A guide to the three-dimensional theory of elasticity: a novel overview of its basics, methods and results
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Neunplus1
2013
|
| Ausgabe: | 3., rev. and extended ed. |
| Schriftenreihe: | Edition Wissenschaft
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | X, 222 S. graph. Darst. |
| ISBN: | 9783936033335 |
Internformat
MARC
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| 245 | 1 | 0 | |a A guide to the three-dimensional theory of elasticity |b a novel overview of its basics, methods and results |c Zia Taheri ; Armin Taheri |
| 250 | |a 3., rev. and extended ed. | ||
| 264 | 1 | |a Berlin |b Neunplus1 |c 2013 | |
| 300 | |a X, 222 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
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| adam_text | TABLE OF CONTENTS
PREFACE IX
1 BASIC EQUATIONS OF THE THEORY OF ELASTICITY - CARTESIAN COORDINATES 1
1.1 STATIC EQUATIONS: DIFFERENTIAL EQUATIONS OF EQUILIBRIUM 1
1.2 BOUNDARY CONDITION EQUATIONS 2
1.3 GEOMETRICAL RELATIONS: DISTORTION EQUATIONS 2
1.4 PHYSICAL EQUATIONS: THE GENERALIZED HOOKE S LAW 3
1.5 CONDITIONS OF EQUILIBRIUM OF THE ELASTIC MOTION 5
2 DIFFERENTIAL EQUATIONS FOR THE DISPLACEMENTS - CARTESIAN COORDINATES
.... 7
2.1 LAME S EQUATIONS 9
2.2 DIFFERENTIAL EQUATIONS OF EQUILIBRIUM IN THE PRESENCE OF A
HOMOGENOUS FIELD
OF GRAVITY 11
2.3 DIFFERENTIAL EQUATION OF EQUILIBRIUM IN THE PRESENCE OF ANY GIVEN
TEMPERATURE
DISTRIBUTION 11
2.4 DIFFERENTIAL EQUATION OF ELASTIC MOTION 11
2.5 BODY SUBJECTED TO THE ACTION OF THE INERTIA FORCE 12
3 DIFFERENTIAL EQUATIONS FOR THE STRESSES - CARTESIAN COORDINATES 13
3.1 BELTRAMI-MICHELPS EQUATIONS 15
4 METHODS FOR GENERAL SOLUTIONS - APPROACHES WITH DISPLACEMENTS -
CARTESIAN COORDINATES 17
4.1 GALERKIN B. - GALERKIN VECTOR 17
4.2 THE LAME - WESTERGAARD SOLUTION FOR SPECIFIC PROBLEMS 21
4.3 EXTENSION OF THE GALERKIN METHOD TO SYSTEMS WITH SMALL MOVEMENTS AND
TO SYSTEMS FOR SMALL MOVEMENTS WITH DAMPING ACCORDING TO LACOVACHE M.
UND MOISIL GR. C 23
4.4 THE SOLUTION OF TIMOSHENKO S. P. 26
4.5 THE NEUBER-PAPKOWICH SOLUTION, THE THREE-FUNCTION APPROACH 27
4.6 THE APPROACHES OF BOUSSINESQ 29
4.7 THE SOLUTION OF GOODIER J.N 31
4.8 THE SOLUTION OF BIEZENO-GRAMMEL 32
4.9 THE APPROACH OF HELMHOLTZ 32
4.10 PAPKOWICH-NEUBER S APPROACH 33
4.11 THE APPROACH OF FREIBERGER 34
5 APPROACHES WITH STRESS FUNCTIONS - CARTESIAN COORDINATES 35
5.1 MAXWELL JAMES CLERK 35
5.2 MORERA 37
5.3 BLOCHW.L 38
HTTP://D-NB.INFO/1042191409
VI
6 THE EQUATIONS OF ELASTICITY IN CYLINDRICAL COORDINATES - BASIC
EQUATIONS 41
6.1 THE CONDITIONS OF EQUILIBRIUM 41
6.2 THE EQUATIONS OF DISTORTION 42
6.3 HOOKE S LAW, STRESS-STRAIN RELATIONS 42
6.4 LAME S EQUATIONS IN CYLINDRICAL COORDINATES - ROTATIONAL SYMMETRY 42
6.5 BELTRAMI-MICHELL EQUATIONS IN CYLINDRICAL COORDINATES 43
6.6 THE APPROACH OF HELMHOLTZ 44
6.7 THE CONDITION OF EQUILIBRIUM OF THE ELASTIC MOTION 45
7 METHODS OF SOLUTION IN CYLINDRICAL COORDINATES 47
7.1 WESTERGAARD H. M., APPROACHES WITH STRESS FUNCTIONS 47
7.2 LOVE A. E., APPROACHES WITH STRESS FUNCTIONS 49
7.3 MARGUERRE K., APPROACHES WITH DISPLACEMENTS 49
7.4 BLOCH W. I. AND KRUTKOW J. A., APPROACHES WITH STRESS FUNCTIONS 53
7.5 LURJE A. I., APPROACH WITH STRESS FUNCTIONS 55
7.6 PAPKOWICH P. F., APPROACH WITH DISPLACEMENTS 55
8 THE EQUATIONS OF ELASTICITY IN SPHERICAL COORDINATES - BASIC EQUATIONS
.. 59
8.1 CONDITIONS OF EQUILIBRIUM 59
8.2 EQUATIONS OF DISTORTION 60
8.3 COMPONENTS OF ROTATION 60
8.4 DEFORMATIONS 60
8.5 STRESS-STRAIN RELATIONS 61
8.6 LAME S EQUATIONS FOR THE SPHERE IN THE ABSCENCE OF THE INERTIA FORCE
62
9 METHODS OF SOLUTION IN SPHERICAL COORDINATES 63
9.1 TIMPEA 63
9.2 WESTERGAARD H. M 64
9.3 PAPKOWICH-LURJE 67
9.4 ZIEMBA S 70
9.5 SPHERE SUBJECTED TO RADIAL DISPLACEMENT 71
10 ROTATIONALLY SYMMETRICAL PROBLEMS OF THE THEORY OF ELASTICITY -
BASIC EQUATIONS 73
10.1 DISTORTIONS AND STRESSES IN CYLINDRICAL COORDINATES ACCORDING TO
SOLJANIK-KRASSA 73
10.2 BOUNDARY CONDITIONS 75
11 SOLUTION OF THE ROTATIONALLY SYMMETRICAL PROBLEMS IN CURVILINEAR
COORDINATES 77
11.1 GENERAL BASES 77
11.2 BOUNDARY CONDITIONS 79
11.3 STRESSES AND DISPLACEMENTS 82
12 STRESS FUNCTIONS IN SPHERICAL COORDINATES 85
12.1 SOLUTION OF DIFFERENTIAL EQUATION V
2
CP = 0 86
12.2 COLLECTION OF THE STRESS FUNCTIONS 87
VII
13 STRESS FUNCTIONS IN ELLIPTICAL AND HYPERBOLIC COORDINATES 89
13.1 BASIC EQUATIONS 89
13.2 SOLUTION OF DIFFERENTIAL EQUATION V
2
TY = 0 90
13.3 COLLECTION OF THE STRESS FUNCTIONS 91
14 SOLUTION IN ELLIPTICAL COORDINATES WHEN THE POLES ARE ARRANGED ON AN
AXIS PERPENDICULAR TO THE ROTATIONAL AXIS 93
14.1 SOLUTION OF DIFFERENTIAL EQUATION V
2
T|J
= 0 93
14.2 COLLECTION OF THE STRESS FUNCTIONS 94
15. SOLUTIONS IN PARABOLIC COORDINATES 95
15.1 SOLUTION OF DIFFERENTIAL EQUATION V
2
^ = 0 96
15.2 COLLECTION OF THE STRESS FUNCTIONS 96
16 STATEMENT OF PROBLEMS 97
16.1 THE DEFORMATION OF A HOLLOW SPHERE (EXTERNAL AND INTERNAL RADII ARE
R
2
AND R
L5
RESPECTIVELY) IN WHOSE INTERIOR THERE IS A PRESSURE
THE EXTERNAL PRESSURE IS P
2
97
16.2 THE DEFORMATION OF A HOLLOW CYLINDRICAL TUBE (EXTERNAL AND INTERNAL
RADII ARE
R
2
AND R], RESPECTIVELY) IN WHOSE INTERIOR THERE IS THE PRESSURE PF,
THERE IS NO EXTERNAL PRESSURE P
2
97
16.3 THE DEFORMATION OF A CYLINDER ROTATING EVENLY AROUND ITS AXIS 98
16.4 THE INFINITE SPACE WITH A CYLINDRICAL HOLE UNDER PERIODIC LOAD 98
16.5 THE INFINITE BODY WITH A CYLINDRICAL HOLE UNDER LOAD ON PARTIAL
SURFACE 100
16.6 THE HOLLOW CYLINDER OF INFINITE LENGTH UNDER PERIOD LOADS ON THE
LATERAL
SURFACES 103
16.7 THE SOLID CYLINDER OF INFINITE LENGTH WITH PERIODIC LOADING ON THE
LATERAL
SURFACE 105
16.8 SEMI-INFINITE SOLID WITH PERIOD LOADING OF THE SURFACE OF THE
SEMI-INFINITE SOLID 108
16.9 SINGLE FORCE ON THE ELASTIC SEMI-INFINITE SOLID: THE BOUSSINESQ
PROBLEM,
SOLVED IN CYLINDRICAL COORDINATES ILL
16.10 THE KELVIN-PROBLEM: A SINGLE FORCE IN AN INFINITE SOLID 114
16.11 SINGLE LOAD IN THE ELASTIC SEMI-INFINITE SOLID 116
16.12 THE HOOPED HOLLOW CYLINDER 119
16.13 A HORIZONTAL LOAD IN THE SEMI-INFINITE SOLID PARALLEL TO THE
SURFACE,
SOLVED BY MINDLIN 120
16.14 THE CONE UNDER A SINGLE LOAD 122
16.15 A BOUSSINESQ PROBLEM: THE SEMI-INFINITE SOLID UNDER A SINGLE LOAD,
SOLVED IN
SPHERICAL COORDINATES 126
16.16 THE HOLLOW CONE UNDER A SINGLE LOAD 127
16.17 LAME S PROBLEM FOR THE HOLLOW SPHERE 129
16.18 THE DEFORMATION OF A SOLID SPHERE (RADIUS R) UNDER THE EFFECT OF
ITS OWN
GRAVITATIONAL FIELD 132
16.19 STRAINING OF HOLLOW SPHERES BY EVENLY DISTRIBUTED SURFACE FORCES
133
16.20 THE STRAIN OF CONES BY LINEARLY DISTRIBUTED FORCES ON THE SURFACE
137
16.21 LOADED RECTANGULAR PRISM 139
VIII
16.22 ELLIPSOID OF REVOLUTION UNDER COMPRESSION LOAD 142
16.23 HYPERBOLOID OF REVOLUTION UNDER COMPRESSION LOAD 144
16.24 THE INFINITE SOLID WITH A CIRCULAR BORE SUBJECTED TO ITS OWN
WEIGHT 147
16.25 PARABOLOID OF ROTATION UNDER TENSION LOAD 149
17 VEKTOR OPERATORS 153
17.1 THE LAPLACE OPERATOR 153
17.2 SOME FORMULAS OF VECTOR ANALYSIS 154
17.3 COLLECTION OF FORMULAS 155
18 SPECIAL CHAPTER 159
18.1 EQUILIBRIUM OF AN ELASTIC SPHERE 159
18.2 SPHERE ON WHOSE INTERIOR THERE A ACT FORCES 160
18.3 THE FREE OSCILLATION OF A SOLID BODY 161
18.4 THE INTEGRATION METHOD OF V CERUTTI [115] 162
18.5 VIBRATIONS OF A CIRCULAR CYLINDER 163
18.6 EQUILIBRIUM OF AN ELASTIC MEDIUM BOUNDED BY A PLANE 167
18.7 DIRECT DETERMINATION OF THE STRESS TENSOR BASED ON THE EXTERNAL
FORCES 168
18.8 THE SOLUTION OF Y. A. KRUTKOV [21] 170
18.9 THE BASIC EQUATIONS OF MOTION 171
18.10 THE RELATIONSHIP BETWEEN DISPLACEMENT, DILATATION AND ROTATION 172
19 PRACTICAL METHODS FOR RESOLVING THEORY OF ELASTICITY BOUNDARY VALUE
TASKS .... 173
19.1 BODY WITH TWO PERFORATIONS UNDER DEAD WEIGHT 173
19.2 SOLID WITH TWO OPENINGS, ONE ABOVE THE OTHER, UNDER DEAD WEIGHT 178
19.3 SEMI-PLATE WITH CIRCULAR HOLE AND SLOPING BOUNDARY UNDER DEAD LOAD
180
19.4 MINDLIN S PROBLEM OF SINGLE FORCE IN A SEMI-INFINITE BODY AND SOME
OF ITS
APPLICATIONS 189
19.5 THE ACTION OF LINE LOADS ALONG CIRCLES AND ELLIPSES IN THE SOLID
PLANE 194
19.6 HOLLOW CYLINDER UNDER COMPRESSIVE LOADING 199
19.7 CYLINDER UNDER A RIGID PUNCH 203
19.8 STRESS STATES IN A CONCRETE CUBE TO DETERMINE THE CUBE STRENGTH 211
20 BIBLIOGRAPHY 217
|
| any_adam_object | 1 |
| author | Taheri, Zia 1947- Taheri, Armin 1978- |
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| dewey-full | 531.382 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
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| dewey-search | 531.382 |
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| discipline | Maschinenbau / Maschinenwesen Physik |
| edition | 3., rev. and extended ed. |
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| id | DE-604.BV041637843 |
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| indexdate | 2024-07-10T01:01:30Z |
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| isbn | 9783936033335 |
| language | English |
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| spelling | Taheri, Zia 1947- Verfasser (DE-588)129873721 aut A guide to the three-dimensional theory of elasticity a novel overview of its basics, methods and results Zia Taheri ; Armin Taheri 3., rev. and extended ed. Berlin Neunplus1 2013 X, 222 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Edition Wissenschaft Literaturangaben Elastizitätstheorie (DE-588)4123124-7 gnd rswk-swf Elastizitätstheorie (DE-588)4123124-7 s DE-604 Taheri, Armin 1978- Verfasser (DE-588)1046618180 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027078699&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Taheri, Zia 1947- Taheri, Armin 1978- A guide to the three-dimensional theory of elasticity a novel overview of its basics, methods and results Elastizitätstheorie (DE-588)4123124-7 gnd |
| subject_GND | (DE-588)4123124-7 |
| title | A guide to the three-dimensional theory of elasticity a novel overview of its basics, methods and results |
| title_auth | A guide to the three-dimensional theory of elasticity a novel overview of its basics, methods and results |
| title_exact_search | A guide to the three-dimensional theory of elasticity a novel overview of its basics, methods and results |
| title_full | A guide to the three-dimensional theory of elasticity a novel overview of its basics, methods and results Zia Taheri ; Armin Taheri |
| title_fullStr | A guide to the three-dimensional theory of elasticity a novel overview of its basics, methods and results Zia Taheri ; Armin Taheri |
| title_full_unstemmed | A guide to the three-dimensional theory of elasticity a novel overview of its basics, methods and results Zia Taheri ; Armin Taheri |
| title_short | A guide to the three-dimensional theory of elasticity |
| title_sort | a guide to the three dimensional theory of elasticity a novel overview of its basics methods and results |
| title_sub | a novel overview of its basics, methods and results |
| topic | Elastizitätstheorie (DE-588)4123124-7 gnd |
| topic_facet | Elastizitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027078699&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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