Introduction to mathematical elasticity:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 300 S. Ill., graph. Darst. |
| ISBN: | 9814273724 9789814273725 |
Internformat
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| 300 | |a XV, 300 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804143560947138560 |
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| adam_text | IMAGE 1
INTRODUCTION TO MATHEMATICAL ELASTICITY
LEONID P. LEBEDEV NATIONALUNIVERSITYOF COLOMBIA
MICHAEL J. CLOUD LAWRENCE TECHNOLOGICAL UNIVERSITY,USA
,I» WORLDSCIENTIFIC NEW JERSEY LONDON * SINGAPORE *SELJING*SHANGHAI*
HONG KONG * TAIPEI. CHENNAI
IMAGE 2
CONTENTS
FOREWORD
PREFACE
SOME NOTATION
V
VLL
XL
1. MODELS AND IDEAS OF CLASSICALMECHANICS
1.1
1.2 1.3
1.4 1.5
1.6 1.7
1.8 1.9 1.10 1.11
1.12 1.13 1.11
1.15
1.16 1.17
1.18 1.19
ORIENTATION . . . . . . . . . . . . . . . . . . . . . .
SOME WORDS ON THE FUNDAMENTALS OF OUR SUBJECT .
.VLETRIC
SPACES AND SPACES OF PARTICLES ..
VECTORS AND VECTOR SPACES .
NORMED SPACES AND INNER PRODUCL SPACES FORCES.
EQUILIBRIUM AND .VLOTION OF ARIGID BODY . D ALEMBERT S PRINCIPLE .
THE MOTION OFA SYSTEM OF PARTIEIES . . . TBE RIGID BODY. . . . . . . . .
. . . . . .
MOTION OF A SYSTEM OF PARTICLES; COMPARISON OF TRAJECTORIES; NOTION OF
OPERATOR .
MATRIX OPERATORS AND MATRIX EQUATIONS CORNPLETE SPACES .
CORNPLETION THEOREM . . . . . . . . . . .
LEBESGUE INTEGRATION AND THE LP SPACES ORTHOGONAL DECOMPOSITION OF
HILBERT SPACE
WORK AND ENERGY .
VIRTUAL WORK PRINCIPLE . . . . . . . . . . . LAGRANGE S EQUATIOLLS OF
THE SECOND KIND
XIII
1
1 2
4 8
11 16
21
23 25
31
33 40 44 48
54 60
63 67
70
IMAGE 3
2. SIMPLE ELASTIC MODELS
XIV
1.20 1.21 1.22
2.1 2.2
2.3 2.4
2.5 2.6
2 ~ ./ 2.8
2.9 2.10
2.11
2.12 2.13
2.14 2.15 2.16
2.17 2.18
INTRODUCTION TO MATHEMATICAL ELASH:CITY
PROBLEM OF MINIMUM OF A FUNCTIONAL . HAMILTON S PRINCIPLE .
ENERGY CONSERVATION REVISITED
INTRODUCTION .
TWO MAIN PRINCIPLES OF EQUILIBRIUHLANEL MOTION FOR BODIES IN CONTIILUUM
MECHALLICS.
EQUILIBRIUM OF ASPRING .
EQUILIBRIUM OF ASTRING .
EQUILIBRIULLL
BOUNDARY VALUE PROBLEMS FORA STRIUG GENERALIZED FORRNULATIOLL OF THE
EQUILIBRIUHL PROBLEM FORA
STRING .
VIRTUAL WORK PRINCIPLE FUER ASTRING. . . . . . . . .... RIESZ
REPRESENTATION THEOREM . . . . . . . . . . . . . .
GENERALIZED SETUP OF THE DIRICHLET PROBLEM FOR ASTRING FIRST THEOREMS OF
IMBEDDILLG . .. .
GENERALIJ :ED
SETUP 01 THE DIRICHLET PROBLEM FOR CL STRING,
CONTINUED . . . . . . . . . . . . . . . . . . . . . . . .
NEUMANN PROBLEM FOR THE STRING. . .... THE GENERALIZED SOLUTION OF
LINEAR MECHANICAL PROBLEMS
AND THE PRINCIPLE OF MINIMUILL TOTAL ENERGY ..
NONLINEAR MODEL OF A MEMBRANC . . . . . ..
LINEAR MEMBRANE THEOL Y=POISSOL1 S EQUATIOIL .
GENER3LIED SETUP 01 THC DIRICHLET PROBLEM FUERA LINEAR
MEMBRANE .
OTHER MEMBRANE EQUILIBRIUM PROBLEMS .
BAL1ACH S
CONTRACTION MAPPING PRINCIPLE .
74 83
85
89
89
89
91 95
WO
105 LO8 112 115 116
120 122
126 128
131
1:12
H5 151
3. THCORY OF ELASTICILY: STATICS AND DY1L3MICS 157
3.1 3.2
:~.;J
3.4
3.5
3.6
3.7
INTROCLUCTION .
AN ELASTIC BAR UNDER STRETCHING BEN DING OF A BEAM . . . . . . . .
GENERALIZED SOLUTIONS TO THE EQUILIBRIUM PROBLEM FUER
A
BCAM .
GENERALIZED SETUP: ROUGH QUALITATIVE DISCUSSIOIL PRESS URE AND STRESSES.
VECTORS AND TENSORS . . . . . . . . . . . . . . . .
157
158 1G8
175 179
181 188
IMAGE 4
XV
196 202
207 208
214 218
DIS-
221 224
227 231
232 235
243 243
245 249 252
255
CORN-
262 267
SELF-
3.8 3.9
3.10 3.11
3.12 3.13 3.14
3.15 3.16 3.17
3.18 3.19 3.20 3.21 3.22
3.23 3.24 3.25 3.26
3.27 3.28
3.29
CONTENTS
THE CAUCHY STRESS TENSOR, CONTINUED . BASIC TENSOR CALCULUS IN
CURVILINEAR COORDINATES
EULER AND LAGRANGE DESCRIPTIONS OF CONTINUA STRAIN TENSORS .
THE VIRTUAL WORK PRINCIPLE . . . . . . HOOKE S LAW IN THREE DIMENSIONS .
THE EQUILIBRIUM EQUATIONS OF LINEAR ELASTICITY IN PLACEMENTS . . . . . .
. . . . . . . . . . . .
VIRTUAL VORK PRINCIPLE IN LINEAR ELASTICITY GENERALIZED SETUP OF
ELASTICITY PROBLEMS
EXISTENCE THEOREM FOR AN ELASTIC DODY EQUILIBRIUM OF AFREE ELASTIC BODY
. . . .
VARIATIONAL METHOC!SFOR EQUILIBRIUM PROBLEMS ABRIEF BUT IMPORTANT REMARK
....
COUNTABLE SETS ANEL SEPARABLE SPACES. . . . FOURIER SERIES. . . . . . .
. . . . . . . . . .
PROBLEM OF VIBRATION FOR ELASTIC STRUETURES SELF-ADJOINTNESS OF IT ANC!
ITS CONSEQUENCES
COMPACTNESS OF IT .. . . . . . . . . . . . .
RIESZ-
FREDHOLM THEORY FORA LINEAR, SELF-ADJOINT, PAET OPERATOR INA HILBERT
SPACE . . . . . . . . . .
WEAK CONVERGENCE IN HILBERT SPACE . COMPLCTENESS OF THE SYSTEM OF
EIGENVECTORS OF A
ADJOINT, COMPACT, STRICTLY POSITIVE LINEAR OPERATOR OTHER STANDARD
MODELS OF ELASTICITY . . . . . . . . .
272 277
APPENDIX A RINTS FORSELECTEDEXERCISES
BIBLIOGRAPHY
INDEX
281
293
295
|
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| author | Lebedev, Leonid P. 1946- Cloud, Michael J. 1960- |
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| author_sort | Lebedev, Leonid P. 1946- |
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| building | Verbundindex |
| bvnumber | BV036861220 |
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| ctrlnum | (OCoLC)699056278 (DE-599)BVBBV036861220 |
| discipline | Physik |
| format | Book |
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| indexdate | 2024-07-09T22:49:37Z |
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| isbn | 9814273724 9789814273725 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020776976 |
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| physical | XV, 300 S. Ill., graph. Darst. |
| publishDate | 2009 |
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| publishDateSort | 2009 |
| publisher | World Scientific |
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| spelling | Lebedev, Leonid P. 1946- Verfasser (DE-588)124355560 aut Introduction to mathematical elasticity Leonid P. Lebedev ; Michael J. Cloud New Jersey [u.a.] World Scientific 2009 XV, 300 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Elastizitätstheorie (DE-588)4123124-7 gnd rswk-swf Elastizitätstheorie (DE-588)4123124-7 s DE-604 Cloud, Michael J. 1960- Verfasser (DE-588)120264242 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020776976&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lebedev, Leonid P. 1946- Cloud, Michael J. 1960- Introduction to mathematical elasticity Elastizitätstheorie (DE-588)4123124-7 gnd |
| subject_GND | (DE-588)4123124-7 |
| title | Introduction to mathematical elasticity |
| title_auth | Introduction to mathematical elasticity |
| title_exact_search | Introduction to mathematical elasticity |
| title_full | Introduction to mathematical elasticity Leonid P. Lebedev ; Michael J. Cloud |
| title_fullStr | Introduction to mathematical elasticity Leonid P. Lebedev ; Michael J. Cloud |
| title_full_unstemmed | Introduction to mathematical elasticity Leonid P. Lebedev ; Michael J. Cloud |
| title_short | Introduction to mathematical elasticity |
| title_sort | introduction to mathematical elasticity |
| 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=020776976&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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