Continuum Mechanics for Engineers, Third Edition

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CRC Press, Dec 12, 2010 - Science - 400 pages
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The second edition of this popular text continues to provide a solid, fundamental introduction to the mathematics, laws, and applications of continuum mechanics. With the addition of three new chapters and eight new sections to existing chapters, the authors now provide even better coverage of continuum mechanics basics and focus even more attention on its applications.

Beginning with the basic mathematical tools needed-including matrix methods and the algebra and calculus of Cartesian tensors-the authors develop the principles of stress, strain, and motion and derive the fundamental physical laws relating to continuity, energy, and momentum. With this basis established, they move to their expanded treatment of applications, including linear and nonlinear elasticity, fluids, and linear viscoelasticity

Mastering the contents of Continuum Mechanics: Second Edition provides the reader with the foundation necessary to be a skilled user of today's advanced design tools, such as sophisticated simulation programs that use nonlinear kinematics and a variety of constitutive relationships. With its ample illustrations and exercises, it offers the ideal self-study vehicle for practicing engineers and an excellent introductory text for advanced engineering students.
  

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Contents

Continuum Theory
1
12 Continuum Mechanics
2
Essential Mathematics
3
22 Tensor Algebra in Symbolic Notation Summation Convention
4
23 Indicial Notation
13
24 Matrices and Determinants
16
25 Transformations of Cartesian Tensors
22
26 Principal Values and Principal Directions of Symmetric SecondOrder Tensors
28
56 Moment of Momentum Angular Momentum Principle
181
57 Law of Conservation of Energy The Energy Equation
182
58 Entropy and the ClausiusDuhem Equation
186
59 Restrictions on Elastic Materials by the Second Law of Thermodynamics
190
510 Invariance
194
511 Restrictions on Constitutive Equations from Invariance
204
512 Constitutive Equations
207
References
210

27 Tensor Fields Tensor Calculus
34
28 Integral Theorems of Gauss and Stokes
36
Problems
37
Stress Principles
47
32 Cauchy Stress Principle
48
33 The Stress Tensor
51
34 Force and Moment Equilibrium Stress Tensor Symmetry
57
35 Stress Transformation Laws
59
36 Principal Stresses Principal Stress Directions
62
37 Maximum and Minimum Stress Values
70
38 Mohrs Circles For Stress
73
39 Plane Stress
80
310 Deviator and Spherical Stress States
85
311 Octahedral Shear Stress
87
Problems
89
Kinematics of Deformation and Motion
103
42 Material and Spatial Coordinates
104
43 Lagrangian and Eulerian Descriptions
109
44 The Displacement Field
111
45 The Material Derivative
113
46 Deformation Gradients Finite Strain Tensors
116
47 Infinitesimal Deformation Theory
122
48 Stretch Ratios
131
49 Rotation Tensor Stretch Tensors
136
410 Velocity Gradient Rate of Deformation Vorticity
140
411 Material Derivative of Line Elements Areas Volumes
146
Problems
149
Fundamental Laws and Equations
169
52 Material Derivatives of Line Surface and Volume Integrals
170
53 Conservation of Mass Continuity Equation
172
54 Linear Momentum Principle Equations of Motion
175
55 The PiolaKirchhoff Stress Tensors Lagrangian Equations of Motion
176
Linear Elasticity
219
62 Hookes Law for Isotropic Media Elastic Constants
224
63 Elastic Symmetry Hookes Law for Anisotropic Media
230
64 Isotropic Elastostatics and Elastodynamics Superposition Principle
235
65 Plane Elasticity
238
66 Linear Thermoelasticity
242
67 Airy Stress Function
244
68 Torsion
256
69 ThreeDimensional Elasticity
264
Problems
273
Classical Fluids
285
72 Basic Equations of Viscous Flow NavierStokes Equations
288
73 Specialized Fluids
290
74 Steady Flow Irrotational Flow Potential Flow
291
75 The Bernoulli Equation Kelvins Theorem
295
Problems
296
Nonlinear Elasticity
301
82 A Strain Energy Theory for Nonlinear Elasticity
309
83 Specific Forms of the Strain Energy
314
84 Exact Solution for an Incompressible NeoHookean Material
316
References
324
Linear Viscoelasticity
329
92 Viscoelastic Constitutive Equations in Linear Differential Operator Form
330
93 OneDimensional Theory Mechanical Models
332
94 Creep and Relaxation
336
95 Superposition Principle Hereditary Integrals
342
96 Harmonic Loadings Complex Modulus and Complex Compliance
344
97 ThreeDimensional Problems The Correspondence Principle
350
References
357
Problems
358
Index
373
Copyright

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