Elasticity in engineering mechanics:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2011
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| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben Includes bibliographical references and index |
| Physical Description: | XVIII, 638 S. graph. Darst. |
| ISBN: | 9780470402559 9780470880364 |
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| 245 | 1 | 0 | |a Elasticity in engineering mechanics |c Arthur P. Boresi and Ken P. Chong and James D. Lee |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2011 | |
| 300 | |a XVIII, 638 S. |b graph. Darst. | ||
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| 500 | |a Literaturangaben | ||
| 500 | |a Includes bibliographical references and index | ||
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| 650 | 4 | |a Strength of materials | |
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Record in the Search Index
| _version_ | 1804145776003121152 |
|---|---|
| adam_text | Titel: Elasticity in engineering mechanics
Autor: Boresi, Arthur P.
Jahr: 2011
CONTENTS
Preface xvii
CHAPTER 1 INTRODUCTORY CONCEPTS AND MATHEMATICS 1
Part I Introduction
1-1 Trends and Scopes
1-2 Theory of Elasticity
1-3 Numerical Stress Analysis
1-4 General Solution of the Elasticity
Problem
1-5 Experimental Stress Analysis
1-6 Boundary Value Problems of Elasticity
Part Il Preliminary Concepts
1-7 Brief Summary of Vector Algebra
1-8 Scalar Point Functions
1-9 Vector Fields
1-10 Differentiation of Vectors
1-11 Differentiation of a Scalar Field
1-12 Differentiation of a Vector Field
1-13 Curl of a Vector Field
1-14 Eulerian Continuity Equation for Fluids
1
7
9
9
10
11
12
16
18
19
21
21
22
22
Vl CONTENTS
1-15 Divergence Theorem 25
1-16 Divergence Theorem in Two
Dimensions 27
1-17 Line and Surface Integrals (Application of
Scalar Product) 28
1-18 Stokes s Theorem 29
1-19 Exact Differential 30
1-20 Orthogonal Curvilinear Coordiantes in
Three-Dimensional Space 31
1-21 Expression for Differential Length in
Orthogonal Curvilinear Coordinates 32
1-22 Gradient and Laplacian in Orthogonal
Curvilinear Coordinates 33
Part III Elements of Tensor Algebra 36
1-23 Index Notation: Summation Convention 36
1-24 Transformation of Tensors under Rotation
of Rectangular Cartesian Coordinate
System 40
1-25 Symmetric and Antisymmetric Parts of a
Tensor 46
1-26 Symbols Sy and ?p (the Kronecker Delta
and the Alternating Tensor) 47
1-27 Homogeneous Quadratic Forms 49
1-28 Elementary Matrix Algebra 52
1-29 Some Topics in the Calculus of
Variations 56
References 60
Bibliography 63
CHAPTER 2 THEORY OF DEFORMATION 65
2-1 Deformable, Continuous Media 65
2-2 Rigid-Body Displacements 66
2-3 Deformation of a Continuous Region.
Material Variables. Spatial Variables 68
2-4 Restrictions on Continuous Deformation
of a Deformable Medium 71
Problem Set 2-4 75
2-5 Gradient of the Displacement Vector.
Tensor Quantity 76
CONTENTS
VII
2-6
Extension of an Infinitesimal Line Element 78
Problem Set 2-6 85
Physical Significance of eii. Strain
Definitions 86
Final Direction of Line Element.
Definition of Shearing Strain. Physical
Significance of e,y(/ f j) 89
Problem Set 2-8 94
Tensor Character of eaß. Strain Tensor 94
Reciprocal Ellipsoid. Principal Strains.
Strain Invariants 96
Determination of Principal Strains.
Principal Axes 100
Problem Set 2-11 106
Determination of Strain Invariants.
Volumetric Strain 108
Rotation of a Volume Element. Relation to
Displacement Gradients 113
Problem Set 2-13 116
Homogeneous Deformation 118
Theory of Small Strains and Small Angles
of Rotation 121
Problem Set 2-15 130
2-16 Compatibility Conditions of the Classical
Theory of Small Displacements 132
Problem Set 2-16 137
Additional Conditions Imposed by
Continuity 138
Kinematics of Deformable Media 140
Problem Set 2-18 146
2-7
2-8
2-9
2-10
2-11
2-12
2-13
14
15
2-17
2-18
Appendix 2A Strain-Displacement Relations in Orthogonal
Curvilinear Coordinates 146
2A-1 Geometrical Preliminaries 146
2A-2 Strain-Displacement Relations 148
Appendix 2B Derivation of Strain-Displacement Relations for
Special Coordinates by Cartesian Methods 151
2B-1 Cylindrical Coordinates 151
2B-2 Oblique Straight-Line Coordinates 153
VIII
CONTENTS
Appendix 2C Strain-Displacement Relations in General
Coordinates
2C-1 Euclidean Metric Tensor
2C-2 Strain Tensors
References
Bibliography
CHAPTER 3 THEORY OF STRESS
3-1
3-2
3-3
3-4
3-5
3-6
3-7
3-8
Definition of Stress
Stress Notation
Summation of Moments. Stress at a Point.
Stress on an Oblique Plane
Problem Set 3-3
Tensor Character of Stress. Transformation
of Stress Components under Rotation of
Coordinate Axes
Problem Set 3-4
Principal Stresses. Stress Invariants.
Extreme Values
Problem Set 3-5
Mean and Deviator Stress Tensors.
Octahedral Stress
Problem Set 3-6
Approximations of Plane Stress. Mohr s
Circles in Two and Three Dimensions
Problem Set 3-7
Differential Equations of Motion of a
Deformable Body Relative to Spatial
Coordinates
Problem Set 3-8
155
155
157
159
160
161
161
164
166
171
175
179
179
183
184
189
193
200
201
205
Appendix 3A Differential Equations of Equilibrium in Curvilinear
Spatial Coordinates
3A
207
1 Differential Equations of Equilibrium in
Orthogonal Curvilinear Spatial
Coordinates 207
3A-2 Specialization of Equations of Equilibrium 208
3A-3 Differential Equations of Equilibrium in
General Spatial Coordinates 210
CONTENTS
IX
Appendix 3B Equations of Equilibrium Including Couple Stress
and Body Couple 211
Appendix 3C Reduction of Differential Equations of Motion for
Small-Displacement Theory 214
3C-1 Material Derivative. Material Derivative
of a Volume Integral 214
3C-2 Differential Equations of Equilibrium
Relative to Material Coordinates 218
References 224
Bibliography 225
CHAPTER 4 THREE-DIMENSIONAL EQUATIONS OF
ELASTICITY 226
4-1
4-2
4-3
4-4
4-5
4-6
4-7
4-8
4-9
4-10
4-11
4-12
4-13
Elastic and Nonelastic Response of a Solid 226
Intrinsic Energy Density Function
(Adiabatic Process) 230
Relation of Stress Components to Strain
Energy Density Function 232
Problem Set 4-3 240
Generalized Hooke s Law 241
Problem Set 4-4 255
Isotropic Media. Homogeneous Media 255
Strain Energy Density for Elastic Isotropic
Medium 256
Problem Set 4-6 262
Special States of Stress 266
Problem Set 4-7 268
Equations of Thermoelasticity 269
Differential Equation of Heat Conduction 270
Elementary Approach to Thermal-Stress
Problem in One and Two Variables 272
Problem 276
Stress-Strain-Temperature Relations 276
Problem Set 4-11 283
Thermoelastic Equations in Terms of
Displacement 285
Spherically Symmetrical Stress
Distribution (The Sphere) 294
Problem Set 4-13 299
CONTENTS
4-14
4-15
4-16
4-17
4-18
4-19
4-20
4-21
4-22
4-23
Thermoelastic Compatibility Equations in
Terms of Components of Stress and
Temperature. Beltrami-Michell
Relations
Problem Set 4-14
Boundary Conditions
Problem Set 4-15
Uniqueness Theorem for Equilibrium
Problem of Elasticity
Equations of Elasticity in Terms of
Displacement Components
Problem Set 4-17
Elementary Three-Dimensional Problems
of Elasticity. Semi-Inverse Method
Problem Set 4-18
Torsion of Shaft with Constant Circular
Cross Section
Problem Set 4-19
Energy Principles in Elasticity
Principle of Virtual Work
Problem Set 4-21
Principle of Virtual Stress (Castigliano s
Theorem)
Mixed Virtual Stress-Virtual Strain
Principles (Reissner s Theorem)
Appendix 4A Application of the Principle of Virtual Work to a
Deformable Medium (Navier-Stokes Equations)
Appendix 4B Nonlinear Constitutive Relationships
4B-1 Variable Stress-Strain Coefficients
4B-2 Higher-Order Relations
4B-3 Hypoelastic Formulations
4B-4 Summary
Appendix 4C Micromorphic Theory
4C-1 Introduction
4C-2 Balance Laws of Micromorphic Theory
4C-3 Constitutive Equations of Micromorphic
Elastic Solid
299
304
305
310
311
314
316
317
323
327
331
332
333
338
339
342
343
345
346
346
346
347
347
347
350
351
CONTENTS
Xl
Appendix 4D Atomistic Field Theory
4D-1 Introduction
4D-2 Phase-Space and Physical-Space
Descriptions
4D-3 Definitions of Atomistic Quantities in
Physical Space
4D-4 Conservation Equations
References
Bibliography
CHAPTER 5 PLANE THEORY OF ELASTICITY IN
RECTANGULAR CARTESIAN COORDINATES
5-1 Plane Strain
Problem Set 5-1
5-2 Generalized Plane Stress
Problem Set 5-2
5-3 Compatibility Equation in Terms of Stress
Components
Problem Set 5-3
5-4 Airy Stress Function
Problem Set 5-4
5-5 Airy Stress Function in Terms of
Harmonic Functions
5-6 Displacement Components for Plane
Elasticity
Problem Set 5-6
5-7 Polynomial Solutions of Two-Dimensional
Problems in Rectangular Cartesian
Coordinates
Problem Set 5-7
5-8 Plane Elasticity in Terms of Displacement
Components
Problem Set 5-8
5-9 Plane Elasticity Relative to Oblique
Coordinate Axes
Appendix 5A Plane Elasticity with Couple Stresses
5A-1 Introduction
5A-2 Equations of Equilibrium
352
353
353
355
357
359
364
365
365
370
371
376
377
382
383
392
399
401
404
408
411
415
416
416
420
420
421
XII
CONTENTS
5A-3 Deformation in Couple Stress Theory 421
5A-4 Equations of Compatibility 425
5A-5 Stress Functions for Plane Problems with
Couple Stresses 426
Appendix 5B Plane Theory of Elasticity in Terms of Complex
Variables
5B-1 Airy Stress Function in Terms of Analytic
Functions ø(z) and x(z)
5B-2 Displacement Components in Terms of
Analytic Functions ø(z) and x(z)
5B-3 Stress Components in Terms of ø(æ) and
X(z)
5B-4 Expressions for Resultant Force and
Resultant Moment
5B-5 Mathematical Form of Functions ø (æ) and
X(z)
5B-6 Plane Elasticity Boundary Value Problems
in Complex Form
5B-7 Note on Conformal Transformation
Problem Set 5B-7
5B-8 Plane Elasticity Formulas in Terms of
Curvilinear Coordinates
5B-9 Complex Variable Solution for Plane
Region Bounded by Circle in the
æ Plane
Problem Set 5B
References
Bibliography
CHAPTER 6 PLANE ELASTICITY IN POLAR COORDINATES
6-1 Equilibrium Equations in Polar
Coordinates
6-2 Stress Components in Terms of Airy
Stress Function F = F(r,0)
6-3 Strain-Displacement Relations in Polar
Coordinates
Problem Set 6-3
6-4 Stress-Strain-Temperature Relations
Problem Set 6-4
428
428
429
430
433
434
438
440
445
445
448
452
453
454
455
455
456
457
460
461
462
6-5
6-6
6-7
6-8
6-9
6-10
6-11
CONTENTS XlIl
Compatibility Equation for Plane Elasticity in Terms of Polar Coordinates 463
Problem Set 6-5 464
Axially Symmetric Problems Problem Set 6-6 467 483
Plane Elasticity Equations in Terms of Displacement Components Plane Theory of Thermoelasticity Problem Set 6-8 485 489 492
Disk of Variable Thickness and Nonhomogeneous Anisotropic Material Problem Set 6-9 494 497
Stress Concentration Problem of Circular Hole in Plate 498
Problem Set 6-10 504
Examples Problem Set 6-11 505 510
Appendix 6A Stress-Couple Theory of Stress Concentration
Resulting from Circular Hole in Plate
Appendix 6B Stress Distribution of a Diametrically Compressed
Plane Disk
References
519
522
525
CHAPTER 7 PRISMATIC BAR SUBJECTED TO END LOAD 527
7-1 General Problem of Three-Dimensional
Elastic Bars Subjected to Transverse End
Loads 527
7-2 Torsion of Prismatic Bars. Saint-Venant s
Solution. Warping Function 529
Problem Set 7-2 534
7-3 Prandtl Torsion Function 534
Problem Set 7-3 538
7-4 A Method of Solution of the Torsion
Problem: Elliptic Cross Section 538
Problem Set 7-4 542
7-5 Remarks on Solutions of the Laplace
Equation, V2F=O 542
Problem Set 7-5 544
XIV
CONTENTS
CHAPTER 8
7-6 Torsion of Bars with Tubular Cavities 547
Problem Set 7-6 549
7-7 Transfer of Axis of Twist 549
7-8 Shearing-Stress Component in Any
Direction 550
Problem Set 7-8 554
7-9 Solution of Torsion Problem by the
Prandtl Membrane Analogy 554
Problem Set 7-9 561
7-10 Solution by Method of Series. Rectangular
Section 562
Problem Set 7-10 566
7-11 Bending of a Bar Subjected to Transverse
End Force 569
Problem Set 7-11 577
7-12 Displacement of a Cantilever Beam
Subjected to Transverse End Force 577
Problem Set 7-12 581
7-13 Center of Shear 581
Problem Set 7-13 582
7-14 Bending of a Bar with Elliptic Cross
Section 584
7-15 Bending of a Bar with Rectangular Cross
Section 586
Problem Set 7-15 590
Review Problems 590
Analysis of Tapered Beams 591
References 595
GENERAL SOLUTIONS OF ELASTICITY 597
8-1 Introduction 597
Problem Set 8-1 598
8-2 Equilibrium Equations 598
Problem Set 8-2 600
8-3 The Helmholtz Transformation 600
Problem Set 8-3 601
8-4 The Galerkin (Papkovich) Vector 602
Problem Set 8-4 603
CONTENTS XV
8-5 Stress in Terms of the Galerkin Vector F 603
Problem Set 8-5 604
8-6 The Galerkin Vector: A Solution of the
Equilibrium Equations of Elasticity 604
Problem Set 8-6 606
8-7 The Galerkin Vector kZ and Love s Strain
Function for Solids of Revolution 606
Problem Set 8-7 608
8-8 Kelvin s Problem: Single Force Applied in
the Interior of an Infinitely Extended Solid 609
Problem Set 8-8 610
8-9 The Twinned Gradient and Its Application
to Determine the Effects of a Change of
Poisson s Ratio 611
8-10 Solutions of the Boussinesq and Cerruti
Problems by the Twinned Gradient
Method 614
Problem Set 8-10 617
8-11 Additional Remarks on
Three-Dimensional Stress Functions 617
References 618
Bibliography 619
INDEX 621
|
| any_adam_object | 1 |
| author | Boresi, Arthur P. 1924- Chong, Ken P. Lee, James D. |
| author_GND | (DE-588)143690604 |
| author_facet | Boresi, Arthur P. 1924- Chong, Ken P. Lee, James D. |
| author_role | aut aut aut |
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| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | UF 3000 |
| ctrlnum | (OCoLC)731699781 (DE-599)BVBBV037468480 |
| dewey-full | 620.1/1232 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.1/1232 |
| dewey-search | 620.1/1232 |
| dewey-sort | 3620.1 41232 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV037468480 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:24:49Z |
| institution | BVB |
| isbn | 9780470402559 9780470880364 |
| language | English |
| lccn | 2010030995 |
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| owner | DE-1050 DE-573 |
| owner_facet | DE-1050 DE-573 |
| physical | XVIII, 638 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Wiley |
| record_format | marc |
| spelling | Boresi, Arthur P. 1924- Verfasser (DE-588)143690604 aut Elasticity in engineering mechanics Arthur P. Boresi and Ken P. Chong and James D. Lee 3. ed. Hoboken, NJ Wiley 2011 XVIII, 638 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Includes bibliographical references and index Elasticity Strength of materials Mechanik (DE-588)4038168-7 gnd rswk-swf Elastizität (DE-588)4014159-7 gnd rswk-swf Elastomechanik (DE-588)4014161-5 gnd rswk-swf Elastomechanik (DE-588)4014161-5 s DE-604 Elastizität (DE-588)4014159-7 s Mechanik (DE-588)4038168-7 s 1\p DE-604 Chong, Ken P. Verfasser aut Lee, James D. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022620291&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Boresi, Arthur P. 1924- Chong, Ken P. Lee, James D. Elasticity in engineering mechanics Elasticity Strength of materials Mechanik (DE-588)4038168-7 gnd Elastizität (DE-588)4014159-7 gnd Elastomechanik (DE-588)4014161-5 gnd |
| subject_GND | (DE-588)4038168-7 (DE-588)4014159-7 (DE-588)4014161-5 |
| title | Elasticity in engineering mechanics |
| title_auth | Elasticity in engineering mechanics |
| title_exact_search | Elasticity in engineering mechanics |
| title_full | Elasticity in engineering mechanics Arthur P. Boresi and Ken P. Chong and James D. Lee |
| title_fullStr | Elasticity in engineering mechanics Arthur P. Boresi and Ken P. Chong and James D. Lee |
| title_full_unstemmed | Elasticity in engineering mechanics Arthur P. Boresi and Ken P. Chong and James D. Lee |
| title_short | Elasticity in engineering mechanics |
| title_sort | elasticity in engineering mechanics |
| topic | Elasticity Strength of materials Mechanik (DE-588)4038168-7 gnd Elastizität (DE-588)4014159-7 gnd Elastomechanik (DE-588)4014161-5 gnd |
| topic_facet | Elasticity Strength of materials Mechanik Elastizität Elastomechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022620291&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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