 33 90 97 332
Displacement function      39 60 63 64 67 75 86 89 91 95 148 155 198 218 219 222 225 228 231 233 237 239 257 301 305 321 324 327 330 350 376 377 383
Displacement method      29 30 38 62 183
Double Fourier Transform      124 186
Duhamel - Neumann equation      25
Dummy index      3
dynamic loading      24
Dynamic pressure      317 349 355
Eigenvalue condition      78
Eigenvalues      80 81 84 91 120 133 135 166 167 251 260 273
Elastic compliance      10 11 21
Elastic constants      19 20 23 103 112 118 150 152 188 294 306 307 329 338
Elastic direction      12
Elastic foundation      327 357 358 361 385
Elastic layer      73 76 109 114 133-135 139 376
Elastic matrix      45
Elastic medium      141 321 322 324 327 356 359 360 385
Elastic properties      1 11 12 16 26 150 152 242
Elastic stiffness      10 11 14 15
Elastically supported boundary conditions      261
Elementary functions      198 218 231 241 380 396
Elliott solution      48 62
Ellipsoidal inclusion      93
Engineering shear strain      2 9
Engineering symbols      15 19
Equation of heat conduction      25 186 189
Equations of equilibrium      8
Equations of motion      4 7 23 29 33 190 275 284 365 383
Equilibrium condition      160
Equilibrium of an elastic layer      73 109
Euler equation      359
Exact solution      197 280 375 376
Exponential matrix      272 279 314 368
External force      160 163 209
External loading      1 94
External normal      4 24 94
Finite Hankel transform      277 383
Finite value condition      346
First class of vibration      255 274 275 336 339 342 348 370
Five-mode shell theory      344 345
Fixed surface      288 292 294 296 299
Fluid density      317 346
Fluid-filled cylindrical shell      319
Fluid-structure interface      317
Foundation modulus      357
Fourier transform      107 123-126 130 135 140 186-188 379 380
Free index      3
Free surface      298
Free vibration      247 249 252 262 266 271 273-275 279 283 285 296 301 305 308 309 311 314 315 318 319 326 327 331-333 338 345 348 350 354 356 360 362 366 369 371 381-383 385
Frequency equation      273 279 286-290 292-296 298 300 304-307 309 315 318 326 334-341 348-350 353 360 361 369 370
Friction coefficients      222 224
Frictional contact      205 216 224 241-244 380
Frictional force      224 241 242 244
Frictionless contact      208 224 380
Frobenius power series method      330 389
Fundamental solution      78 128 375 376 378
General solution      29 38 41-43 47 48 51 52 54 58-62 65 66 69 71 74 78 94 119 123 125 128 130 132 135 143 147 148 155 158 183-185 187 189-195 200 201 203 214 247 257 330 373 374 376-378 381 389-391 395
General thermoelasticity solution      184 185
Generalized Hooke's law      1 8 12 14 15 19-21 25 31 32 56
Geometric equations      4-6 23 33
Governing equations      29 30 33 38 58 62 64 155 183 190 333 334 344 369 383
Green's function      214 216 375 380
Hamilton's principle      344
Hankel function      394 395
Hankel transform      189 199 277 280 376 378 380 383
Harmonic equation      147
Harmonic function      46 95 123 147 148 195 378 379
Heat flux      187
Helmholtz equation      387 388
Helmholtz separation theorem      321
Hertzian contact      380
Hollow sphere      147 200 202 313 327 331 342 345 348-352 354-356 360 366 371 378 383-385
Homogeneous equations      43 58 59 60 65 132 305 306
Hyperbolic functions      252 260
Imaginary part      350 351
Improved shell theory      320
In-plane vibration      265 274
Incompressible fluid      320 349 351-353 356
Incompressible material      245
Indentation depth      233
Induced variables      33 268 270 274 370
Infinite body      80 83 90 94 130-132 135 376
Infinite solid      71 75 79 93 195
Initial conditions      23-25
Inner fluid      345 346 348 349
Inner radius      148 314 331 357 366 368 371
Inner surface      325
Integral transform      378
Inverse method      25
Inverse transform      135 186 188 189
Isotropic material      20 21 74 99 111 117 132 139 157 205 210 216 217 219-221 224 242 245 274 280 301 315 336-338 374-377 379 382
Isotropic plane      16 71 73-75 79 80 85 107 139 148 161 195 271 374 375 379
Kelvin solution      74 78
Kronecker delta      197 391
l'Hospital's rule      216
Lame constants      20 321
Laminated circular plate      275 276
Laminated cylindrical shell      308 310 313 326 382
Laminated rectangular plate      266 268 271 275 381
Laminated spherical shell      327 364 366
Laminated structure      93
Laplace operator      46 190 192 247 257 316 345 366 387
Lateral surface      158 160 162 163 167
Layerwise method      313 367 371 385
Legendre functions      100 103 177 328 331 333 383 389 390
Legendre polynomial      100 389
Lekhnitskii solution      61
Linear algebraic equations      252 268
Linear elasticity      8
Lorentz solution      119
Love solution      61
Lowest natural frequency      256 266 281 307 336 352
Maple      75 287
Material constants      79 97 139 220 280 312 315 338 339 342 351 353
Material properties      22 23 71 158 242 265 361 379
Mathcad      287 307
Mathematica      75 287 307 315
MATLAB      307
Matrix form      1 5 10 26
Method of initial functions      33
Method of small damping coefficient      350 353
Michell solution      62
Mindlin plate theory      254 264 381
Mindlin solution      119
Mixed method      29 30 33
Modified Bessel function      286 303 304 307 393 394
Modified Bessel's equation      393 394
Modified shear factor      254 307
Multi-layered coatings      141
Multi-layered composites      141
Multi-layered spherical shell      332 333 336
Newton - Raphson method      351
Non - Hertzian contact      380
Non-axisymmetric vibration      306
Non-breathing mode      343 344 349 352 353 355 356 360 361
Non-dimensional frequency      274 344 367 371
Non-homogeneous equations      42 60
Non-uniform stress field      94
Non-viscous fluid      318
Nontrivial solution      253 263 306 309 319 326 334 370
Normal load      112 118 251 260
Operator matrix      5 37
Ordinary differential equation      125 329 330 385 388
Orthotropic material      12-15 19 30-32
Orthotropic medium      310
Orthotropic solid      13 26
Out-of-plane vibration      265 381
Outer fluid      345 346 348 349
Outer radius      148 314 331 338 357 368 371
Outer surface      176 200 289 309 318 332 348
Output variables      33
Partial differential equations      6 29 30 60 65
Partial differentiation      8 126 185
Particular solution      155 156 184-187 200 201 203
Pasternak foundation model      357
Plane of elastic symmetry      12 14 20
Plane of isotropy      186 247 257
Point force      71 74 75 80 85 90 99 100 107 108 112 118 119 121 123 128 129 132 134-136 139 214 375 376
Point force solution      71 79 119 123 132 133 214
Poisson's ratio      21 98 157 220 242 274 324 338
Potential function      380
Potential theory      195 197 216 380
Pressure distribution      209
Primary variables      33 36
Principal curvatures      206
Principal direction of the material      12 13
Principle of minimum potential energy      357
Principle of superposition      108 217 224 230
Punch edge      226-228
Pure torsion      52
Quasi-static general solution      200
Quasi-static problem      185
Radial vibration      292 335 338 341 343 344 384
Radius of the contact area      217 231 232
Real part      350 351 354
Rectangular plate      24 247 248 256 258 265 266 381
Resultant force      100 160 218 230 233
Rigid-body rotation      336 342
Rigid-body translation      336 343 350 352 361
Rigidly slipping condition      256 280 285 302 309
Rotary vibration      334 383
Rotatory inertia      344 383
Second class of vibration      255 274 275 341 343 349 350 370
Secondary variables      33 36
Sectorial annular plate      381
Seismic wave      325
Semi-inverse method      25 30 216
Separation formulae      190 268 365 385
Separation of variables      316 345 348 387 388
Shear deformation      344 357 383
Shear layer      357 358
shear modulus      21 359
Shear shell theory      307 319
Sine functions      251 268
Six-mode shell theory      344-345
Small deformation      1 224
Smooth contact      79 83 84 89 92 133 256
Solid harmonics      391
Solid-inclusion interface      93
Solution matrix      127 128
Special solutions      43 65 67
Specific heat      190
Spheres      147 213 255 352 361 378 383-385
Spherical anisotropy      15 364
Spherical Bessel function      329 345 396
Spherical Bessel's equation      389
Spherical cavity      99 101 102
Spherical coordinate system      1 4 27 68 101 227
Spherical coordinates      2 5 7 15 19 21 26 32 327 345 364 387 388 396
Spherical Hankel function      345 350
Spherical harmonics      166 202 366 390 391
Spherical inclusion      98 383
Spherical isotropy      67
Spherical shells      327 356 383-385
Spherical surface      16 330 360 366 370
Spherical symmetry      336 361
Spherically concave half-space      214
Spherically isotropic bodies      62
Spherically isotropic material      19 29 71 99 199 327 333 336 364 374
Spherically isotropic spherical shell      327 338 356 383 385
Spherically orthotropic material      15 19
Spherically symmetric problem      102
Stability      247 249 256 266 275 381
State equation      268 310 313 367 385
state variables      33 268 270 273 274 279 369
State-space formulation      266 267 274 310 327 364 373 381 385
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