The linearized theory of elasticity:
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| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2002
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 533 - 535 |
| Physical Description: | XXV, 543 S. graph. Darst. : 24 cm |
| ISBN: | 0817641173 3764341173 9781461266082 |
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| 001 | BV014222897 | ||
| 003 | DE-604 | ||
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| 008 | 020326s2002 gw d||| |||| 00||| eng d | ||
| 016 | 7 | |a 963979361 |2 DE-101 | |
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| 020 | |a 3764341173 |c hbk |9 3-7643-4117-3 | ||
| 020 | |a 9781461266082 |c pbk |9 978-1-4612-6608-2 | ||
| 035 | |a (OCoLC)47072911 | ||
| 035 | |a (DE-599)BVBBV014222897 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-703 |a DE-83 |a DE-91G | ||
| 050 | 0 | |a QA931 | |
| 082 | 0 | |a 532/.0535 |2 21 | |
| 084 | |a UF 3000 |0 (DE-625)145570: |2 rvk | ||
| 084 | |a PHY 202f |2 stub | ||
| 084 | |a 74Bxx |2 msc | ||
| 100 | 1 | |a Slaughter, William S. |e Verfasser |0 (DE-588)123627036 |4 aut | |
| 245 | 1 | 0 | |a The linearized theory of elasticity |c William S. Slaughter |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2002 | |
| 300 | |a XXV, 543 S. |b graph. Darst. : 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 533 - 535 | ||
| 650 | 7 | |a Elasticidade |2 larpcal | |
| 650 | 4 | |a Élasticité | |
| 650 | 4 | |a Elasticity | |
| 650 | 0 | 7 | |a Lineare Elastizitätstheorie |0 (DE-588)4139506-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Elastizitätstheorie |0 (DE-588)4139506-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4612-0093-2 |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009752008&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009752008 | |
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| _version_ | 1826205057343815680 |
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| adam_text |
CONTENTS
PREFACE
XV
LIST
OF
FIGURES
XIX
LIST
OF
TABLES
XXV
1
REVIEW
OF
MECHANICS
OF
MATERIALS
1
1.1
FORCES
AND
STRESS
.
2
1.1.1
NORMAL
STRESS
.
2
1.1.2
SHEAR
STRESS
.
3
1.1.3
COMPONENTS
OF
STRESS
.
3
1.2
STRESS
AND
STRAIN
.
5
1.2.1
LONGITUDINAL
STRAIN
UNDER
AXIAL
LOADING
.
5
1.2.2
HOOKE
'
S
LAW
AND
YOUNG
'
S
MODULUS
.
5
1.2.3
POISSON
'
S
RATIO
.
6
1.2.4
SHEAR
STRAIN
.
6
1.2.5
COMPONENTS
OF
STRAIN
.
7
1.2.6
GENERALIZED
HOOKE
'
S
LAW
.
8
1.2.7
BULK
MODULUS
.
9
1.3
TORSION
OF
CIRCULAR
CYLINDERS
.
10
1.4
BENDING
OF
PRISMATIC
BEAMS
.
12
1.4.1
SHEAR
FORCE
AND
BENDING
MOMENT
.
12
1.4.2
PURE
BENDING
.
14
1.4.3
TRANSVERSE
LOADING
.
16
1.4.4
DEFLECTION
.
17
PROBLEMS
.
19
2
MATHEMATICAL
PRELIMINARIES
23
2.1
SCALARS
AND
VECTORS
.
23
2.1.1
SCALAR
QUANTITIES
.
23
2.1.2
VECTOR
QUANTITIES
.
24
2.2
INDICIAL
NOTATION
.
31
VIII
CONTENTS
2.2.1
RANGE
CONVENTION
.
32
2.2.2
SUMMATION
CONVENTION
.
32
2.2.3
GUIDELINES
.
I
.
33
2.2.4
CONTRACTION
.
34
2.2.5
KRONECKER
DELTA
.
35
2.2.6
ORTHOGONALITY
CONDITION
.
36
2.2.7
PERMUTATION
SYMBOL
.
36
2.3
TENSORS
.
38
2.3.1
TENSOR
ALGEBRA
.
42
2.3.2
HIGHER-ORDER
TENSORS
.
43
2.3.3
DYADIC
NOTATION
.
44
2.3.4
ISOTROPIC
TENSORS
.
50
2.3.5
TENSORS
OF
ORDER
2
.
51
2.3.6
EIGENVALUE
PROBLEMS
.
57
2.4
TENSOR
CALCULUS
.
63
2.4.1
COORDINATE
SYSTEMS
.
64
2.4.2
GRADIENT
.
68
2.4.3
DIVERGENCE
.
69
2.4.4
CURL
.
70
2.4.5
LAPLACIAN
.
72
2.4.6
LINE,
SURFACE,
AND
VOLUME
INTEGRALS
.
72
2.5
CYLINDRICAL
AND
SPHERICAL
COORDINATES
.
77
2.5.1
CYLINDRICAL
COORDINATES
.
78
2.5.2
SPHERICAL
COORDINATES
.
84
PROBLEMS
.
91
3
KINEMATICS
97
3.1
CONFIGURATIONS
.
97
3.1.1
MATERIAL
LINES,
SURFACES,
AND
VOLUMES
.
100
3.1.2
MATERIAL
AND
SPATIAL
DESCRIPTIONS
.
101
3.1.3
DISPLACEMENT
.
104
3.1.4
MATERIAL
TIME
DERIVATIVE
.
106
3.1.5
DEFORMATION
GRADIENT
TENSOR
.
107
3.1.6
COMPATIBILITY
.
110
3.1.7
POLAR
DECOMPOSITION
THEOREM
.
ILL
3.2
STRAIN
TENSORS:
REFERENTIAL
FORMULATION
.
112
3.2.1
LOCAL
PHYSICAL
INTERPRETATION
.
115
3.2.2
STRAIN-DISPLACEMENT
RELATIONS
.
125
3.3
STRAIN
TENSORS:
SPATIAL
FORMULATION
.
126
3.3.1
LOCAL
PHYSICAL
INTERPRETATION
.
128
3.3.2
STRAIN-DISPLACEMENT
RELATIONS
.
133
3.4
KINEMATIC
LINEARIZATION
.
134
3.4.1
INFINITESIMAL
STRAIN
AND
ROTATION
TENSORS
.
136
3.4.2
PHYSICAL
INTERPRETATION
.
138
CONTENTS
IX
3.4.3
PRINCIPAL
STRAINS
AND
PRINCIPAL
DIRECTIONS
OF
STRAIN
.
143
3.4.4
COMPATIBILITY
.
145
3.5
CYLINDRICAL
AND
SPHERICAL
COORDINATES
.
148
3.5.1
CYLINDRICAL
COORDINATES
.
148
3.5.2
SPHERICAL
COORDINATES
.
149
PROBLEMS
.
150
4
FORCES
AND
STRESS
157
4.1
STRESS
TENSORS:
REFERENTIAL
FORMULATION
.
158
4.1.1
SURFACE
FORCES
.
158
4.1.2
BODY
FORCES
.
160
4.1.3
BALANCE
OF
LINEAR
AND
ANGULAR
MOMENTUM
.
161
4.1.4
GENERALIZATION
OF
NEWTON
'
S
THIRD
LAW
.
163
4.1.5
FIRST
PIOLA-KIRCHHOFF
STRESS
.
165
4.1.6
EQUATIONS
OF
MOTION
.
168
4.2
STRESS
TENSORS:
SPATIAL
FORMULATION
.
170
4.2.1
SURFACE
FORCES
.
170
4.2.2
BODY
FORCES
.
172
4.2.3
BALANCE
OF
LINEAR
AND
ANGULAR
MOMENTUM
.
173
4.2.4
GENERALIZATION
OF
NEWTON
'
S
THIRD
LAW
.
174
4.2.5
CAUCHY
STRESS
.
175
4.2.6
EQUATIONS
OF
MOTION
.
177
4.2.7
RELATIONS
BETWEEN
STRESS
TENSORS
.
178
4.3
KINEMATIC
LINEARIZATION
.
179
4.3.1
NORMAL
AND
SHEAR
TRACTIONS
.
183
4.3.2
PRINCIPAL
STRESSES
AND
PRINCIPAL
DIRECTIONS
OF
STRESS
.
185
4.4
CYLINDRICAL
AND
SPHERICAL
COORDINATES
.
187
4.4.1
CYLINDRICAL
COORDINATES
.
187
4.4.2
SPHERICAL
COORDINATES
.
188
PROBLEMS
.
189
5
CONSTITUTIVE
EQUATIONS
193
5.1
ELASTICITY
.
193
5.1.1
MATERIAL
FRAME-INDIFFERENCE
.
194
5.1.2
KINEMATIC
LINEARIZATION
.
198
5.2
CONSTITUTIVE
LINEARIZATION
.
199
5.3
MATERIAL
SYMMETRY
.
201
5.3.1
ENGINEERING
NOTATION
.
202
5.3.2
MONOCLINIC
MATERIALS
.
205
5.3.3
ORTHOTROPIC
MATERIALS
.
206
5.3.4
TRANSVERSELY
ISOTROPIC
MATERIALS
.
207
5.3.5
PRINCIPAL
DIRECTIONS
OF
STRESS
AND
STRAIN
.
209
X
CONTENTS
5.4
ISOTROPIC
MATERIALS
.
211
5.4.1
EQUIVALENT
FORMS
OF
THE
CONSTITUTIVE
EQUATION
.
.
.
212
5.4.2
RESTRICTIONS
ON
VALUES
OF
THE
ELASTIC
MODULI
.
214
5.5
CYLINDRICAL
AND
SPHERICAL
COORDINATES
.
218
PROBLEMS
.
218
6
LINEARIZED
ELASTICITY
PROBLEMS
221
6.1
FIELD
EQUATIONS
.
221
6.1.1
LAME-NAVIER
EQUATIONS
.
222
6.1.2
MICHELL
'
S
AND
BELTRAMI
'
S
EQUATIONS
.
224
6.2
BOUNDARY
CONDITIONS
.
226
6.2.1
SAINT-VENANT
'
S
PRINCIPLE
.
231
6.3
USEFUL
CONSEQUENCES
OF
LINEARITY
.
232
6.3.1
SUPERPOSITION
PRINCIPLE
.
233
6.3.2
UNIQUENESS
OF
SOLUTIONS
.
234
6.3.3
CLAPEYRON
'
S
THEOREM
.
236
6.3.4
BETTI-RAYLEIGH
RECIPROCITY
RELATIONS
.
237
6.4
SOLUTION
METHODS
.
240
6.4.1
EXAMPLE:
SPHERICAL
PRESSURE
VESSEL
.
241
6.4.2
EXAMPLE:
HANGING
BEAM
.
246
PROBLEMS
.
250
7
TWO-DIMENSIONAL
PROBLEMS
255
7.1
ANTIPLANE
STRAIN
.
256
7.1.1
CYLINDRICAL
COORDINATES
.
258
7.1.2
EXAMPLE:
SCREW
DISLOCATION
.
259
7.2
PLANE
STRAIN
.
260
7.2.1
CYLINDRICAL
COORDINATES
.
262
7.2.2
EXAMPLE:
CYLINDRICAL
PRESSURE
VESSEL
.
263
7.3
PLANE
STRESS
.
267
7.3.1
CYLINDRICAL
COORDINATES
.
269
7.3.2
GENERALIZED
PLANE
STRESS
.
270
7.3.3
EXAMPLE:
SPINNING
THIN
DISK
.
273
7.3.4
EQUIVALENCE
OF
PLANE
STRESS
AND
PLANE
STRAIN
.
276
7.4
AIRY
STRESS
FUNCTION
.
278
7.4.1
DISPLACEMENTS
.
281
7.4.2
CYLINDRICAL
COORDINATES
.
283
7.4.3
EXAMPLE:
CANTILEVERED
BEAM
.
.
284
7.4.4
EXAMPLE:
DAM
PROBLEM
.
289
7.4.5
EXAMPLE:
AXIALLY
LOADED
WEDGE
.
293
PROBLEMS
.
300
CONTENTS
XI
8
TORSION
OF
NONCIRCULAR
CYLINDERS
305
8.1
WARPING
FUNCTION
.
306
8.1.1
STRESS
.
307
8.1.2
EQUILIBRIUM
.
307
8.1.3
BOUNDARY
CONDITIONS
.
308
8.1.4
EXAMPLE:
CIRCULAR
CYLINDER
.
310
8.1.5
EXAMPLE:
ELLIPTICAL
CYLINDER
.
312
8.1.6
EXAMPLE:
RECTANGULAR
CYLINDER
.
314
8.2
PRANDTL
STRESS
FUNCTION
.
318
8.2.1
EXAMPLE:
ELLIPTICAL
CYLINDER
(REVISITED)
.
323
8.2.2
EXAMPLE:
EQUILATERAL
TRIANGULAR
CYLINDER
.
324
PROBLEMS
.
327
9
THREE-DIMENSIONAL
PROBLEMS
331
9.1
FIELD
THEORY
RESULTS
.
331
9.1.1
POISSON
'
S
EQUATION
.
332
9.1.2
THREE-DIMENSIONAL
DIRAC
DELTA
FUNCTION
.
333
9.1.3
HELMHOLTZ
'
S
REPRESENTATION
THEOREM
.
334
9.1.4
GREEN
'
S
THEOREM
.
335
9.2
POTENTIALS
IN
ELASTICITY
.
336
9.2.1
DISPLACEMENT
POTENTIALS
.
336
9.2.2
PAPKOVICH
REPRESENTATION
.
337
9.2.3
KELVIN
'
S
PROBLEM
.
340
9.2.4
MINDLIN
'
S
PROBLEM
.
346
9.2.5
FUNDAMENTAL
PROBLEM
.
352
9.3
DISLOCATION
SURFACE
.
354
9.3.1
SOLID
ANGLE
OF
A
SURFACE
.
360
9.4
ESHELBY
'
S
INCLUSION
PROBLEMS
.
362
9.4.1
TRANSFORMING
INCLUSIONS
.
362
9.4.2
DISSIMILAR,
ELLIPSOIDAL
INCLUSIONS
.
377
PROBLEMS
.
382
10
VARIATIONAL
METHODS
387
10.1
CALCULUS
OF
VARIATIONS
.
387
10.1.1
PROCESS
OF
"
TAKING
VARIATIONS
"
.
393
10.1.2
USING
LAGRANGE
MULTIPLIERS
.
395
10.2
ENERGY
THEOREMS
IN
ELASTICITY
.
399
10.2.1
PRINCIPLE
OF
VIRTUAL
WORK
.
399
10.2.2
STRAIN
ENERGY
DENSITY
.
400
10.2.3
PRINCIPLE
OF
MINIMUM
POTENTIAL
ENERGY
.
402
10.2.4
COMPLEMENTARY
STRAIN
ENERGY
DENSITY
.
406
10.2.5
PRINCIPLE
OF
MINIMUM
COMPLEMENTARY
ENERGY
.
.
.
407
10.3
APPROXIMATE
SOLUTIONS
.
411
10.3.1
RAYLEIGH-RITZ
METHOD
.
412
XII
CONTENTS
10.3.2
APPROXIMATE
SOLUTIONS
TO
TORSION
PROBLEMS
.
414
PROBLEMS
.
426
11
COMPLEX
VARIABLE
METHODS
431
11.1
FUNCTIONS
OF
A
COMPLEX
VARIABLE
.
431
11.1.1
COMPLEX
NUMBERS
.
431
11.1.2
COMPLEX
VARIABLES
.
435
11.1.3
FUNCTIONS
OF
A
COMPLEX
VARIABLE
.
438
11.1.4
BRANCH
CUTS
AND
BRANCH
POINTS
.
441
11.1.5
DIFFERENTIABILITY
AND
ANALYTICITY
.
443
11.1.6
CONTOUR
INTEGRALS
.
449
11.1.7
POWER
SERIES
.
451
11.1.8
ANALYTIC
CONTINUATION
.
453
11.1.9
CONFORMAL
MAPPING
.
454
11.2
ANTIPLANE
STRAIN
.
458
11.2.1
TRACTION-STRESS
RELATION
.
459
11.2.2
CYLINDRICAL
COORDINATES
.
460
11.2.3
BOUNDARY
VALUE
PROBLEM
.
460
11.2.4
EXAMPLE:
INFINITE
TWO-DIMENSIONAL
BODY
WITH
A
CIRCULAR
HOLE
UNDER
FAR-FIELD
SHEAR
.
461
11.2.5
ASYMPTOTIC
CRACK
TIP
FIELDS
(MODE
III)
.
464
11.2.6
EXAMPLE:
INFINITE
TWO-DIMENSIONAL
BODY
WITH
A
FINITE
CRACK
UNDER
FAR-FIELD
SHEAR
.
469
11.3
PLANE
STRAIN/STRESS
.
474
11.3.1
DISPLACEMENTS
.
476
11.3.2
RIGID-BODY
MOTION
.
478
11.3.3
HOMOGENEOUS
STRESS
.
479
11.3.4
TRACTION-STRESS
RELATION
.
480
11.3.5
BOUNDARY
VALUE
PROBLEM
.
481
11.3.6
IMPLICATIONS
OF
SYMMETRY
.
482
11.3.7
CYLINDRICAL
COORDINATES
.
483
11.3.8
EXAMPLE:
INFINITE
TWO-DIMENSIONAL
BODY
WITH
A
CIRCULAR
HOLE
UNDER
FAR-FIELD
UNIAXIAL
TENSION
.
.
485
11.3.9
CONFORMAL
MAPPING
APPLIED
TO
PLANE
STRAIN/STRESS
PROBLEMS
.
490
11.3.10
EXAMPLE:
INFINITE
TWO-DIMENSIONAL
BODY
WITH
AN
ELLIPTICAL
HOLE
UNDER
FAR-FIELD
UNIAXIAL
TENSION
.
.
493
11.3.11
ASYMPTOTIC
CRACK
TIP
FIELDS
(MODES
I
AND
II)
.
.
.
499
11.3.12
EXAMPLE:
INFINITE
TWO-DIMENSIONAL
BODY
WITH
A
FINITE
CRACK
UNDER
FAR-FIELD
UNIAXIAL
TENSION
.
.
.
506
PROBLEMS
.
509
CONTENTS
XIII
APPENDIX:
GENERAL
CURVILINEAR
COORDINATES
513
A.L
GENERAL
VECTOR
BASES
.
513
A.
1.1
COVARIANT
AND
CONTRAVARIANT
COMPONENTS
.
515
A.
1.2
RECIPROCAL
BASES
.
516
A.
1.3
HIGHER-ORDER
TENSORS
.
518
A.
2
CURVILINEAR
COORDINATES
.
521
A.
2.1
CARTESIAN
COORDINATES
.
522
A.
2.2
CYLINDRICAL
COORDINATES
.
522
A.
2.3
SPHERICAL
COORDINATES
.
524
A.
2.4
METRIC
TENSOR
IN
A
NATURAL
VECTOR
BASIS
.
525
A.
2.5
TRANSFORMATION
RULE
FOR
CHANGE
OF
COORDINATES
.
.
526
A.
3
TENSOR
CALCULUS
.
527
A.
3.1
GRADIENT
.
530
REFERENCES
533
INDEX
537 |
| any_adam_object | 1 |
| author | Slaughter, William S. |
| author_GND | (DE-588)123627036 |
| author_facet | Slaughter, William S. |
| author_role | aut |
| author_sort | Slaughter, William S. |
| author_variant | w s s ws wss |
| building | Verbundindex |
| bvnumber | BV014222897 |
| callnumber-first | Q - Science |
| callnumber-label | QA931 |
| callnumber-raw | QA931 |
| callnumber-search | QA931 |
| callnumber-sort | QA 3931 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | UF 3000 |
| classification_tum | PHY 202f |
| ctrlnum | (OCoLC)47072911 (DE-599)BVBBV014222897 |
| dewey-full | 532/.0535 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.0535 |
| dewey-search | 532/.0535 |
| dewey-sort | 3532 3535 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV014222897 |
| illustrated | Illustrated |
| indexdate | 2025-03-10T11:07:37Z |
| institution | BVB |
| isbn | 0817641173 3764341173 9781461266082 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009752008 |
| oclc_num | 47072911 |
| open_access_boolean | |
| owner | DE-703 DE-83 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-83 DE-91G DE-BY-TUM |
| physical | XXV, 543 S. graph. Darst. : 24 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Slaughter, William S. Verfasser (DE-588)123627036 aut The linearized theory of elasticity William S. Slaughter Boston [u.a.] Birkhäuser 2002 XXV, 543 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 533 - 535 Elasticidade larpcal Élasticité Elasticity Lineare Elastizitätstheorie (DE-588)4139506-2 gnd rswk-swf Lineare Elastizitätstheorie (DE-588)4139506-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4612-0093-2 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009752008&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Slaughter, William S. The linearized theory of elasticity Elasticidade larpcal Élasticité Elasticity Lineare Elastizitätstheorie (DE-588)4139506-2 gnd |
| subject_GND | (DE-588)4139506-2 |
| title | The linearized theory of elasticity |
| title_auth | The linearized theory of elasticity |
| title_exact_search | The linearized theory of elasticity |
| title_full | The linearized theory of elasticity William S. Slaughter |
| title_fullStr | The linearized theory of elasticity William S. Slaughter |
| title_full_unstemmed | The linearized theory of elasticity William S. Slaughter |
| title_short | The linearized theory of elasticity |
| title_sort | the linearized theory of elasticity |
| topic | Elasticidade larpcal Élasticité Elasticity Lineare Elastizitätstheorie (DE-588)4139506-2 gnd |
| topic_facet | Elasticidade Élasticité Elasticity Lineare Elastizitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009752008&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT slaughterwilliams thelinearizedtheoryofelasticity |