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9780521671095

Applied Solid Mechanics

by
  • ISBN13:

    9780521671095

  • ISBN10:

    0521671094

  • Edition: 1st
  • Format: Paperback
  • Copyright: 2009-01-12
  • Publisher: Cambridge University Press

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Summary

The world around us, natural or man-made, is built and held together by solid materials. Understanding their behaviour is the task of solid mechanics, which is in turn applied to many areas, from earthquake mechanics to industry, construction to biomechanics. The variety of materials (metals, rocks, glasses, sand, flesh and bone) and their properties (porosity, viscosity, elasticity, plasticity) is reflected by the concepts and techniques needed to understand them: a rich mixture of mathematics, physics and experiment. These are all combined in this unique book, based on years of experience in research and teaching. Starting from the simplest situations, models of increasing sophistication are derived and applied. The emphasis is on problem-solving and building intuition, rather than a technical presentation of theory. The text is complemented by over 100 carefully-chosen exercises, making this an ideal companion for students taking advanced courses, or those undertaking research in this or related disciplines.

Table of Contents

List of illustrationsp. viii
Prologuep. xiii
Modelling solidsp. 1
Introductionp. 1
Hooke's lawp. 2
Lagrangian and Eulerian coordinatesp. 3
Strainp. 4
Stressp. 7
Conservation of momentump. 10
Linear elasticityp. 11
The incompressibility approximationp. 13
Energyp. 14
Boundary conditions and well-posednessp. 16
Coordinate systemsp. 19
Exercisesp. 24
Linear elastostaticsp. 28
Introductionp. 28
Linear displacementsp. 29
Antiplane strainp. 37
Torsionp. 39
Multiply-connected domainsp. 42
Plane strainp. 47
Compatibilityp. 68
Generalised stress functionsp. 70
Singular solutions in elastostaticsp. 82
Concluding remarkp. 93
Exercisesp. 93
Linear elastodynamicsp. 103
Introductionp. 103
Normal modes and plane wavesp. 104
Dynamic stress functionsp. 121
Waves in cylinders and spheresp. 124
Initial-value problemsp. 132
Moving singularitiesp. 138
Concluding remarksp. 143
Exercisesp. 143
Approximate theoriesp. 150
Introductionp. 150
Longitudinal displacement of a barp. 151
Transverse displacements of a stringp. 152
Transverse displacements of a beamp. 153
Linear rod theoryp. 158
Linear plate theoryp. 162
Von Karman plate theoryp. 172
Weakly curved shell theoryp. 177
Nonlinear beam theoryp. 187
Nonlinear rod theoryp. 195
Geometrically nonlinear wave propagationp. 198
Concluding remarksp. 204
Exercisesp. 205
Nonlinear elasticityp. 215
Introductionp. 215
Stress and strain revisitedp. 216
The constitutive relationp. 221
Examplesp. 233
Concluding remarksp. 239
Exercisesp. 239
Asymptotic analysisp. 245
Introductionp. 245
Antiplane strain in a thin platep. 246
The linear plate equationp. 248
Boundary conditions and Saint-Venant's principlep. 253
The von Karman plate equationsp. 261
The Euler-Bernoulli plate equationsp. 267
The linear rod equationsp. 273
Linear shell theoryp. 278
Concluding remarksp. 282
Exercisesp. 283
Fracture and contactp. 287
Introductionp. 287
Static brittle fracturep. 288
Contactp. 309
Concluding remarksp. 320
Exercisesp. 321
Plasticityp. 328
Introductionp. 328
Models for granular materialp. 330
Dislocation theoryp. 337
Perfect plasticity theory for metalsp. 344
Kinematicsp. 358
Conservation of momentump. 360
Conservation of energyp. 360
The flow rulep. 362
Simultaneous elasticity and plasticityp. 364
Examplesp. 365
Concluding remarksp. 370
Exercisesp. 372
More general theoriesp. 378
Introductionp. 378
Viscoelasticityp. 379
Thermoelasticityp. 388
Composite materials and homogenisationp. 391
Poroelasticityp. 408
Anisotropyp. 413
Concluding remarksp. 417
Exercisesp. 417
Epiloguep. 426
Orthogonal curvilinear coordinatesp. 428
Referencesp. 440
Indexp. 442
Table of Contents provided by Ingram. All Rights Reserved.

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