Nonlinear theory of shallow shells:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Deutsch |
| Veröffentlicht: |
New York
Springer
1999
|
| Schriftenreihe: | Applied mathematical sciences
133 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008428542&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Aus dem Russ. übers. |
| Umfang: | XVI, 388 S. graph. Darst. |
| ISBN: | 0387983392 |
Internformat
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| 245 | 1 | 0 | |a Nonlinear theory of shallow shells |c I. I. Vorovich |
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Datensatz im Suchindex
| _version_ | 1819324807011893248 |
|---|---|
| adam_text | LI. VOROVICH NONLINEAR THEORY OF SHALLOW SHELLS ENGLISH EDITION EDITED
BY L.P. LEBEDEV TRANSLATED BY MICHAEL GRINFELD WITH 46 ILLUSTRATIONS
SPRINGER CONTENTS PREFACE TO THE ENGLISH EDITION V PREFACE TO THE
RUSSIAN EDITION VI FROM THE EDITOR X I THE MAIN BOUNDARY VALUE PROBLEMS
IN THE NONLINEAR THEORY OF SHALLOW SHELLS 1 1. RESULTS FROM THE THEORY
OF SURFACES 1 2. S-COORDINATES IN SPACE. FORMATION OF A SHELL.
COMPONENTS OF FINITE DEFORMATION IN 5-COORDINATES AND THEIR
SIMPLIFICATION . 14 3. THE KIRCHHOFF-LOVE HYPOTHESES. THEIR MATHEMATICAL
AND MECHANICAL CONTENT. COMPUTATION OF DEFORMATIONS OF A SHALLOW SHELL
USING THE KIRCHHOFF-LOVE HYPOTHESES 19 4. POTENTIALENERGY OF DEFORMATION
OF A SHALLOW SHELL 26 5. INDEPENDENT DISPLACEMENTS, GENERALIZED STRESSES
AND THE WORK OF EXTERNAL FORCES UNDER THE KIRCHHOFF-LOVE HYPOTHESES 33
6. BOUNDARY VALUE PROBLEMS IN DISPLACEMENTS OF THE MODERATE BENDING
THEORY FOR SHALLOW SHELLS 36 7. BOUNDARY VALUE PROBLEMS WITH AIRY STRESS
FUNCTION IN THE MODERATE BENDING THEORY FOR SHALLOW SHELLS 44 8. SOME
REMARKS ON NONLINEAR SHALLOW SHELL THEORY. A HISTORICAL SURVEY - 56 II
GENERAL MATHEMATICAL QUESTIONS 60 9. SOME GENERAL MATHEMATICAL RESULTS
60 XIV CONTENTS 10. GENERAL MATHEMATICAL RESULTS (CONTINUED) 73 11. THE
FUNCTION SPACES H,, T * 5, 6, 7, 8. PROPERTIES OF THEIR ELEMENTS 82 12.
THE FUNCTION SPACES H K , K = 1, 2, 3, 4. PROPERTIES OF THEIR ELEMENTS
96 III TOPOLOGICAL METHODS APPLIED TO SOLVABILITY OF THE MAIN BOUNDARY
VALUE PROBLEMS OF THE NONLINEAR THEORY OF SHALLOW SHELLS IN
DISPLACEMENTS 107 13. THE GENERALIZED FORMULATION OF BOUNDARY VALUE
PROBLEMS IN DISPLACEMENTS. REDUCTION TO OPERATOR EQUATIONS. THE PHYSICAL
MEANING OF GENERALIZED SOLUTIONS 107 14. SOME PROPERTIES OF THE
OPERATORS K IIC , G KK 116 15. COMPUTATION OF THE WINDING NUMBER OF THE
VECTOR FIELD W R- G/ACIW) ON SPHERES OF LARGE RADIUS IN H K :
PRELIMINARY LEMMAS 123 16. COMPUTATION OF THE WINDING NUMBER OF THE
VECTOR FIELD W * G^W) ON SPHERES OF LARGE RADIUS IN H K . SOLVABILITY OF
THE MAIN BOUNDARY VALUE PROBLEMS IN DISPLACEMENTS 130 IV THE TOPOLOGICAL
METHOD IN THE PROBLEM OF SOLVABILITY OF THE MAIN BOUNDARY VALUE PROBLEMS
IN THE NONLINEAR THEORY OF SHALLOW SHELLS WITH AN AIRY STRESS FUNCTION
145 17. THE GENERALIZED FORMULATION OF THE BOUNDARY VALUE PROBLEMS OF
SHALLOW SHELLS WITH AN AIRY STRESS FUNCTION. REDUCTION TO OPERATOR
EQUATIONS. PHYSICAL INTERPRETATION OF GENERALIZED SOLUTIONS 145 18. MAIN
PROPERTIES OF THE OPERATORS K 9IC (W), G K (W) 153 19. COMPUTATION OF
THE WINDING NUMBER OF THE VECTOR FIELD W * G K (W) ON SPHERES OF LARGE
RADIUS IN H K . SOLVABILITY OF THE MAIN BOUNDARY VALUE PROBLEMS OF THE
THEORY OF SHALLOW SHELLS WITH AN AIRY STRESS FUNCTION 159 20.
DIFFERENTIABILITY PROPERTIES OF GENERALIZED SOLUTIONS OF THE PROBLEMS
TIC AND 9K. CONDITIONS FOR THE EXISTENCE OF CLASSICAL SOLUTIONS 169 V
THE VARIATIONAL APPROACH TO THE PROBLEM OF SOLVABILITY OF BOUNDARY VALUE
PROBLEMS OF NONLINEAR SHALLOW SHELL THEORY 181 21. THE VARIATIONAL
APPROACH TO THE PROBLEM OF SOLVABILITY OF BOUNDARY VALUE PROBLEMS OF
NONLINEAR SHALLOW SHELL THEORY IN DISPLACEMENTS 181 22. THE VARIATIONAL
APPROACH TO THE PROBLEM OF SOLVABILITY OF BOUNDARY VALUE PROBLEMS OF
NONLINEAR SHALLOW SHELL THEORY WITH AN AIRY STRESS FUNCTION 195 CONTENTS
XV VI NUMERICAL-ANALYTICAL METHODS IN THE NONLINEAR THEORY OF SHALLOW
SHELLS 206 23. EXPANSION IN POWERS OF A SMALL-PARAMETER (NONSINGULAR
SOLUTIONS) 206 24. EXPANSION IN POWERS OF A SMALL-PARAMETER (SINGULAR
SOLUTIONS). THE LIAPUNOV-SCHMIDT METHOD 212 25. THE NEWTON-KANTOROVICH
METHOD 219 VII DIRECT METHODS IN THE NONLINEAR THEORY OF SHALLOW SHELLS
229 26. VARIATIONAL METHODS FOR APPROXIMATE SOLUTIONS OF PROBLEMS TIC (K
= 1, 2, 3, 4; T = 5, 6, 7, 8). THE VERSION OF PAPKOVICH . 229 27. THE
BUBNOV-GALERKIN-RITZ METHOD FOR APPROXIMATE SOLUTION OF PROBLEMS TIC (K
- 1, 2, 3, 4; T = 5, 6, 7, 8). THE VERSIONS OF MUSHTARI AND VLASOV 240
28. ERROR ESTIMATES FOR THE BUBNOV-GALERKIN-RITZ (BGR) METHOD IN SOME
PROBLEMS OF THE NONLINEAR THEORY OF SHALLOW SHELLS . 251 VIII
FORMULATION OF THE PROBLEM OF STABILITY. GLOBAL UNIQUENESS OF SOLUTIONS.
STIFFNESS OF SHELLS. WELL-POSEDNESS CLASSES 263 29. FORMULATION OF THE
PROBLEM OF STABILITY IN THE NONLINEAR THEORY OF SHALLOW SHELLS. LOCAL
UNIQUENESS OF SOLUTIONS. CONDITIONS FOR GLOBAL UNIQUENESS 263 30.
PHYSICAL STIFFNESS OF SHELLS. CONNECTION WITH GEOMETRICAL STIFFNESS OF
THE MIDDLE SURFACE 273 31. WELL-POSEDNESS OF PROBLEMS OF THE NONLINEAR
THEORY OF SHALLOW SHELLS: ITS RELATION TO PHYSICAL STABILITY 281 IX
STABILITY IN THE LARGE OF THE MEMBRANE STATE OF A SHALLOW SHELL.
EXISTENCE OF THE LOWER CRITICAL VALUE 296 32. MOMENTLESS STATE OF
SHELLS. PASSAGE TO THE LINEARIZED PROBLEM. SPECTRAL PROPERTIES OF THE
LINEARIZED PROBLEM .... 296 33. GLOBAL STABILITY OF SHELLS IN PROBLEMS
TIC. EXISTENCE OF LOWER CRITICAL NUMBERS. SOME ESTIMATES FOR
(/-DECOMPOSITIONS . . . 306 34. GLOBAL STABILITY OF SHELLS IN PROBLEMS
9K . EXISTENCE OF LOWER CRITICAL VALUES. SOME ESTIMATES FOR
(/-DECOMPOSITIONS .... 320 35. BIFURCATION OF SOLUTIONS IN A
NEIGHBORHOOD OF THE MOMENTLESS STATE 325 36. VARIATIONAL METHODS IN
GLOBAL STABILITY OF SHALLOW SHELLS ... 330 37. SOME PROBLEMS OF GLOBAL
STABILITY OF PLATES 336 X A PROBABILISTIC APPROACH TO THE PROBLEM OF
STABILITY OF SHALLOW SHELLS 343 38. A PROBABILISTIC MODEL OF OPERATIONS
OF A SHALLOW SHELL UNDER MODERATE BENDING 343 XVI CONTENTS SOME UNSOLVED
PROBLEMS OF THE MATHEMATICAL THEORY OF SHELLS 353 REFERENCES 355 LIST OF
SYMBOLS 375 INDEX 381
|
| any_adam_object | 1 |
| author | Vorovič, Iosif I. 1920-2001 |
| author_GND | (DE-588)120780178 |
| author_facet | Vorovič, Iosif I. 1920-2001 |
| author_role | aut |
| author_sort | Vorovič, Iosif I. 1920-2001 |
| author_variant | i i v ii iiv |
| building | Verbundindex |
| bvnumber | BV012421573 |
| classification_rvk | SK 950 |
| ctrlnum | (OCoLC)439176313 (DE-599)BVBBV012421573 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012421573 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:30:00Z |
| institution | BVB |
| isbn | 0387983392 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008428542 |
| oclc_num | 439176313 |
| open_access_boolean | |
| owner | DE-703 DE-83 |
| owner_facet | DE-703 DE-83 |
| physical | XVI, 388 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spellingShingle | Vorovič, Iosif I. 1920-2001 Nonlinear theory of shallow shells Applied mathematical sciences Randwertproblem (DE-588)4048395-2 gnd Schale (DE-588)4052003-1 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4052003-1 (DE-588)4042095-4 |
| title | Nonlinear theory of shallow shells |
| title_auth | Nonlinear theory of shallow shells |
| title_exact_search | Nonlinear theory of shallow shells |
| title_full | Nonlinear theory of shallow shells I. I. Vorovich |
| title_fullStr | Nonlinear theory of shallow shells I. I. Vorovich |
| title_full_unstemmed | Nonlinear theory of shallow shells I. I. Vorovich |
| title_short | Nonlinear theory of shallow shells |
| title_sort | nonlinear theory of shallow shells |
| topic | Randwertproblem (DE-588)4048395-2 gnd Schale (DE-588)4052003-1 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd |
| topic_facet | Randwertproblem Schale Nichtlineare Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008428542&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT voroviciosifi nonlineartheoryofshallowshells |