Principles of Continuum Mechanics: A Study of Conservation Principles with Applications

by J. N. Reddy

• ISBN13: 9780521513692
• ISBN10: 0521513693
• Edition: 1st
• Format: Hardcover
• Copyright: 2010-06-28
• Publisher: Cambridge University Press
• More Book Details
• Purchase Benefits

Summary

As most modern technologies are no longer discipline-specific but involve multidisciplinary approaches, undergraduate engineering students should be introduced to the principles of mechanics so that they have a strong background in the basic principles common to all disciplines and are able to work at the interface of science and engineering disciplines. This textbook is designed for a first course on principles of mechanics and provides an introduction to the basic concepts of stress and strain and conservation principles. It prepares engineer-scientists for advanced courses in traditional as well as emerging fields such as biotechnology, nanotechnology, energy systems, and computational mechanics. This simple book presents the subjects of mechanics of materials, fluid mechanics, and heat transfer in a unified form using the conservation principles of mechanics.

Author Biography

J. N. Reddy is a Distinguished Professor and holder of the Oscar S. Wyatt Endowed Chair in the Department of Mechanical Engineering at Texas AM University (http://www.tamu.edu/acml).

Table of Contents

Preface	p. xi
Introduction	p. 1
Continuum mechanics	p. 1
Objective of the study	p. 7
Summary	p. 8
Vectors and Tensors	p. 10
Motivation	p. 10
Definition of a vector	p. 10
Vector algebra	p. 11
Unit vector	p. 11
Zero vector	p. 12
Vector addition	p. 12
Multiplication of a vector by a scalar	p. 14
Scalar product of vectors	p. 14
Vector product	p. 15
Triple products of vectors	p. 18
Plane area as a vector	p. 20
Components of a vector	p. 22
Index notation and summation convention	p. 24
Summation convention	p. 24
Dummy index	p. 25
Free index	p. 25
Kronecker delta and permutation symbols	p. 26
Transformation law for different bases	p. 29
Theory of matrices	p. 31
Definition	p. 31
Matrix addition and multiplication of a matrix by a scalar	p. 32
Matrix transpose and symmetric and skew symmetric matrices	p. 33
Matrix multiplication	p. 34
Inverse and determinant of a matrix	p. 36
Vector calculus	p. 39
The del operator	p. 39
Divergence and curl of a vector	p. 41
Cylindrical and spherical coordinate systems	p. 43
Gradient, divergence, and curl theorems	p. 45
Tensors	p. 46
Dyads	p. 46
Nonion form of a dyad	p. 48
Transformation of components of a dyad	p. 49
Tensor calculus	p. 49
Summary	p. 51
Problems	p. 51
Kinematics of a Continuum	p. 55
Deformation and configuration	p. 55
Engineering strains	p. 56
Normal strain	p. 56
Shear strain	p. 57
General kinematics of a solid continuum	p. 61
Configurations of a continuous medium	p. 61
Material and spatial descriptions	p. 62
Displacement field	p. 65
Analysis of deformation	p. 66
Deformation gradient tensor	p. 66
Various types of deformations	p. 69
Pure dilatation	p. 70
Simple extension	p. 70
Simple shear	p. 71
Nonhomogeneous deformation	p. 71
Green strain tensor	p. 72
Infinitesimal strain tensor	p. 77
Principal values and principal planes of strains	p. 79
Rate of deformation and vorticity tensors	p. 81
Velocity gradient tensor	p. 81
Rate of deformation tensor	p. 81
Vorticity tensor and vorticity vector	p. 82
Compatibility equations	p. 84
Summary	p. 86
Problems	p. 87
Stress Vector and Stress Tensor	p. 93
Introduction	p. 93
Stress vector, stress tensor, and Cauchy's formula	p. 94
Transformations of stress components and principal stresses	p. 102
Transformation of stress components	p. 102
Principal stresses and principal planes	p. 104
Summary	p. 107
Problems	p. 107
Conservation of Mass, Momentum, and Energy	p. 111
Introduction	p. 111
Conservation of mass	p. 112
Preliminary discussion	p. 112
Conservation of mass in spatial description	p. 112
Conservation of mass in material description	p. 117
Reynolds transport theorem	p. 119
Conservation of momenta	p. 119
Principle of conservation of linear momentum	p. 119
Principle of conservation of angular momentum	p. 134
Thermodynamic principles	p. 136
Introduction	p. 136
Energy equation for one-dimensional flows	p. 136
Energy equation for a three-dimensional continuum	p. 140
Summary	p. 142
Problems	p. 143
Constitutive Equations	p. 149
Introduction	p. 149
Elastic solids	p. 150
Introduction	p. 150
Generalized Hooke's law for orthotropic materials	p. 151
Generalized Hooke's law for isotropic materials	p. 153
Constitutive equations for fluids	p. 156
Introduction	p. 156
Ideal fluids	p. 157
Viscous incompressible fluids	p. 157
Heat transfer	p. 158
General introduction	p. 158
Fourier's heat conduction law	p. 158
Newton's law of cooling	p. 159
Stefan-Boltzmann law	p. 159
Summary	p. 160
Problems	p. 160
Applications in Heat Transfer, Fluid Mechanics, and Solid Mechanics	p. 162
Introduction	p. 162
Heat transfer	p. 162
Governing equations	p. 162
Analytical solutions of one-dimensional heat transfer	p. 165
Steady-state heat transfer in a cooling fin	p. 165
Steady-state heat transfer in a surface-insulated rod	p. 167
Axisymmetric heat conduction in a circular cylinder	p. 169
Two-dimensional heat transfer	p. 170
Fluid mechanics	p. 172
Preliminary comments	p. 172
Summary of equations	p. 173
Inviscid fluid statics	p. 174
Parallel flow (Navier-Stokes equations)	p. 175
Steady flow of viscous incompressible fluid between parallel plates	p. 176
Steady flow of viscous incompressible fluid through a pipe	p. 177
Diffusion processes	p. 179
Solid mechanics	p. 182
Governing equations	p. 182
Analysis of bars	p. 184
Analysis of beams	p. 188
Principle of superposition	p. 195
Analysis of plane elasticity problems	p. 196
Plane strain and plane stress problems	p. 196
Plane strain problems	p. 196
Plane stress problems	p. 198
Solution methods	p. 199
Airy stress function	p. 202
Summary	p. 204
Problems	p. 205
Answers to Selected Problems	p. 215
References and Additional Readings	p. 225
Subject Index	p. 227
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