Homogenisation: averaging processes in periodic media: mathematical problems in the mechanics of composite materials
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer Acad. Publ.
1989
|
| Schriftenreihe: | Mathematics and its applications / Soviet series
36 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | XXXV, 336 S. |
| ISBN: | 0792300491 |
Internformat
MARC
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| 100 | 1 | |a Bachvalov, Nikolaj Sergeevič |d 1934-2005 |e Verfasser |0 (DE-588)1061193896 |4 aut | |
| 240 | 1 | 0 | |a Osrednenie processov v periodičeskich sredach |
| 245 | 1 | 0 | |a Homogenisation: averaging processes in periodic media |b mathematical problems in the mechanics of composite materials |c by N. Bakhvalov and G. Panasenko |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1989 | |
| 300 | |a XXXV, 336 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications / Soviet series |v 36 | |
| 500 | |a Aus dem Russ. übers. | ||
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| 700 | 1 | |a Panasenko, Grigorij P. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804117957901549568 |
|---|---|
| adam_text | TABLE OF CONTENTS
Notations xi
Preface xiii
Preface to English Edition xvii
Introduction xix
§1. Medium With Periodic Structure xix
§2. What Are Effective Coefficients? xxii
§3. A Scheme for Calculating Effective Coefficients xxiii
§4. Investigating the Microscopic Structure of a Field xxv
§5. What is the Asymptotic Averaging Method? xxvi
§6. Where can these Methods Help? xxxi
§7. Advantages and Disadvantages of the Averaging Method xxxii
§8. A Brief Review of the Literature xxxiii
Chapter 1. Formulation of Elementary Boundary Value
Problems 1
§1. The Concept of the Classical Formulation of a Boundary
Value Problem for Equations with Discontinuous Coefficients 1
§2. The Concept of Generalized Solution 2
§3. Generalized Formulations of Problems for the Basic
Equations of Mathematical Physics 4
Chapter 2. The Concept of Asymptotic Expansion. A
Model Example to Illustrate the Averaging Method 12
§1. Asymptotic expansion. A Formal Asymptotic Solution 12
§2. Asymptotic Expansion of a Solution of the Equation
u = 1 + eu3 14
§3. Asymptotic Expansion of a Solution of the Equation
(K(x/e)u ) =: f(x) by the Averaging Method 16
§4. Generalization of the Averaging Method in the Case of a
Piecewise Smooth Coefficient 26
§5. Averaging the System of Differential Equations 29
Chapter 3. Averaging Processes in Layered Media 32
§1. Problem of Small Longitudinal Vibrations of a Rod 34
viii Contents
§2. Nonstationary Problem of Heat Conduction 42
§3. Averaging Maxwell Equations 43
§4. Averaging Equations of a Viscoelastic Medium 45
§5. Media with Slowly Changing Geometric Characteristics 54
§6. Heat Transfer Through a System of Screens 57
§7. Averaging a Nonlinear Problem of the Elasticity Theory
in an Inhomogeneous Rod 61
§8. The System of Equations of Elasticity Theory in a Layered
Medium 68
§9. Considerations Permitting Reduction of Calculations in
Constructing Averaged Equations 77
§10. Nonstationary Nonlinear Problems 80
§11. Averaging Equations with Rapidly Oscillating
Nonperiodic Coefficients 81
§12. Problems of Plasticity and Dynamics of Viscous Fluid
as Described by Functions Depending on Fast Variables 89
Chapter 4. Averaging Basic Equations of Mathematical
Physics 102
§1. Averaging Stationary Thermal Fields in a Composite 104
§2. Asymptotic Expansion of Solution of the Stationary
Heat Conduction Problem 125
§3. Stationary Thermal Field in a Porous Medium 132
§4. Averaging a Stationary System of Equations of Elasticity
Theory in Composite and Porous Materials 137
§5. Nonstationary Systems of Equations of Elasticity
and Diffusion Theory 142
§6. Averaging Nonstationary Nonlinear System of
Equations of Elasticity Theory 147
§7. Averaging Stokes and Navier Stokes Equations. The
Derivation of the Percolation Law for a Porous Medium
(Darcy s Law) 151
§8. Averaging in case of Short Wave Propagation 157
§9. Averaging the Transition Equation for a Periodic Medium 165
§10. Eigenvalue Problems 168
Chapter 5. General Formal Averaging Procedure 171
§1. Averaging Nonlinear Equations 171
§2. Averaged Equations of Infinite Order for a Linear
Periodic Medium and for the Equation of Moment Theory 175
§3. A Method of Describing Multi Dimensional Periodic Media
that does not Involve Separating Fast and Slow Variables 191
Contents ix
Chapter 6. Properties of Effective Coefficients. Relationship
Among Local and Averaged Characteristics of a Solution 196
§1. Maintaining the Properties of Convexity and Symmetry of
the Minimized Functional in Averaging 196
§2. On the Principle of Equivalent Homogeneity 205
§3. The Symmetry Properties of Effective Coefficients and
Reduction of Periodic Problems to Boundary Value Problems 212
§4. Agreement Between Theoretically Predicted Values of Effective
Coefficients and Those Determined by an Ideal Experiment 222
Chapter 7. Composite Materials Containing High Modulus
Reinforcement 224
§1. The Stationary Field in a Layered Material 225
§2. Composite Materials with Grains for Reinforcement 229
§3. Dissipation of Waves in Layered Media 236
§4. High Modulus 3D Composite Materials 239
§5. The Splitting Principle for the Averaged Operator for 3D
High Modulus Composites 245
Chapter 8. Averaging of Processes in Skeletal Structures 257
§1. An Example of Averaging a Problem on the Simplest Framework 262
§2. A Geometric Model of a Framework 272
§3. The Splitting Principle for the Averaged Operator for a
Periodic Framework 273
§4. The Splitting Principle for the Averaged Operator for
Trusses and Thin walled Structures 295
§5. On Refining the Splitting Principle for the Averaged Operator 298
§6 Asymptotic Expansion of a Solution of a Linear Equation in
Partial Derivatives for a Rectangular Framework 299
§7 Skeletal Structures with Random Properties 310
Chapter 9. Mathematics of Boundary Layer Theory in
Composite Materials 312
§1. Problem on the Contact of Two Layered Media 314
§2. The Boundary Layer for an Elliptic Equation Defined on a
Half Plane 317
§3. The Boundary Layer Near the Interface of Two Periodic
Structures 324
§4. Problem on the Contact of Two Media Divided by a Thin
Inter layer 331
§5. The Boundary Layer for the Nonstationary System of
Equations of Elasticity Theory 334
§6. On the Ultimate Strength of a Composite 339
x Contents
§7. Boundary Conditions of Other Types 340
§8. On the Averaging of Fields in Layer Media with
Layers of Composite Materials 343
§9. The Time Boundary Layer for the Cauchy Parabolic Problem 344
Supplement: Existence and Uniqueness Theorems for
the Problem on a Cell 346
Bibliography 351
Subject Index 365
|
| any_adam_object | 1 |
| author | Bachvalov, Nikolaj Sergeevič 1934-2005 Panasenko, Grigorij P. |
| author_GND | (DE-588)1061193896 |
| author_facet | Bachvalov, Nikolaj Sergeevič 1934-2005 Panasenko, Grigorij P. |
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| author_sort | Bachvalov, Nikolaj Sergeevič 1934-2005 |
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| classification_tum | MTA 009f WER 420f |
| ctrlnum | (OCoLC)643044782 (DE-599)BVBBV003607729 |
| discipline | Physik Werkstoffwissenschaften Mathematik |
| format | Book |
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| id | DE-604.BV003607729 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:02:40Z |
| institution | BVB |
| isbn | 0792300491 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002297489 |
| oclc_num | 643044782 |
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| physical | XXXV, 336 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Bachvalov, Nikolaj Sergeevič 1934-2005 Verfasser (DE-588)1061193896 aut Osrednenie processov v periodičeskich sredach Homogenisation: averaging processes in periodic media mathematical problems in the mechanics of composite materials by N. Bakhvalov and G. Panasenko Dordrecht u.a. Kluwer Acad. Publ. 1989 XXXV, 336 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 36 Aus dem Russ. übers. Verbundwerkstoff (DE-588)4062670-2 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Verbundwerkstoff (DE-588)4062670-2 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Panasenko, Grigorij P. Verfasser aut Soviet series Mathematics and its applications 36 (DE-604)BV004708148 36 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002297489&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bachvalov, Nikolaj Sergeevič 1934-2005 Panasenko, Grigorij P. Homogenisation: averaging processes in periodic media mathematical problems in the mechanics of composite materials Verbundwerkstoff (DE-588)4062670-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4062670-2 (DE-588)4114528-8 |
| title | Homogenisation: averaging processes in periodic media mathematical problems in the mechanics of composite materials |
| title_alt | Osrednenie processov v periodičeskich sredach |
| title_auth | Homogenisation: averaging processes in periodic media mathematical problems in the mechanics of composite materials |
| title_exact_search | Homogenisation: averaging processes in periodic media mathematical problems in the mechanics of composite materials |
| title_full | Homogenisation: averaging processes in periodic media mathematical problems in the mechanics of composite materials by N. Bakhvalov and G. Panasenko |
| title_fullStr | Homogenisation: averaging processes in periodic media mathematical problems in the mechanics of composite materials by N. Bakhvalov and G. Panasenko |
| title_full_unstemmed | Homogenisation: averaging processes in periodic media mathematical problems in the mechanics of composite materials by N. Bakhvalov and G. Panasenko |
| title_short | Homogenisation: averaging processes in periodic media |
| title_sort | homogenisation averaging processes in periodic media mathematical problems in the mechanics of composite materials |
| title_sub | mathematical problems in the mechanics of composite materials |
| topic | Verbundwerkstoff (DE-588)4062670-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Verbundwerkstoff Mathematisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002297489&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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