The integral equations of the theory of elasticity:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stuttgart [u.a.]
Teubner
1995
|
| Series: | Teubner-Texte zur Mathematik
135 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | 375 S. graph. Darst. |
| ISBN: | 3815420601 |
Staff View
MARC
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| 100 | 1 | |a Michlin, Solomon G. |d 1908-1990 |e Verfasser |0 (DE-588)172258243 |4 aut | |
| 245 | 1 | 0 | |a The integral equations of the theory of elasticity |c by Solomon G. Mikhlin ; Nikita F. Morozov ; Michael V. Paukshto |
| 264 | 1 | |a Stuttgart [u.a.] |b Teubner |c 1995 | |
| 300 | |a 375 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Teubner-Texte zur Mathematik |v 135 | |
| 500 | |a Aus d. Russ. übers. | ||
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| 650 | 0 | 7 | |a Integralgleichung |0 (DE-588)4027229-1 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Integralgleichung |0 (DE-588)4027229-1 |D s |
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| 700 | 1 | |a Morozov, Nikita F. |d 1932- |e Verfasser |0 (DE-588)121439976 |4 aut | |
| 700 | 1 | |a Paukšto, Michail V. |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804124338932154368 |
|---|---|
| adam_text | CONTENTS
PART I. INTEGRAL EQUATIONS 9
Chapter 1. General results on linear integral equations . 9
§1. Compact operators and Predholm s theorems 9
§2. The concept of symbol. Examples 16
§3. Regularization 19
§4. The index of an operator 23
§5. Noether operators and Noether s theorems 27
Chapter 2. One dimensional singular integral equations ... 28
§1. The Cauchy operator on Hoelder functions 28
§2. Cauchy operator in 2/2. The general singular operator .... 33
§3. Symbol and regularization 40
§4. Introduction to boundary value problems 43
§5. Evaluation of the index 46
§6. Systems of singular equations 49
§7. Equations on open contours and with discontinuous
coefficients 50
§8. Wiener Hopf integral equations 59
§9. Factorization of functions and matrix functions 66
Chapter 3. Two dimensional singular integral equations ... 76
§1. Brief survey of results 76
§2. Definition and basic properties of two dimensional
integrals 77
§3. Singular integrals over Hoelderian functions 80
§4. Differentiation of integrals with weak singularities 86
§5. Singular integrals in the space of square summable
functions 88
§6. Symbol and regularization 97
§7. The index of a singular operator 102
§8. Singular integrals on a smooth surface without edge .... 106
§9. Matrix singular operators of systems of singular
equations 108
Contents 7
Chapter 4. Approximate solution of integral equations ... 114
§1. Computation of singular integrals 114
§2. The most important methods of solution of singular
equations 117
§3. On projection methods of solution of Wiener Hopf
equations 120
PART II. PROBLEMS OF THE THEORY OF ELASTICITY
AND CRACKS MECHANICS 128
Chapter 5. The integral equations of classical
two dimensional problems 128
§1. The plane problem of the theory of elasticity 128
§2. Complex representation 136
§3. Integral equations of N.I.Muskhelishvili 139
§4. Generalization to multiply connected regions 143
§5. The potential theory equations of N.I. Muskhelishvili . . . 147
§6. The equations of Lauricella Sherman 149
§7. Plane strain in anisotropic media 152
Chapter 6. Potential theory for basic three dimensional
problems 165
§1. The equilibrium equations in terms of displacements .... 165
§2. Fundamental solutions of the equations of the theory
of elasticity 172
§3. Lichtenstein s boundary integral equations 174
§4. Solution of space problems by the potential method .... 177
§5. Direct methods of construction of the boundary integral
equations 189
§6. New schemes for the classical space problems 192
§7. On non classical integral equations of the theory of
elasticity 196
Chapter 7. The contact problems of the theory
of elasticity 200
§1. Mathematical formulation of problems 200
§2. Formulation of variational problems 207
§3. The integral equations of the simplest contact problems . . 211
g Contents
§4. Reduction of sectionally homogeneous problems to
integral equations 214
§5. The new singular integral equations of contact problems
of the theory of elasticity 222
§6. On a method of successive approximations for the
solution of 3D problems 224
Chapter 8. Problems of the theory of cracks 229
§1. Muskhelishvili s integral equations 229
§2. The equations for branching cracks 240
§3. Problem of a crack in a layered medium 245
§4. The problem of elastic inclusions with sharp points .... 257
§5. Space problems of the theory of cracks 263
APPENDIX I. Cosserat spectrum 273
§1. The investigations of Eugene and Francis Cosserat .... 276
§2. Problem I for finite regions 281
§3. Isolated points of the essential Cosserat spectrum 291
§4. The second boundary value problem 294
§5. The case of infinite regions 302
§6. Plane problems 306
§7. A qualitative study of the solutions for Poisson
coefficients with values near 1/2 310
APPENDIX II. The Calderon Seely projectors and the
reduction of boundary value problems of elliptic
operators to boundary equations 312
§1. Basic principles of the reduction on a boundary 318
§2. The difference potentials method 332
§3. The Sokhotskii Plemelj theorems and the theorem
on the involutions of the boundary operator in
electro elasticity 341
References 357
Index 372
|
| any_adam_object | 1 |
| author | Michlin, Solomon G. 1908-1990 Morozov, Nikita F. 1932- Paukšto, Michail V. |
| author_GND | (DE-588)172258243 (DE-588)121439976 |
| author_facet | Michlin, Solomon G. 1908-1990 Morozov, Nikita F. 1932- Paukšto, Michail V. |
| author_role | aut aut aut |
| author_sort | Michlin, Solomon G. 1908-1990 |
| author_variant | s g m sg sgm n f m nf nfm m v p mv mvp |
| building | Verbundindex |
| bvnumber | BV009965665 |
| classification_rvk | SK 640 SK 950 |
| classification_tum | MAT 450f PHY 202f |
| ctrlnum | (OCoLC)260202378 (DE-599)BVBBV009965665 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV009965665 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:44:05Z |
| institution | BVB |
| isbn | 3815420601 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006605170 |
| oclc_num | 260202378 |
| open_access_boolean | |
| owner | DE-384 DE-91G DE-BY-TUM DE-12 DE-29T DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-188 DE-11 |
| owner_facet | DE-384 DE-91G DE-BY-TUM DE-12 DE-29T DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-188 DE-11 |
| physical | 375 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Teubner |
| record_format | marc |
| series | Teubner-Texte zur Mathematik |
| series2 | Teubner-Texte zur Mathematik |
| spelling | Michlin, Solomon G. 1908-1990 Verfasser (DE-588)172258243 aut The integral equations of the theory of elasticity by Solomon G. Mikhlin ; Nikita F. Morozov ; Michael V. Paukshto Stuttgart [u.a.] Teubner 1995 375 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Teubner-Texte zur Mathematik 135 Aus d. Russ. übers. Elastizitätstheorie (DE-588)4123124-7 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Elastizitätstheorie (DE-588)4123124-7 s Integralgleichung (DE-588)4027229-1 s DE-604 Morozov, Nikita F. 1932- Verfasser (DE-588)121439976 aut Paukšto, Michail V. Verfasser aut Teubner-Texte zur Mathematik 135 (DE-604)BV000012607 135 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006605170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Michlin, Solomon G. 1908-1990 Morozov, Nikita F. 1932- Paukšto, Michail V. The integral equations of the theory of elasticity Teubner-Texte zur Mathematik Elastizitätstheorie (DE-588)4123124-7 gnd Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4123124-7 (DE-588)4027229-1 |
| title | The integral equations of the theory of elasticity |
| title_auth | The integral equations of the theory of elasticity |
| title_exact_search | The integral equations of the theory of elasticity |
| title_full | The integral equations of the theory of elasticity by Solomon G. Mikhlin ; Nikita F. Morozov ; Michael V. Paukshto |
| title_fullStr | The integral equations of the theory of elasticity by Solomon G. Mikhlin ; Nikita F. Morozov ; Michael V. Paukshto |
| title_full_unstemmed | The integral equations of the theory of elasticity by Solomon G. Mikhlin ; Nikita F. Morozov ; Michael V. Paukshto |
| title_short | The integral equations of the theory of elasticity |
| title_sort | the integral equations of the theory of elasticity |
| topic | Elastizitätstheorie (DE-588)4123124-7 gnd Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Elastizitätstheorie Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006605170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012607 |
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