The finite element analysis of shells: fundamentals
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2003
|
| Schriftenreihe: | Computational fluid and solid mechanics
Engineering online library |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 330 S. Ill., graph. Darst. |
| ISBN: | 3540413391 |
Internformat
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| 245 | 1 | 0 | |a The finite element analysis of shells |b fundamentals |c D. Chapelle ; K. J. Bathe |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2003 | |
| 300 | |a XI, 330 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804129440257540096 |
|---|---|
| adam_text | CONTENTS 1. INTRODUCTION
***********************************************************************************************
1 1.1 SHELL STRUCTURES IN ENGINEERING DESIGNS . . . . . . . . . . . . .
. . . . . . . . . . . 1 1.2 THE FINITE ELEMENT ANALYSIS OF SHELLS AS
APPROACHED IN THIS BOOK . 4 2. GEOMETRICAL PRELIMINARIES
***********************************************************************
7 2.1 VECTORS AND TENSORS IN THREE-DIMENSIONAL CURVILINEAR COORDINATES 7
2.1.1 VECTORS AND TENSORS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 7 2.1.2 COVARIANT AND CONTRAVARIANT BASES.
METRIC TENSOR . . . . . . . . . . 9 2.1.3 CURVILINEAR COORDINATE SYSTEMS
. . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.4 COVARIANT
DIFFERENTIATION . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 18 2.2 THE SHELL GEOMETRY . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 21 2.2.1 GEOMETRIC DEFINITION OF A
SHELL . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.2
DIFFERENTIAL GEOMETRY ON THE MIDSURFACE . . . . . . . . . . . . . . . .
. 23 2.2.3 3D DIFFERENTIAL GEOMETRY FOR SHELLS . . . . . . . . . . . . .
. . . . . . . . . 36 3. ELEMENTS OF FUNCTIONAL AND NUMERICAL ANALYSIS
*********************************** 39 3.1 SOBOLEV SPACES AND ASSOCIATED
NORMS . . . . . . . . . . . . . . . . . . . . . . . . 39 3.1.1 GENERAL
CONCEPTS IN VECTOR SPACES . . . . . . . . . . . . . . . . . . . . . . 40
3.1.2 *** AND OTHER SOBOLEV SPACES . . . . . . . . . . . . . . . . . . .
. . . . . . . . 46 3.2 VARIATIONAL FORMULATIONS AND FINITE ELEMENT
APPROXIMATIONS . . . . . 55 3.2.1 BASIC ERROR ESTIMATES FOR
DISPLACEMENT-BASED AND MIXED FORMULATIONS . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2.2 INTERPOLATION
AND A PRIORI ERROR ESTIMATES . . . . . . . . . . . . . . . . 74 3.2.3
EFFECT OF NUMERICAL INTEGRATION . . . . . . . . . . . . . . . . . . . .
. . . . . 79 4. SHELL MATHEMATICAL MODELS
********************************************************************* 81
4.1 SHELL KINEMATICS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 81 4.2 DERIVATION OF SHELL MODELS . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.2.1
THE *BASIC SHELL MODEL* . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 86 4.2.2 THE *SHEAR-MEMBRANE-BENDING MODEL* . . . . . . .
. . . . . . . . . . . 89 4.2.3 THE *MEMBRANE-BENDING MODEL* . . . . . .
. . . . . . . . . . . . . . . . . 90 4.2.4 PLATE MODELS . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.2.5
HIGHER-ORDER SHELL MODELS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 96 4.3 MATHEMATICAL ANALYSIS OF THE SHELL MODELS . . . . . .
. . . . . . . . . . . . . . . 98 X CONTENTS 4.3.1 ANALYSIS OF THE S-M-B
SHELL MODEL . . . . . . . . . . . . . . . . . . . . . . 98 4.3.2
ANALYSIS OF THE M-B SHELL MODEL . . . . . . . . . . . . . . . . . . . .
. . . . 107 4.3.3 ANALYSIS OF THE BASIC SHELL MODEL . . . . . . . . . .
. . . . . . . . . . . . . 109 5. ASYMPTOTIC BEHAVIORS OF SHELL MODELS
*************************************************** 115 5.1 GENERAL
ASYMPTOTIC ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 115 5.2 ANALYSIS OF THE SUBSPACE OF PURE BENDING
DISPLACEMENTS . . . . . . . . . 133 5.2.1 ELLIPTIC SURFACES . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.2.2
HYPERBOLIC SURFACES . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 135 5.2.3 PARABOLIC SURFACES . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 136 5.3 INFLUENCE OF THE
LOADING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 138 5.3.1 EFFECT OF THE LOADINGS THAT DO NOT ACTIVATE THE PURE
BENDING DISPLACEMENTS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 139 5.3.2 EFFECT OF NON-ADMISSIBLE MEMBRANE
LOADINGS . . . . . . . . . . . . . 144 5.4 ASYMPTOTIC ANALYSIS OF THE
BASIC SHELL MODEL . . . . . . . . . . . . . . . . . . 158 5.4.1 THE CASE
OF NON-INHIBITED PURE BENDING . . . . . . . . . . . . . . . . . . 160
5.4.2 THE CASE OF INHIBITED PURE BENDING . . . . . . . . . . . . . . . .
. . . . . . 164 5.4.3 CONCLUSIONS ON THE ASYMPTOTIC ANALYSIS OF THE
BASIC SHELL MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 169 6. DISPLACEMENT-BASED SHELL
FINITE ELEMENTS ********************************************* 171 6.1
DISCRETIZATIONS OF SHELL MATHEMATICAL MODELS . . . . . . . . . . . . . .
. . . . . 171 6.2 FACET-SHELL ELEMENTS . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 176 6.3 GENERAL SHELL
ELEMENTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 179 7. INFLUENCE OF THE THICKNESS IN THE FINITE ELEMENT
APPROXIMATION ******* 207 7.1 NUMERICAL LOCKING IN THIN STRUCTURES . . .
. . . . . . . . . . . . . . . . . . . . . . 208 7.2 TREATMENTS OF
NUMERICAL LOCKING BY MIXED FORMULATIONS . . . . . . . . 214 7.2.1 BASIC
PRINCIPLES: THE TIMOSHENKO BEAM EXAMPLE . . . . . . . . . . 215 7.2.2
APPLICATIONS TO THE REISSNER-MINDLIN PLATE MODEL . . . . . . . . . 222
7.2.3 BASIC PRINCIPLES OF STABILIZED MIXED FORMULATIONS . . . . . . . .
. 240 7.2.4 MITC PLATE ELEMENTS . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 245 7.3 SPECIFIC DIFFICULTIES ARISING IN THE
ANALYSIS OF SHELLS . . . . . . . . . . . . . 252 8. TOWARDS THE
FORMULATION OF EFFECTIVE GENERAL SHELL ELEMENTS *********** 263 8.1
GUIDELINES FOR ASSESSING AND IMPROVING THE RELIABILITY OF SHELL FINITE
ELEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 263 8.1.1 CONSIDERATIONS ON PROPER SELECTION AND
USE OF TEST PROBLEMS 263 8.1.2 PROPOSED SET OF TEST PROBLEMS . . . . . .
. . . . . . . . . . . . . . . . . . . . 270 8.2 FORMULATION OF MITC
SHELL ELEMENTS AND SOME ASSESSMENT RESULTS273 8.2.1 FORMULATION . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 274 8.2.2 ASSESSMENT RESULTS . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 280 CONTENTS XI 9. ON THE NONLINEAR ANALYSIS
OF SHELLS ******************************************************* 293
9.1 THE INCREMENTAL ANALYSIS TO OBTAIN NONLINEAR RESPONSE SOLUTIONS .
293 9.2 THE FINITE ELEMENT DISCRETIZATION OF A SHELL FOR GENERAL
NONLINEAR ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 295 9.3 THE FUNDAMENTAL
CONSIDERATIONS OF LINEAR ANALYSIS USED IN NON- LINEAR ANALYSIS . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 298 9.4 DEMONSTRATIVE SOLUTIONS . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 300 9.4.1 CONTACT ANALYSIS OF
SCORDELIS-LO ROOF . . . . . . . . . . . . . . . . . . . 300 9.4.2
NONLINEAR DEFORMATION ANALYSIS OF A SIMPLY-SUPPORTED PLATE . 301 A.
TABLES OF SYMBOLS
*************************************************************************************
305 A.1 LATIN SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 305 A.2 GREEK SYMBOLS . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 308 A.3 SPECIAL SYMBOLS . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 309 B. SOME USEFUL
MATHEMATICAL FORMULAS *
*************************************************** 311 C.
DISTRIBUTIONS: BASIC DEFINITIONS AND PROPERTIES *
*********************************** 313 REFERENCES
*********************************************************************************************************
317 INDEX
*******************************************************************************************************************
327
|
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| indexdate | 2024-07-09T19:05:10Z |
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| isbn | 3540413391 |
| language | English |
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| physical | XI, 330 S. Ill., graph. Darst. |
| publishDate | 2003 |
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| spelling | Chapelle, Dominique Verfasser aut The finite element analysis of shells fundamentals D. Chapelle ; K. J. Bathe Berlin [u.a.] Springer 2003 XI, 330 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computational fluid and solid mechanics Engineering online library Cascas (engenharia) larpcal Método dos elementos finitos larpcal Finite element method Shells (Engineering) Schale (DE-588)4052003-1 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Technische Mechanik (DE-588)4059231-5 gnd rswk-swf Schale (DE-588)4052003-1 s Finite-Elemente-Methode (DE-588)4017233-8 s Technische Mechanik (DE-588)4059231-5 s 1\p DE-604 Bathe, Klaus-Jürgen Verfasser aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009965405&sequence=000001&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 | Chapelle, Dominique Bathe, Klaus-Jürgen The finite element analysis of shells fundamentals Cascas (engenharia) larpcal Método dos elementos finitos larpcal Finite element method Shells (Engineering) Schale (DE-588)4052003-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Technische Mechanik (DE-588)4059231-5 gnd |
| subject_GND | (DE-588)4052003-1 (DE-588)4017233-8 (DE-588)4059231-5 |
| 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 D. Chapelle ; K. J. Bathe |
| title_fullStr | The finite element analysis of shells fundamentals D. Chapelle ; K. J. Bathe |
| title_full_unstemmed | The finite element analysis of shells fundamentals D. Chapelle ; K. J. Bathe |
| title_short | The finite element analysis of shells |
| title_sort | the finite element analysis of shells fundamentals |
| title_sub | fundamentals |
| topic | Cascas (engenharia) larpcal Método dos elementos finitos larpcal Finite element method Shells (Engineering) Schale (DE-588)4052003-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Technische Mechanik (DE-588)4059231-5 gnd |
| topic_facet | Cascas (engenharia) Método dos elementos finitos Finite element method Shells (Engineering) Schale Finite-Elemente-Methode Technische Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009965405&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT chapelledominique thefiniteelementanalysisofshellsfundamentals AT batheklausjurgen thefiniteelementanalysisofshellsfundamentals |