Continuum mechanics for engineers:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
2010
|
| Edition: | 3. ed. |
| Series: | CRC series in computational mechanics and applied analysis
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | 370 S. graph. Darst. |
| ISBN: | 9781420085389 1420085387 |
Staff View
MARC
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| 245 | 1 | 0 | |a Continuum mechanics for engineers |c G. Thomas Mase ; Ronald E. Smelser ; George E. Mase |
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| 650 | 4 | |a Mécanique des milieux continus | |
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| 650 | 4 | |a Mécanique analytique | |
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Record in the Search Index
| _version_ | 1804140731953053696 |
|---|---|
| adam_text | Contents
List of Figures
List of Tables
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
Authors
Nomenclature
1
Continuum Theory
1
1.1
Continuum Mechanics
.............................. 1
1.2
Starting Over
.................................... 2
1.3
Notation
...................................... 3
2
Essential Mathematics
5
2.1
Scalars, Vectors and Cartesian Tensors
..................... 5
2.2
Tensor Algebra in Symbolic Notation
-
Summation Convention
...... 7
2.2.1 Kronecker
Delta
.............................. 9
2.2.2
Permutation Symbol
........................... 10
2.2.3
ε
-
б
Identity
................................ 10
2.2.4
Tensor/Vector Algebra
.......................... 11
2.3
Indiciai
Notation
................................. 16
2.4
Matrices and Determinants
........................... 19
2.5
Transformations of Cartesian Tensors
..................... 25
2.6
Principal Values and Principal Directions
................... 30
2.7
Tensor Fields, Tensor Calculus
......................... 37
2.8
Integral Theorems of Gauss and Stokes
.................... 40
Problems
.......................................... 42
3
Stress Principles
53
3.1
Body and Surface Forces, Mass Density
.................... 53
3.2
Cauchy Stress Principle
............................. 54
3.3
The Stress Tensor
................................. 56
3.4
Force and Moment Equilibrium; Stress Tensor Symmetry
.......... 61
3.5
Stress Transformation Laws
........................... 63
3.6
Principal Stresses; Principal Stress Directions
................. 66
3.7
Maximum and Minimum Stress Values
.................... 71
3.8 Mohr s
Circles for
Stress
............................. 74
3.9
Plane Stress
.................................... 80
3.10
Deviator and Spherical Stress States
...................... 85
3.11
Octahedral Shear Stress
............................. 87
Problems
.......................................... 90
Kinematics of Deformation and Motion
103
4.1
Particles, Configurations, Deformations and Motion
............. 103
4.2
Material and Spatial Coordinates
........................ 104
4.3
Langrangian and Eulerian Descriptions
.................... 108
4.4
The Displacement Field
............................. 110
4.5
The Material Derivative
.............................
Ill
4.6
Deformation Gradients, Finite Strain Tensors
................. 116
4.7
Infinitesimal Deformation Theory
....................... 120
4.8
Compatibility Equations
............................. 128
4.9
Stretch Ratios
................................... 131
4.10
Rotation Tensor, Stretch Tensors
......................... 134
4.11
Velocity Gradient, Rate of Deformation, Vorticity
............... 137
4.12
Material Derivative of Line Elements, Areas, Volumes
............ 143
Problems
.......................................... 147
Fundamental Laws and Equations
167
5.1
Material Derivatives of Line, Surface and Volume Integrals
......... 167
5.2
Conservation of Mass, Continuity Equation
.................. 169
5.3
Linear Momentum Principle, Equations of Motion
.............. 171
5.4
Piola-Kirchhoff Stress Tensors, Lagrangian Equations of Motion
...... 172
5.5
Moment of Momentum (Angular Momentum) Principle
.......... 176
5.6
Law of Conservation of Energy, The Energy Equation
............ 177
5.7
Entropy and the Clausius-Duhem Equation
.................. 179
5.8
The General Balance Law
............................ 182
5.9
Restrictions on Elastic Materials by the Second Law of Thermodynamics
. 186
5.10
Invariance
..................................... 189
5.11
Restrictions on Constitutive Equations from
Invariance
........... 196
5.12
Constitutive Equations
.............................. 198
References
......................................... 201
Problems
.......................................... 202
Linear Elasticity
211
6.1
Elasticity, Hooke s Law, Strain Energy
..................... 211
6.2
Hooke s Law for
Isotropie
Media, Elastic Constants
............. 214
6.3
Elastic Symmetry; Hooke s Law for
Anisotropie
Media
........... 219
6.4 Isotropie
Elastostatics and Elastodynamics, Superposition Principle
. . . 223
6.5
Saint-Venant
Problem
............................... 226
6.5.1
Extension
................................. 227
6.5.2
Torsion
................................... 228
6.5.3
Pure Bending
............................... 234
6.5.4
Flexure
................................... 236
6.6
Plane Elasticity
.................................. 238
6.7
Airy Stress Function
............................... 242
6.8
Linear Thermoelasticity
............................. 252
6.9
Three-Dimensional Elasticity
.......................... 253
Problems.......................................... 260
7
Classical Fluids
271
7.1
Viscous Stress Tensor, Stokesian, and Newtonian Fluids
........... 271
7.2
Basic Equations of Viscous Flow, Navier-Stokes Equations
......... 273
7.3
Specialized Fluids
................................. 275
7.4
Steady Flow, Irrotational Flow, Potential Flow
................ 276
7.5
The Bernoulli Equation, Kelvin s Theorem
.................. 280
Problems
.......................................... 282
8
Nonlinear Elasticity
285
8.1
Molecular Approach to Rubber Elasticity
................... 287
8.2
A Strain Energy Theory for Nonlinear Elasticity
............... 292
8.3
Specific Forms of the Strain Energy
....................... 296
8.4
Exact Solution for an Incompressible, Neo-Hookean Material
....... 297
Bibliography
....................................... 302
Problems
.......................................... 304
9
Linear Viscoelasticity
309
9.1
Viscoelastic Constitutive Equations in Linear Differential Operator Form
. 309
9.2
One-Dimensional Theory, Mechanical Models
................ 311
9.3
Creep and Relaxation
............................... 315
9.4
Superposition Principle, Hereditary Integrals
................. 318
9.5
Harmonic Loadings, Complex Modulus, and Complex Compliance
.... 320
9.6
Three-Dimensional Problems, The Correspondence Principle
....... 324
References
......................................... 330
Problems
.......................................... 331
Appendix A: General Tensors
343
A.I Representation of Vectors in General Bases
.................. 343
A.2 The Dot Product and the Reciprocal Basis
................... 345
A.3 Components of a Tensor
............................. 346
A.4 Determination of the Base Vectors
....................... 348
A.5 Derivatives of Vectors
............................... 350
A.5.1 Time Derivative of a Vector
....................... 350
A.5.2 Covariant Derivative of a Vector
.................... 351
A.6
Christoffel
Symbols
................................ 353
A.6.1 Types of
Christoffel
Symbols
...................... 353
A.6.2 Calculation of the
Christoffel
Symbols
................. 354
A.7 Covariant Derivatives of Tensors
........................ 355
A.8 General Tensor Equations
............................ 356
A.9 General Tensors and Physical Components
.................. 358
References
......................................... 360
Appendix B: Viscoelastic Creep and Relaxation
361
Index
365
CONTINUUM MECHANICS
FOR ENGINEERS
HIRD EDITION
Continuum Mechanics for Engineers, Third Edition remains a favored source for the
introductory background and practical examples needed to make effective use of
continuum mechanics in today s advanced engineering design environment. This
perennial bestseller continues to provide engineering students with a complete, concise
introduction to continuum mechanics that encourages and does not intimidate—and
it also gives professionals an excellent self-study guide to enhance their skills. This
latest edition offers new material relevant for use in emerging engineering areas, such
as micro-mechanics and biomechanics. It continues with numerous worked examples,
end-of-chapter problems, and illustrations, carefully explaining needed mathematics
as required.
The authors have altered the book s notation—a common struggle for many—to make
it more consistent with modern continuum mechanics literature. And, as in the second
edition, this book addresses students need to understand the sophisticated simulation
programs that use nonlinear kinematics and various constitutive relationships. It
presents an introduction to problem-solving using
MATLAB®,
placing emphasis on the
value of this language in enabling users to stay focused on fundamentals.
Offering a wealth of practical information, this volume:
•
Provides a much-needed exploration of a key area in engineering mechanics
Offers a consistent instructional approach, carefully explaining mathematical
concepts as they are first introduced
•
Adds coverage useful in emerging areas such as biomechanics and micro-
mechanics
Includes numerous illustrations, problems, and worked examples that
demonstrate problem-solving steps used in continuum mechanics analysis
Through a mastery of this volume s contents and additional rigorous finite element
training, readers will develop the mechanics foundation necessary to skillfully use
modern advanced design tools.
|
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| id | DE-604.BV035791186 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:39Z |
| institution | BVB |
| isbn | 9781420085389 1420085387 |
| language | English |
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| spelling | Mase, George Thomas Verfasser (DE-588)139139281 aut Continuum mechanics for engineers G. Thomas Mase ; Ronald E. Smelser ; George E. Mase 3. ed. Boca Raton, Fla. [u.a.] CRC Press 2010 370 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier CRC series in computational mechanics and applied analysis Mécanique des milieux continus Élasticité Viscoélasticité Mécanique analytique Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 s DE-604 Smelser, Ronald E. 1942- Sonstige (DE-588)1020862548 oth Mase, George E. 1920-2007 Sonstige (DE-588)139139346 oth Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650519&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650519&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Mase, George Thomas Continuum mechanics for engineers Mécanique des milieux continus Élasticité Viscoélasticité Mécanique analytique Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4032296-8 |
| title | Continuum mechanics for engineers |
| title_auth | Continuum mechanics for engineers |
| title_exact_search | Continuum mechanics for engineers |
| title_full | Continuum mechanics for engineers G. Thomas Mase ; Ronald E. Smelser ; George E. Mase |
| title_fullStr | Continuum mechanics for engineers G. Thomas Mase ; Ronald E. Smelser ; George E. Mase |
| title_full_unstemmed | Continuum mechanics for engineers G. Thomas Mase ; Ronald E. Smelser ; George E. Mase |
| title_short | Continuum mechanics for engineers |
| title_sort | continuum mechanics for engineers |
| topic | Mécanique des milieux continus Élasticité Viscoélasticité Mécanique analytique Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Mécanique des milieux continus Élasticité Viscoélasticité Mécanique analytique Continuum mechanics Kontinuumsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650519&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650519&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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