Mathematical elasticity 3 Theory of shells
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| Format: | Buch |
| Sprache: | English |
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Amsterdam u.a.
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2000
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| Ausgabe: | 1. ed. |
| Schriftenreihe: | Studies in mathematics and its applications
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| 245 | 1 | 0 | |a Mathematical elasticity |n 3 |p Theory of shells |c Philippe G. Ciarlet |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Amsterdam u.a. |b North-Holland |c 2000 | |
| 300 | |a LX, 599 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 PHY 210f 2001 A 11710 |
|---|---|
| DE-BY-TUM_katkey | 1196318 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020261061 |
| DE-BY-UBR_call_number | 805/UF 3000 C566 |
| DE-BY-UBR_katkey | 3260157 |
| DE-BY-UBR_media_number | TEMP11822517 |
| _version_ | 1822696474857701377 |
| adam_text | Titel: Bd. 3. Mathematical elasticity. Theory of shells
Autor: Ciarlet, Philippe G
Jahr: 2000
TABLE OF CONTENTS1
Mathematical Elasticity: General plan........... ii
Mathematical Elasticity: General preface......... v
Preface to Volume I....................... ix
Preface to Volume II...................... xv
Preface to Volume III.....................xxvii
Differential geometry at a glance..............xxxix
Three-dimensional elasticity in curvilinear coordinates at
a glance.......................xlvii
Two-dimensional linear shell equations at a glance ... Ii
Two-dimensional nonlinear shell equations at a glance . lvii
PART A. LINEAR SHELL THEORY
Chapter 1. Three-dimensional linearized elasticity and
Korn s inequalities in curvilinear coordinates 3
Introduction....................... 3
1.1. Three-dimensional linearized elasticity in Cartesian
coordinates........................ 5
1.2. Curvilinear coordinates and metric tensor in a three-
dimensional domain................... 12
1.3. The variational equations of three-dimensional linea-
rized elasticity in curvilinear coordinates....... 22
1.4. Covariant derivatives and Christoffel symbols in a three-
dimensional domain................... 32
1.5. Linearized change of metric tensor in curvilinear co-
ordinates ......................... 35
1.6. The boundary value problem of three-dimensional lin-
earized elasticity in curvilinear coordinates...... 37
The symbol indicates a section where most results are stated without proof.
1.7. A lemma of J. L. Lions; three-dimensional Korn s in-
equalities and infinitesimal rigid displacement lemma
in curvilinear coordinates................ 40
1.8. Existence and uniqueness theorem in curvilinear co-
ordinates ......................... 50
1.9V. Complement: Recovery of a three-dimensional mani-
fold from its metric tensor field............. 54
Exercises......................... 56
Chapter 2. Inequalities of Korn s type on surfaces ... CI
Introduction....................... 61
2.1. Curvilinear coordinates and metric tensor on a surface 03
2.2. Curvature tensor on a surface ............. 73
2.3. Covariant derivatives and Christoffel symbols on a
surface.......................... 85
2.4. Linearized change of metric tensor on a surface .... 90
2.5. Linearized change of curvature tensor on a surface . . 93
2.6. Inequalities of Korn s type and infinitesimal rigid dis-
placement lemma on a general surface......... 100
2.7. Inequality of Korn s type and infinitesimal rigid dis-
placement lemma on an elliptic surface........ 117
2.8 . Complement: Recovery of a surface from its metric
and curvature tensor fields............... 130
Exercises......................... 132
Chapter 3. Asymptotic analysis of linearly elastic shells:
Preliminaries and outline............137
Introduction.......................137
3.1. The three-dimensional equations of a linearly elastic
shell............................141
3.2. The three-dimensional equations over a domain inde-
pendent of e...................... . 149
3.3. Geometrical and mechanical preliminaries.......154
3.4. The two-dimensional equations of linearly elastic mem-
brane and flexural shells derived by means of a
formal asymptotic analysis...............161
3.5. Summary of the convergence theorems.........183
Exercises.........................190
Chapter 4. Linearly elastic elliptic membrane shells . . 193
Introduction.......................193
4.1. Linearly elastic elliptic membrane shells: Definition,
example, and assumptions on the data; the three-
dimensional equations over a domain independent
ofe............................196
4.2. Averages with respect to the transverse variable . . . 201
4.3. A three-dimensional inequality of Korn s type for a
family of linearly elastic elliptic membrane shells . . . 205
4.4. Convergence of the scaled displacements as e ? 0 . . 209
4.5. The two-dimensional equations of a linearly elastic el-
liptic membrane shell; existence, uniqueness, and reg-
ularity of solutions; formulation as a boundary value
problem..........................223
4.6. Justification of the two-dimensional equations of a lin-
early elastic elliptic membrane shell; commentary and
refinements........................230
Exercises.........................235
Chapter 5. Linearly elastic generalized membrane
shells.........................241
Introduction.......................241
5.1. Linearly elastic generalized membrane shells: Defini-
tion and assumptions on the data; the three-dimensional
equations over a domain independent of e.......245
5.2. Analytical preliminaries.................248
5.3. A three-dimensional inequality of Korn s type for a
family of linearly elastic shells.............258
5.4. Generalized membrane shells of the first and second
kinds...........................261
5.5. Admissible applied forces................264
5.6. Convergence of the scaled displacements as e -» 0 . . 266
5.7. The two-dimensional equations of a linearly elastic
generalized membrane shell; existence and uniqueness
of solutions........................287
5.8. Justification of the two-dimensional equations of a lin-
early elastic generalized membrane shell; examples,
commentary, and refinements..............291
Exercises.........................297
Chapter 6. Linearly elastic flexural shells.........299
Introduction.......................299
6.1. Linearly elastic flexural shells: Definition, examples,
and assumptions on the data; the three-dimensional
equations over a domain independent of e.......302
6.2. Convergence of the scaled displacements as e -- 0 . 308
6.3. The two-dimensional equations of a linearly elastic
flexural shell; existence and uniqueness of solutions . 317
6.4. Justification of the two-dimensional equations of a lin-
early elastic flexural shell; commentary and refine-
ments ...........................323
Exercises.........................328
Chapter 7. Koiter s equations and other two-dimensional
linear shell theories................333
Introduction.......................333
7.1. The two-dimensional Koiter equations for a linearly
elastic shell: Existence, uniqueness, and regularity of
solutions; formulation as a boundary value problem . 335
7.2. Justification of Koiter s equations for all types of lin-
early elastic shells....................345
7.3. Koiter s equations: Additional commentary and bib-
liographical notes ....................360
7.4. The two-dimensional Naghdi equations for a linearly
elastic shell; existence and uniqueness of solutions . . 363
7.5. Other linear shell theories................367
7.6. Linear shallow shell theories..............369
Exercises.........................372
PART B. NONLINEAR SHELL THEORY
Chapter 8. Asymptotic analysis of nonlinearly elastic shells:
Preliminaries.................... 381
Introduction....................... 381
8.1. Three-dimensional nonlinear elasticity in Cartesian co-
ordinates ......................... 386
8.2. Three-dimensional nonlinear elasticity in curvilinear
coordinates........................ 392
8.3. The three-dimensional equations of a nonhnearly elas-
tic shell..........................403
8.4. The three-dimensional equations over a domain inde-
pendent of e.......................407
8.5. Geometrical and mechanical preliminaries.......411
8.6. The method of formal asymptotic expansions.....413
8.7. The leading term is of order zero............415
8.8. Identification of a two-dimensional variational prob-
lem satisfied by the leading term............424
Exercises.........................430
Chapter 9. Nonlinearly elastic membrane shells.....433
Introduction.......................433
9.1. Nonlinearly elastic membrane shells: Definition, ex-
amples, and assumptions on the data.........436
9.2. The two-dimensional equations as a variational prob-
lem ............................443
9.3. The two-dimensional equations as a minimization prob-
lem ............................445
9.4. The two-dimensional equations of a nonlinearly elastic
membrane shell derived by means of a formal asymp-
totic analysis; commentary...............447
9.5. The two-dimensional equations of a nonlinearly elastic
membrane shell derived by means of T-convergence
theory; commentary...................453
Exercises.........................465
Chapter 10. Nonlinearly elastic flexural shells......469
Introduction.......................469
10.1. Identification of a two-dimensional variational prob-
lem satisfied by the leading term when there are nonzero
admissible inextensional displacements ........472
10.2. Nonhnearly elastic flexural shells: Definition, exam-
ples, and assumptions on the data...........502
10.3. The two-dimensional equations as a variational prob-
lem ............................507
10.4. The two-dimensional equations as a minimization prob-
lem ............................519
10.5. The two-dimensional equations of a nonlinearly elastic
flexural shell derived by means of a formal asymptot ic
analysis; commentary..................521
10.6. Existence of solutions to the minimization problem . 526
Exercises.........................539
Chapter 11. Koiter s equations and other two-dimensional
nonlinear shell theories.............545
Introduction.......................545
11.1. The two-dimensional Koiter equations for a nonlin-
early elastic shell.....................545
11.2. Other nonlinear shell theories..............5 19
11.3. Nonlinear shallow shell theories ............552
References ............................557
Index................................583
|
| any_adam_object | 1 |
| author | Ciarlet, Philippe G. 1938- |
| author_GND | (DE-588)143368362 |
| author_facet | Ciarlet, Philippe G. 1938- |
| author_role | aut |
| author_sort | Ciarlet, Philippe G. 1938- |
| author_variant | p g c pg pgc |
| building | Verbundindex |
| bvnumber | BV013266013 |
| classification_rvk | SK 950 |
| ctrlnum | (OCoLC)175052863 (DE-599)BVBBV013266013 |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-12-23T15:24:40Z |
| institution | BVB |
| isbn | 0444828915 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009043867 |
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| physical | LX, 599 S. graph. Darst. |
| publishDate | 2000 |
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| publisher | North-Holland |
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| series | Studies in mathematics and its applications |
| series2 | Studies in mathematics and its applications |
| spellingShingle | Ciarlet, Philippe G. 1938- Mathematical elasticity Studies in mathematics and its applications |
| title | Mathematical elasticity |
| title_auth | Mathematical elasticity |
| title_exact_search | Mathematical elasticity |
| title_full | Mathematical elasticity 3 Theory of shells Philippe G. Ciarlet |
| title_fullStr | Mathematical elasticity 3 Theory of shells Philippe G. Ciarlet |
| title_full_unstemmed | Mathematical elasticity 3 Theory of shells Philippe G. Ciarlet |
| title_short | Mathematical elasticity |
| title_sort | mathematical elasticity theory of shells |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009043867&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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