The finite element analysis of shells: fundamentals
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
2011
|
| Edition: | 2. ed. |
| Series: | Computational fluid and solid mechanics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XV, 410 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9783642164071 |
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IMAGE 1
CONTENTS
1. INTRODUCTION 1
1.1 SHELLS: FROM NATURE TO ENGINEERING DESIGNS 1
1.2 THE FINITE ELEMENT ANALYSIS OF SHELLS AS APPROACHED IN THIS BOOK 4
2. GEOMETRICAL PRELIMINARIES 9
2.1 VECTORS AND TENSORS IN THREE-DIMENSIONAL CURVILINEAR COOR- DINATES 9
2.1.1 VECTORS AND TENSORS 9
2.1.2 COVARIANT AND CONTRAVARIANT BASES. METRIC TENSOR 11 2.1.3
CURVILINEAR COORDINATE SYSTEMS 17
2.1.4 COVARIANT DIFFERENTIATION 20
2.2 THE SHELL GEOMETRY 23
2.2.1 GEOMETRIC DEFINITION OF A SHELL 23
2.2.2 DIFFERENTIAL GEOMETRY ON THE MIDSURFACE 25
2.2.3 3D DIFFERENTIAL GEOMETRY FOR SHELLS 37
3. ELEMENTS OF FUNCTIONAL AND NUMERICAL ANALYSIS 41
3.1 SOBOLEV SPACES AND ASSOCIATED NORMS 41
3.1.1 GENERAL CONCEPTS IN VECTOR SPACES 42
3.1.2 I? AND OTHER SOBOLEV SPACES 48
3.2 VARIATIONAL FORMULATIONS AND FINITE ELEMENT APPROXIMATIONS 58 3.2.1
BASIC ERROR ESTIMATES FOR DISPLACEMENT-BASED AND MIXED FORMULATIONS 59
3.2.2 INTERPOLATION AND A PRIORI ERROR ESTIMATES 88
3.2.3 EFFECT OF NUMERICAL INTEGRATION 93
4. SHELL MATHEMATICAL MODELS 95
4.1 SHELL KINEMATICS 95
4.2 DERIVATION OF SHELL MODELS 99
4.2.1 THE "BASIC SHELL MODEL" 100
4.2.2 THE "SHEAR-MEMBRANE-BENDING MODEL" 103
4.2.3 THE "MEMBRANE-BENDING MODEL" 104
4.2.4 PLATE MODELS 107
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1006645039
DIGITALISIERT DURCH
IMAGE 2
XIV CONTENTS
4.2.5 HIGHER-ORDER SHELL MODELS, AND THE 3D-SHELL MODEL 110 4.3
MATHEMATICAL ANALYSIS OF THE SHELL MODELS 114
4.3.1 ANALYSIS OF THE S-M-B SHELL MODEL 114
4.3.2 ANALYSIS OF THE M-B SHELL MODEL 123
4.3.3 ANALYSIS OF THE BASIC SHELL MODEL 125
4.3.4 ANALYSIS OF THE 3D-SHELL MODEL 130
5. ASYMPTOTIC BEHAVIORS OF SHELL MODELS 135
5.1 GENERAL ASYMPTOTIC ANALYSIS 136
5.1.1 NON-INHIBITED PURE BENDING 143
5.1.2 INHIBITED PURE BENDING 146
5.1.3 SUMMARY OF ASYMPTOTIC BEHAVIORS 150
5.1.4 COMPARISON OF ASYMPTOTIC BEHAVIORS FOR SPECIFIC SHELL MODELS 152
5.2 ANALYSIS OF THE SUBSPACE OF PURE BENDING DISPLACEMENTS . . . 156
5.2.1 ELLIPTIC SURFACES 157
5.2.2 HYPERBOLIC SURFACES 158
5.2.3 PARABOLIC SURFACES 159
5.3 INFLUENCE OF THE LOADING 161
5.3.1 EFFECT OF THE LOADINGS THAT DO NOT ACTIVATE THE PURE BENDING
DISPLACEMENTS 161
5.3.2 EFFECT OF NON-ADMISSIBLE MEMBRANE LOADINGS 166 5.4 ASYMPTOTIC
ANALYSIS OF THE 3D-BASED SHELL MODELS 179 5.4.1 ASYMPTOTIC ANALYSIS OF
THE BASIC SHELL MODEL 180
5.4.2 ASYMPTOTIC ANALYSIS OF THE 3D-SHELL MODEL 192
5.5 ASYMPTOTIC CONSIDERATIONS IN DYNAMIC ANALYSIS 208
5.5.1 NON-INHIBITED PURE BENDING 208
5.5.2 INHIBITED PURE BENDING 209
5.5.3 DETAILED NUMERICAL ILLUSTRATION FOR A CLAMPED CYLINDER . 210
6. DISPLACEMENT-BASED SHELL FINITE ELEMENTS 219
6.1 DISCRETIZATIONS OF SHELL MATHEMATICAL MODELS 219
6.2 FACET-SHELL ELEMENTS 224
6.3 GENERAL SHELL ELEMENTS 228
6.4 3D-SHELL ELEMENTS 253
7. INFLUENCE OF THE THICKNESS IN THE FINITE ELEMENT APPROXI- MATION 259
7.1 NUMERICAL LOCKING IN THIN STRUCTURES 260
7.2 TREATMENTS OF NUMERICAL LOCKING BY MIXED FORMULATIONS 266 7.2.1
BASIC PRINCIPLES: THE TIMOSHENKO BEAM EXAMPLE 267 7.2.2 APPLICATIONS TO
THE REISSNER-MINDLIN PLATE MODEL 276 7.2.3 BASIC PRINCIPLES OF
STABILIZED MIXED FORMULATIONS 291
7.2.4 MITC PLATE ELEMENTS 295
7.3 SPECIFIC DIFFICULTIES ARISING IN THE ANALYSIS OF SHELLS 304
IMAGE 3
CONTENTS XV
8. TOWARDS THE FORMULATION OF EFFECTIVE GENERAL SHELL ELE- MENTS 315
8.1 GUIDELINES FOR ASSESSING AND IMPROVING THE RELIABILITY OF SHELL
FINITE ELEMENTS 315
8.1.1 CONSIDERATIONS ON PROPER SELECTION AND USE OF TEST PROBLEMS 315
8.1.2 PROPOSED SET OF TEST PROBLEMS 323
8.2 FORMULATION OF MITC SHELL ELEMENTS 326
8.2.1 FORMULATION OF QUADRILATERAL MITC ELEMENTS 326 8.2.2 FORMULATION
OF TRIANGULAR MITC ELEMENTS 327
8.2.3 INSIGHT INTO MITC SHELL FORMULATIONS 332
8.2.4 CONSIDERATIONS REGARDING 3D-SHELL ELEMENTS 336 8.3 ASSESSMENT
RESULTS 338
8.3.1 SHELL ELEMENTS USED IN PLATE BENDING 338
8.3.2 AXISYMMETRIC HYPERBOLOID 344
9. ON THE NONLINEAR ANALYSIS OF SHELLS 365
9.1 THE INCREMENTAL ANALYSIS TO OBTAIN NONLINEAR RESPONSE SO- LUTIONS
365
9.2 THE FINITE ELEMENT DISCRETIZATION OF A SHELL FOR GENERAL NON- LINEAR
ANALYSIS 367
9.3 THE FUNDAMENTAL CONSIDERATIONS OF LINEAR ANALYSIS USED IN NONLINEAR
ANALYSIS 370
9.4 DEMONSTRATIVE SOLUTIONS 372
9.4.1 THE "MYTH OF NO-LOCKING" IN NONLINEAR ANALYSIS OF SHELLS 372
9.4.2 LARGE DEFORMATION ANALYSIS OF A SIMPLY-SUPPORTED PLATE 375 9.4.3
NONLINEAR ANALYSIS OF THICK CANTILEVER BEAM 376 9.4.4 CONTACT ANALYSIS
OF SCORDELIS-LO ROOF 377
9.4.5 CRASH ANALYSIS OF A TUBE * 380
A. TABLES OF SYMBOLS 383
A.I LATIN SYMBOLS 383
A.2 GREEK SYMBOLS 386
A.3 SPECIAL SYMBOLS 387
B. SOME USEFUL MATHEMATICAL FORMULAS 389
C. DISTRIBUTIONS: BASIC DEFINITIONS AND PROPERTIES 391
BIBLIOGRAPHY 395
INDEX 407 |
| any_adam_object | 1 |
| author | Chapelle, Dominique Bathe, Klaus-Jürgen |
| author_facet | Chapelle, Dominique Bathe, Klaus-Jürgen |
| author_role | aut aut |
| author_sort | Chapelle, Dominique |
| author_variant | d c dc k j b kjb |
| building | Verbundindex |
| bvnumber | BV036956512 |
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| classification_tum | MTA 100f MAT 674f |
| ctrlnum | (OCoLC)706968782 (DE-599)DNB1006645039 |
| dewey-full | 624.177620151825 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 624 - Civil engineering |
| dewey-raw | 624.177620151825 |
| dewey-search | 624.177620151825 |
| dewey-sort | 3624.177620151825 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Bauingenieurwesen Mathematik |
| edition | 2. ed. |
| format | Book |
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| spelling | Chapelle, Dominique Verfasser aut The finite element analysis of shells fundamentals Dominique Chapelle ; Klaus-Jürgen Bathe 2. ed. Berlin Springer 2011 XV, 410 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Computational fluid and solid mechanics Technische Mechanik (DE-588)4059231-5 gnd rswk-swf Schale (DE-588)4052003-1 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Schale (DE-588)4052003-1 s Finite-Elemente-Methode (DE-588)4017233-8 s Technische Mechanik (DE-588)4059231-5 s DE-604 Bathe, Klaus-Jürgen Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-16408-8 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3534032&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020871478&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chapelle, Dominique Bathe, Klaus-Jürgen The finite element analysis of shells fundamentals Technische Mechanik (DE-588)4059231-5 gnd Schale (DE-588)4052003-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4059231-5 (DE-588)4052003-1 (DE-588)4017233-8 |
| title | The finite element analysis of shells fundamentals |
| title_auth | The finite element analysis of shells fundamentals |
| title_exact_search | The finite element analysis of shells fundamentals |
| title_full | The finite element analysis of shells fundamentals Dominique Chapelle ; Klaus-Jürgen Bathe |
| title_fullStr | The finite element analysis of shells fundamentals Dominique Chapelle ; Klaus-Jürgen Bathe |
| title_full_unstemmed | The finite element analysis of shells fundamentals Dominique Chapelle ; Klaus-Jürgen Bathe |
| title_short | The finite element analysis of shells |
| title_sort | the finite element analysis of shells fundamentals |
| title_sub | fundamentals |
| topic | Technische Mechanik (DE-588)4059231-5 gnd Schale (DE-588)4052003-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Technische Mechanik Schale Finite-Elemente-Methode |
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