Principles of continuum mechanics: a study of conservation principles with applications
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | this book is a simplified version of the author's book "An introduction to continuum mechanics with applications" (New York, 2008) |
| Physical Description: | XIII, 230 S. graph. Darst. |
| ISBN: | 9780521513692 |
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| adam_text | PRINCIPLES OF CONTINUUM MECHANICS
A Study of Conservation Principles with Applications
As most modern technologies are no longer discipline-specific but involve multidis-
ciplinary approaches, undergraduate engineering students should be introduced to
the principles of mechanics so that they have a strong background in the basic prin¬
ciples 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 engineers and 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.
Contents
Preface
page
xi
1
Introduction
_________________________________________________1
1.1
Continuum mechanics
1
1.2
Objective of the study
7
1.3
Summary
8
2
Vectors and Tensors
_____________________________________ 10
2.1
Motivation
10
2.2
Definition of a vector
10
2.3
Vector algebra
11
2.3.1
Unit vector
11
2.3.2
Zero vector
12
2.3.3
Vector addition
12
2.3.4
Multiplication of a vector by a scalar
14
2.3.5
Scalar product of vectors
14
2.3.6
Vector product
15
2.3.7
Triple products of vectors
18
2.3.8
Plane area as a vector
20
2.3.9
Componentsofa
vector
22
2.4
Index notation and summation convention
24
2.4.1
Summation convention
24
2.4.2
Dummy index
25
2.4.3
Free index
25
2.4.4 Kronecker
delta and permutation symbols
26
2.4.5
Transformation law for different bases
29
2.5
Theory of matrices
31
2.5.1
Definition
31
2.5.2
Matrix addition and multiplication of a matrix by a scalar
32
2.5.3
Matrix transpose and symmetric and skew symmetric matrices
33
2.5.4
Matrix multiplication
34
2.5.5
Inverse and determinant of a matrix
36
vii
Contents
2.6
Vector
calculus
39
2.6.1
The del operator
39
2.6.2
Divergence and curl of a vector
41
2.6.3
Cylindrical and spherical coordinate systems
43
2.6.4
Gradient, divergence, and curl theorems
45
2.7
Tensors
46
2.7.1
Dyads
46
2.7.2
Nonion form of a dyad
48
2.7.3
Transformation of components of a dyad
49
2.7.4
Tensor calculus
49
2.8
Summary
51
Problems
51
3
Kinematics of a Continuum
______________________ 55
3.1
Deformation and configuration
55
3.2
Engineering strains
56
3.2.1
Normal strain
56
3.2.2
Shear strain
57
3.3
General kinematics of a solid continuum
61
3.3.1
Configurations of a continuous medium
61
3.3.2
Material and spatial descriptions
62
3.3.3
Displacement field
65
3.4
Analysis of deformation
66
3.4.1 *
Deformation gradient tensor
66
3.4.2*
Various types of deformations
69
3.4.2.1
Pure dilatation
70
3.4.2.2
Simple extension
70
3.4.2.3
Simple shear
71
3.4.2.4
Nonhomogeneous deformation
71
3.4.3
Green strain tensor
72
3.4.4
Infinitesimal strain tensor
77
3.4.5
Principal values and principal planes of strains
79
3.5
Rate of deformation and vorticity tensors
81
3.5.1
Velocity gradient tensor
81
3.5.2
Rate of deformation tensor
81
3.5.3
Vorticity tensor and vorticity vector
82
3.6
Compatibility equations
84
3.7
Summary
86
Problems
87
4
Stress Vector and Stress Tensor
__________________________________93
4.1
Introduction
93
4.2
Stress vector, stress tensor, and Cauchy s formula
94
4.3
Transformations of stress components and principal stresses
102
4.3.1 Transformation
of stress
components
102
4.3.2
Principal
stresses and principal planes
104
4.4
Summary
107
Problems
107
5
Conservation of Mass, Momentum, and Energy
____________________
щ
5.1
Introduction 111
5.2
Conservation of mass
112
5.2.1
Preliminary discussion
Π
2
5.2.2
Conservation of mass in spatial description
112
5.2.3
Conservation of mass in material description
1 17
5.2.4
Reynolds transport theorem
119
5.3
Conservation of momenta
119
5.3.1
Principle of conservation of linear momentum
119
5.3.2
Principle of conservation of angular momentum
134
5.4
Thermodynamic principles
136
5.4.1
Introduction
136
5.4.2
Energy equation for one-dimensional flows
136
5.4.3
Energy equation for a three-dimensional continuum
140
5.5
Summary
142
Problems
143
β
Constitutive Equations
________________________________________149
6.1
Introduction
149
6.2
Elastic solids
150
6.2.1
Introduction
150
6.2.2
Generalized Hooke s law for orthotropic materials
151
6.2.3
Generalized Hooke s law for
isotropie
materials
153
6.3
Constitutive equations for fluids
156
6.3.1
Introduction
156
6.3.2
Ideal fluids
157
6.3.3
Viscous incompressible fluids
157
6.4
Heat transfer
158
6.4.1
General introduction
158
6.4.2
Fourier s heat conduction law
158
6.4.3
Newton s law of cooling
159
6.4.4
Stefan-Boltzmann law
159
6.5
Summary
160
Problems
160
7
Applications in Heat Transfer, Fluid Mechanics, and Solid Mechanics
162
7.1
Introduction
162
7.2
Heat transfer
162
7.2.1
Governing equations
162
Contents
7.2.2
Analytical
solutions
of one-dimensional heat
transfer
165
7.2.2.1
Steady-state heat transfer in a cooling fin
165
7.2.2.2
Steady-state heat transfer in a surface-insulated rod
167
7.2.3
Axisymmetric heat conduction in a circular cylinder
169
7.2.4
Two-dimensional heat transfer
170
7.3
Fluid mechanics
172
7.3.1
Preliminary comments
172
7.3.2
Summary of equations
173
7.3.3
Inviscid fluid statics
174
7.3.4
Parallel flow
(Navier—
Stokes equations)
175
7.3.4.1
Steady flow of viscous incompressible fluid between
parallel plates
176
7.3.4.2
Steady flow of viscous incompressible fluid through a
pipe
177
7.3.5
Diffusion processes
179
7.4
Solid mechanics
182
7.4.1
Governing equations
182
7.4.2
Analysis of bars
184
7.4.3
Analysis of beams
188
7.4.3.1
Principle of superposition
195
7.4.4
Analysis of plane elasticity problems
196
7.4.4.1
Plane strain and plane stress problems
196
7.4.4.2
Plane strain problems
196
7.4.4.3
Plane stress problems
198
7.4.4.4
Solution methods
199
7.4.4.5
Airy stress function
202
7.5
Summary
204
Problems
205
Answers to Selected Problems
215
References and Additional Readings
225
Subject Index
227
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:36:47Z |
| institution | BVB |
| isbn | 9780521513692 |
| language | English |
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| physical | XIII, 230 S. graph. Darst. |
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| spelling | Reddy, Junuthula Narasimha 1945- Verfasser (DE-588)108393232 aut Principles of continuum mechanics a study of conservation principles with applications J.N. Reddy 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2010 XIII, 230 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier this book is a simplified version of the author's book "An introduction to continuum mechanics with applications" (New York, 2008) Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025961551&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025961551&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Reddy, Junuthula Narasimha 1945- Principles of continuum mechanics a study of conservation principles with applications Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4032296-8 |
| title | Principles of continuum mechanics a study of conservation principles with applications |
| title_auth | Principles of continuum mechanics a study of conservation principles with applications |
| title_exact_search | Principles of continuum mechanics a study of conservation principles with applications |
| title_full | Principles of continuum mechanics a study of conservation principles with applications J.N. Reddy |
| title_fullStr | Principles of continuum mechanics a study of conservation principles with applications J.N. Reddy |
| title_full_unstemmed | Principles of continuum mechanics a study of conservation principles with applications J.N. Reddy |
| title_short | Principles of continuum mechanics |
| title_sort | principles of continuum mechanics a study of conservation principles with applications |
| title_sub | a study of conservation principles with applications |
| topic | Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Continuum mechanics Kontinuumsmechanik |
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