Asymptotical mechanics of thin walled structures:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin
Springer
2004
|
| Series: | Foundations of engineering mechanics
Engineering online library |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 535 S. graph. Darst. |
| ISBN: | 3540408762 |
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Record in the Search Index
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| adam_text | I. V. ANDRIANOV * J. AWREJCEWICZ * L. I. MANEVITCH ASYMPTOTICAL
MECHANICS OF THIN-WALLED STRUCTURES WITH 91 FIGURES AND 30 TABLES
SPRINGER TABLE OF CONTENTS PREFACE 15 ACKNOWLEDGMENTS 17 1 ASYMPTOTIC
APPROXIMATIONS 19 1.1 ASYMPTOTIC SERIES 19 1.2 FUNDAMENTAL CONCEPTS OF
ASYMPTOTICS [129] 21 1.3 TRANSFORMATIONS OF ASYMPTOTICAL SERIES [129] 23
1.4 NONUNIFORM EXPANSIONS [129] 25 1.5 NON-DIMENSIONALIZATION 27 1.6
ASYMPTOTICS OF INTEGRALS [129] 29 2 REGULAR PERTURBATIONS OF PARAMETERS
47 2. 1 EIGENVALUE PROBLEMS 47 2.2 STABILITY OF OVAL CYLINDRICAL SHELL
UNIFORMLY LOADED BY EXTERNAL PRESSURE 58 2.3 STABILITY OF THE CANTILEVER
BEAM 60 2.4 ADJOINT OPERATORS METHOD 62 2.5 TRANSFORMATION OF
COORDINATES AND VARIABLES 65 2.6 ASYMPTOTIC AND REAL ERROR 71 2.7
NUMERICAL VERIFICATION OF ASYMPTOTIC SOLUTION 75 2.8 REMOVAL OF
NONUNIFORMITIES 77 2.9 NONLINEAR VIBRATIONS OF A STRINGER SHELL 81 2.10
NON-QUASILINEAR ASYMPTOTICS OF NONLINEAR SYSTEM 84 2.11 ARTIFICIAL SMALL
PARAMETERS 88 2.12 METHOD OF SMALL 5 91 2.13 METHOD OF LARGE 5 94 2.14
CHOICE OF ZERO APPROXIMATION 98 2.15 LYAPUNOV-SCHMIDT PROCEDURE 101 2.16
NONLINEAR PERIODICAL VIBRATIONS OF CONTINUOUS STRUCTURES 103 3 SINGULAR
PERTURBATION PROBLEMS 117 3.1 THE METHOD OF
GOL DENVEIZER-VISHIK-LYUSTERNIK [313, 645, 672, 673, 674] 117 3.2
MULTISCALE METHOD 122 8 TABLE OF CONTENTS 3.3 NEWTON POLYGON AND
ASYMPTOTIC INTEGRATION PARAMETERS 125 3.4 STRETCHED PLATE BENDING 131
3.5 SIMPLIFICATION OF THE STATIC EQUATIONS OF A CYLINDRICAL SHELL 133
3.6 BOUNDARY LAYER: PAPKOVITCH APPROACH 136 3.7 EDGE BOUNDARY LAYER 138
3.8 INCORPORATING OF THE SINGULAR PART OF SOLUTION 140 3.9 PLANE THEORY
OF ELASTICITY 140 3.10 ASYMPTOTIC FOUNDATION MODEL 144 3.11 VIBRATIONS
OF REINFORCED CONICAL SHELLS 149 4 BOUNDARY VALUE PROBLEMS OF ISOTROPIC
CYLINDRICAL SHELLS 157 4.1 GOVERNING RELATIONS 157 4.2 OPERATOR METHOD
159 4.3 SIMPLIFIED BOUNDARY VALUE PROBLEMS 160 5 BOUNDARY VALUE PROBLEMS
- ORTHOTROPIC SHELLS ... 169 5.1 GOVERNING RELATIONS 169 5.2 STATICAL
PROBLEMS 173 5.3 NON-LINEAR DYNAMICAL PROBLEMS 182 5.4 STABILITY
PROBLEMS 189 5.5 ERROR ESTIMATION USING NEWTON S METHOD 197 6 COMPOSITE
BOUNDARY VALUE PROBLEMS - ISOTROPIC SHELLS 201 6.1 STATICAL PROBLEMS 202
6.2 EQUATIONS OF HIGHER ORDER APPROXIMATIONS 206 6.3 ERROR ESTIMATION
208 6.4 DYNAMICAL PROBLEMS 211 6.5 NON-LINEAR DYNAMICAL PROBLEMS 217 7
COMPOSITE BOUNDARY VALUE PROBLEMS - ORTHOTROPIC SHELLS 223 7. 1 STATICAL
PROBLEMS 223 7.2 DYNAMICAL PROBLEMS 234 7.3 NON-LINEAR DYNAMICAL
PROBLEMS 235 7.4 STABILITY PROBLEMS 239 8 AVERAGING 241 8.1 TWO-SCALES
APPROACH 241 8.2 VISCO-ELASTIC PROBLEMS AND FREEZING METHOD 244 8.3
THE SUCCESSIVE CHANGE OF VARIABLES 246 8.4 APPLICATION OF THE LIE GROUPS
249 8.5 WHITHAM METHOD (NON-LINEAR WKB APPROACH) 256 TABLE OF CONTENTS 9
9 CONTINUALIZATION 259 10 HOMOGENIZATION 267 10.1 ODES WITH RAPIDLY
OSCILLATING COEFFICIENTS 267 10.2 AXISYMMETRIC BENDING OF CORRUGATED
CIRCLE PLATE 272 10.3 DEFORMATION OF REINFORCED MEMBRANE 276 10.4 RIBBED
STRIP - TWO-SCALE AND FOURIER HOMOGENIZATION 280 10.5 RIBBED PLATE -
DIRECT HOMOGENIZATION 284 10.6 PERFORATED MEMBRANE 292 10.7 COMPOSITE
WITH PERIODIC CUBIC INCLUSIONS 302 10.8 TORSION OF BAR WITH PERIODIC
PARALLELEPIPED INCLUSIONS 307 10.9 SOLUTION OF CELL PROBLEM:
PERTURBATION OF BOUNDARY FORM 313 10.10 LINEAR VIBARTIONS OF A BEAM WITH
CONCENTRATED MASSES AND DISCRETE SUPPORTS 319 11 INTERMEDIATE
ASYMPTOTICS - DYNAMICAL EDGE EFFECT METHOD 333 11.1 LINEAR PRELIMINARIES
333 11.2 NONLINEAR BEAM VIBRATIONS 336 11.3 NONLINEAR RECTANGULAR PLATE
VIBRATIONS 340 11.4 NONLINEAR SHALLOW SHELL VIBRATIONS 345 11.5
RAYLEIGH-RITZ-BOLOTIN APPROACH 353 11.6 PARALLELOGRAM PLATE VIBRATIONS
357 11.7 SECTORIAL PLATE NONLINEAR VIBRATIONS 360 12 LOCALIZATION 363
12.1 LOCALIZATION IN LINEAR CHAINS 363 12.2 LOCALIZATION IN NONLINEAR
CHAIN 370 12.3 LOCALIZATION OF SHELL BUCKLING 372 12.4 LOCALIZATION OF
VIBRATION IN PLATES AND SHELLS 373 13 IMPROVEMENT OF PERTURBATION SERIES
377 13.1 PADE APPROXIMANTS (PA) 377 13.2 THE EFFECT OF AUTOCORRECTION
379 13.3 EXTENDING OF PERTURBATION SERIES 381 13.4 IMPROVEMENT
ITERATIONAL PROCEDURES CONVERGENCE 384 13.5 NONUNIFORMITIES ELIMINATION
387 13.6 ERROR ESTIMATION OF ASYMPTOTIC APPROACHES 388 13.7 LOCALIZED
SOLUTIONS AND BLOW-UP PHENOMENON 388 13.8 GIBBS PHENOMENA 389 13.9
BOUNDARY CONDITIONS PERTURBATION METHOD 392 13.10 BIFURCATION PROBLEM
401 13.11 BOREL SUMMATION AND SUPERASYMPTOTICS 402 13.12 DOMB-SYKES PLOT
[340, 659] 404 13.13 EXTRACTION OF SINGULARITIES FROM PERTURBATION
SERIES [340, 659].... 406 10 TABLE OF CONTENTS 13.14 ANALYTICAL
CONTINUATION [407] 409 14 MATCHING OF LIMITING ASYMPTOTIC EXPANSIONS 417
14.1 TWO-POINT PADE APPROXIMANTS 417 14.2 QUASIFRACTIONAL APPROXIMANTS
424 14.3 POST-BUCKLING BEHAVIOUR OF SHALLOW CONVEX SHELL 429 15 COMPLEX
VARIABLES IN NONLINEAR DYNAMICS 435 15.1 NONLINEAR OSCILLATOR WITH CUBIC
ANHARMONICITY 436 15.2 SYSTEM OF TWO WEAKLY COUPLED NONLINEAR
OSCILLATORS 447 15.3 NONJINEAR DYNAMICS OF AN INFINITE CHAIN OF COUPLED
OSCILLATORS.... 453 15.4 NONLINEAR DYNAMICS OF AN INFINITE CHAIN OF
COUPLED PARTICLES 460 16 OTHER ASYMPTOTICAL APPROACHES 463 16.1 MATCHED
ASYMPTOTIC PROCEDURE 463 16.2 HILBERT TRANSFORM 465 16.3 NORMAL FORMS IN
NON-LINEAR PROBLEMS 467 16.4 WKB - APPROACH 470 16.5 THE WKB METHOD AND
TURNING POINTS 473 16.6 A DISTRIBUTIONAL APPROACH 478 AFTERWORD 483
ASYMPTOTICS AND COMPUTERS 483 ARE ASYMPTOTIC METHODS A PANACEA? 485
REFERENCES 489 SUBJECT INDEX 529
|
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| author | Andrianov, I. V. 1948- Awrejcewicz, Jan 1952- Manevič, Leonid I. 1938- |
| author_GND | (DE-588)120089106 (DE-588)120089122 (DE-588)120089157 |
| author_facet | Andrianov, I. V. 1948- Awrejcewicz, Jan 1952- Manevič, Leonid I. 1938- |
| author_role | aut aut aut |
| author_sort | Andrianov, I. V. 1948- |
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| indexdate | 2024-07-09T19:18:06Z |
| institution | BVB |
| isbn | 3540408762 |
| language | German |
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| physical | 535 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | Springer |
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| series2 | Foundations of engineering mechanics Engineering online library |
| spelling | Andrianov, I. V. 1948- Verfasser (DE-588)120089106 aut Asymptotical mechanics of thin walled structures I. V. Andrianov ; J. Awrejcewicz ; L. I. Manevitch Berlin Springer 2004 535 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Foundations of engineering mechanics Engineering online library Asymptotic expansions Thin-walled structures Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Dünne Schale (DE-588)4150826-9 gnd rswk-swf Dünnwandiges Bauelement (DE-588)4210413-0 gnd rswk-swf Platte (DE-588)4046304-7 gnd rswk-swf Dünne Schale (DE-588)4150826-9 s Asymptotische Methode (DE-588)4287476-2 s DE-604 Platte (DE-588)4046304-7 s Dünnwandiges Bauelement (DE-588)4210413-0 s Awrejcewicz, Jan 1952- Verfasser (DE-588)120089122 aut Manevič, Leonid I. 1938- Verfasser (DE-588)120089157 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010510877&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andrianov, I. V. 1948- Awrejcewicz, Jan 1952- Manevič, Leonid I. 1938- Asymptotical mechanics of thin walled structures Asymptotic expansions Thin-walled structures Asymptotische Methode (DE-588)4287476-2 gnd Dünne Schale (DE-588)4150826-9 gnd Dünnwandiges Bauelement (DE-588)4210413-0 gnd Platte (DE-588)4046304-7 gnd |
| subject_GND | (DE-588)4287476-2 (DE-588)4150826-9 (DE-588)4210413-0 (DE-588)4046304-7 |
| title | Asymptotical mechanics of thin walled structures |
| title_auth | Asymptotical mechanics of thin walled structures |
| title_exact_search | Asymptotical mechanics of thin walled structures |
| title_full | Asymptotical mechanics of thin walled structures I. V. Andrianov ; J. Awrejcewicz ; L. I. Manevitch |
| title_fullStr | Asymptotical mechanics of thin walled structures I. V. Andrianov ; J. Awrejcewicz ; L. I. Manevitch |
| title_full_unstemmed | Asymptotical mechanics of thin walled structures I. V. Andrianov ; J. Awrejcewicz ; L. I. Manevitch |
| title_short | Asymptotical mechanics of thin walled structures |
| title_sort | asymptotical mechanics of thin walled structures |
| topic | Asymptotic expansions Thin-walled structures Asymptotische Methode (DE-588)4287476-2 gnd Dünne Schale (DE-588)4150826-9 gnd Dünnwandiges Bauelement (DE-588)4210413-0 gnd Platte (DE-588)4046304-7 gnd |
| topic_facet | Asymptotic expansions Thin-walled structures Asymptotische Methode Dünne Schale Dünnwandiges Bauelement Platte |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010510877&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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