Modelling analysis and control of thin plates:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Paris [u.a.]
Masson [u.a.]
1989
|
| Series: | Recherches en mathématiques appliquées
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 174 S. |
| ISBN: | 2225814295 354051550X 038751550X |
Staff View
MARC
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| 100 | 1 | |a Lagnese, John E. |d 1937- |e Verfasser |0 (DE-588)112132812 |4 aut | |
| 245 | 1 | 0 | |a Modelling analysis and control of thin plates |c J. E. Lagnese ; J.-L. Lions |
| 264 | 1 | |a Paris [u.a.] |b Masson [u.a.] |c 1989 | |
| 300 | |a VI, 174 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Recherches en mathématiques appliquées |v 6 | |
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Record in the Search Index
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|---|---|
| adam_text | Table of contents
Introduction 1
Chapter I. Plate Models 7
1. Introduction 7
2. Kirchhoff Model 9
3. Mindlin Timoshenko Model 13
4. Equations for the Stretching Components 17
5. Nonlinear Models 18
6. Linear Thermoelastic Plates 25
7. Linear Viscoelastic Plates 32
8. Comments 38
Chapter II. The Mindlin Timoshenko Model and its Limit as K » «• 41
1. Notation. Variational Formulation 41
2. Well Posedness of the M T Model 42
3. The Behavior of the M T Model as K » m 47
3.1. The Case rQ * $ 47
3.2. The Case rQ = f 51
4. Various Remarks 52
Chapter III. A Priori Estimates and Exact Controllability for Mindlin
Timoshenko Plates 59
1. Introduction 59
2. Function Spaces and Coerciveness. The Case FQ * $ 60
3. Well Posedness of (1.1) (1.4) 61
3.1. Some Special Subspaces 63
3.2. The Nonhomogeneous Problem 64
4. A Priori Estimates. The Case rQ * $ 68
5. Exact Boundary Controllability. The Case rQ * t 75
6. A Priori Estimates and Exact Controllability.
The Case rQ = f 80
7. Hinged Plates 89
7.1. Well Posedness of the Homogeneous Problem 90
7.2. A Priori Estimates and Application of HUM 91
7.3. Proof of Theorem 7.1 96
Chapter IV. The One Dimensional Case 101
1. Orientation 101
2. The Estimates for HUM 102
2.1. Variational Formulation 102
2.2. HUM S Inequality 104
2.3. An Estimate Based on a Non constructive Argument 106
2.4. The Main Inequality 107
3. Uniform Exact Controllability 108
VI TABLE OF CONTENTS
4. Weakening of the Norm 110
4.1. Orientation 110
4.2. Characterization of F2 111
5. Uniform Exact Controllability. (II) 112
5.1. Orientation 112
5.2. A Priori Estimate 112
5.3. Application of HUM 115
5.4. The Limits of the Controls 115
Chapter V. Exact Controllability for Kirchhoff Plates 119
1. The Problems to be Considered 119
2. Study of Case (i) 120
3. Study of Case (i). A Supplementary Resul t 127
4. Study of Case (ii) 131
5. Study of Case (iii). (I) The Case rQ * 0 137
5.1. Preliminaries 137
5.2. Uniform Exact Controllability 142
6. Study of Case (iii). (II) The Case r = f 146
Chapter VI. Partial Exact Controllability for Thermoelastic Plates 151
1. Setting of the Problem 151
2. The Principle of RHUM 152
2.1. Transformation of the Problem 153
2.2. The Principle of RHUM 154
3. Study of a New Norm. Perturbation Method 156
3.1. Adjoint System 156
3.2. Further Properties of the Adjoint System 157
3.3. The Main Lemma 158
3.4. Conclusions 160
3.5. Open Questions 160
Chapter VII. Reachability for Linear Plates with a Long Memory 162
1. Setting of the Problem 162
2. The Main Lemma 163
3. Proof of Theorem 2.1 163
3.1. Formal Description of the Method 163
3.2. Property of u 164
3.3. Proof of Lemma 3.1 165
4. Final Remarks 168
Bibliography 171
Index 175
|
| any_adam_object | 1 |
| author | Lagnese, John E. 1937- Lions, Jacques-Louis 1928-2001 |
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| dewey-search | 624.1/7765 |
| dewey-sort | 3624.1 47765 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Bauingenieurwesen |
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| id | DE-604.BV004117905 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:08:39Z |
| institution | BVB |
| isbn | 2225814295 354051550X 038751550X |
| language | English |
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| physical | VI, 174 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Masson [u.a.] |
| record_format | marc |
| series | Recherches en mathématiques appliquées |
| series2 | Recherches en mathématiques appliquées |
| spelling | Lagnese, John E. 1937- Verfasser (DE-588)112132812 aut Modelling analysis and control of thin plates J. E. Lagnese ; J.-L. Lions Paris [u.a.] Masson [u.a.] 1989 VI, 174 S. txt rdacontent n rdamedia nc rdacarrier Recherches en mathématiques appliquées 6 Mathematisches Modell Plates (Engineering) Mathematical models Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Platte (DE-588)4046304-7 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 s Platte (DE-588)4046304-7 s DE-604 Lions, Jacques-Louis 1928-2001 Verfasser (DE-588)124055397 aut Recherches en mathématiques appliquées 6 (DE-604)BV002654185 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002570177&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lagnese, John E. 1937- Lions, Jacques-Louis 1928-2001 Modelling analysis and control of thin plates Recherches en mathématiques appliquées Mathematisches Modell Plates (Engineering) Mathematical models Numerisches Verfahren (DE-588)4128130-5 gnd Platte (DE-588)4046304-7 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4046304-7 |
| title | Modelling analysis and control of thin plates |
| title_auth | Modelling analysis and control of thin plates |
| title_exact_search | Modelling analysis and control of thin plates |
| title_full | Modelling analysis and control of thin plates J. E. Lagnese ; J.-L. Lions |
| title_fullStr | Modelling analysis and control of thin plates J. E. Lagnese ; J.-L. Lions |
| title_full_unstemmed | Modelling analysis and control of thin plates J. E. Lagnese ; J.-L. Lions |
| title_short | Modelling analysis and control of thin plates |
| title_sort | modelling analysis and control of thin plates |
| topic | Mathematisches Modell Plates (Engineering) Mathematical models Numerisches Verfahren (DE-588)4128130-5 gnd Platte (DE-588)4046304-7 gnd |
| topic_facet | Mathematisches Modell Plates (Engineering) Mathematical models Numerisches Verfahren Platte |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002570177&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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