Applied Solid Mechanics

by Peter Howell , Gregory Kozyreff , John Ockendon

• ISBN13: 9780521671095
• ISBN10: 0521671094
• Edition: 1st
• Format: Paperback
• Copyright: 2009-01-12
• Publisher: Cambridge University Press

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 illustrations	p. viii
Prologue	p. xiii
Modelling solids	p. 1
Introduction	p. 1
Hooke's law	p. 2
Lagrangian and Eulerian coordinates	p. 3
Strain	p. 4
Stress	p. 7
Conservation of momentum	p. 10
Linear elasticity	p. 11
The incompressibility approximation	p. 13
Energy	p. 14
Boundary conditions and well-posedness	p. 16
Coordinate systems	p. 19
Exercises	p. 24
Linear elastostatics	p. 28
Introduction	p. 28
Linear displacements	p. 29
Antiplane strain	p. 37
Torsion	p. 39
Multiply-connected domains	p. 42
Plane strain	p. 47
Compatibility	p. 68
Generalised stress functions	p. 70
Singular solutions in elastostatics	p. 82
Concluding remark	p. 93
Exercises	p. 93
Linear elastodynamics	p. 103
Introduction	p. 103
Normal modes and plane waves	p. 104
Dynamic stress functions	p. 121
Waves in cylinders and spheres	p. 124
Initial-value problems	p. 132
Moving singularities	p. 138
Concluding remarks	p. 143
Exercises	p. 143
Approximate theories	p. 150
Introduction	p. 150
Longitudinal displacement of a bar	p. 151
Transverse displacements of a string	p. 152
Transverse displacements of a beam	p. 153
Linear rod theory	p. 158
Linear plate theory	p. 162
Von Karman plate theory	p. 172
Weakly curved shell theory	p. 177
Nonlinear beam theory	p. 187
Nonlinear rod theory	p. 195
Geometrically nonlinear wave propagation	p. 198
Concluding remarks	p. 204
Exercises	p. 205
Nonlinear elasticity	p. 215
Introduction	p. 215
Stress and strain revisited	p. 216
The constitutive relation	p. 221
Examples	p. 233
Concluding remarks	p. 239
Exercises	p. 239
Asymptotic analysis	p. 245
Introduction	p. 245
Antiplane strain in a thin plate	p. 246
The linear plate equation	p. 248
Boundary conditions and Saint-Venant's principle	p. 253
The von Karman plate equations	p. 261
The Euler-Bernoulli plate equations	p. 267
The linear rod equations	p. 273
Linear shell theory	p. 278
Concluding remarks	p. 282
Exercises	p. 283
Fracture and contact	p. 287
Introduction	p. 287
Static brittle fracture	p. 288
Contact	p. 309
Concluding remarks	p. 320
Exercises	p. 321
Plasticity	p. 328
Introduction	p. 328
Models for granular material	p. 330
Dislocation theory	p. 337
Perfect plasticity theory for metals	p. 344
Kinematics	p. 358
Conservation of momentum	p. 360
Conservation of energy	p. 360
The flow rule	p. 362
Simultaneous elasticity and plasticity	p. 364
Examples	p. 365
Concluding remarks	p. 370
Exercises	p. 372
More general theories	p. 378
Introduction	p. 378
Viscoelasticity	p. 379
Thermoelasticity	p. 388
Composite materials and homogenisation	p. 391
Poroelasticity	p. 408
Anisotropy	p. 413
Concluding remarks	p. 417
Exercises	p. 417
Epilogue	p. 426
Orthogonal curvilinear coordinates	p. 428
References	p. 440
Index	p. 442
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