Author:
Publisher:
ISBN: 9780444558367
Category : Elasticity
Languages : en
Pages : 398

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Book Description

Author: O.A. Oleinik
Publisher: Elsevier
ISBN: 0080875475
Category : Mathematics
Languages : en
Pages : 413

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Book Description
This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof. It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.

Author: A. S. Shamaev
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description

Author: Gregoire Allaire
Publisher: Springer Science & Business Media
ISBN: 1468492861
Category : Technology & Engineering
Languages : en
Pages : 470

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Book Description
This book provides an introduction to the theory and numerical developments of the homogenization method. It's main features are: a comprehensive presentation of homogenization theory; an introduction to the theory of two-phase composite materials; a detailed treatment of structural optimization by using homogenization; a complete discussion of the resulting numerical algorithms with many documented test problems. It will be of interest to researchers, engineers, and advanced graduate students in applied mathematics, mechanical engineering, and structural optimization.

Author: Philippe G. Ciarlet
Publisher: Walter de Gruyter
ISBN: 3110873729
Category : Mathematics
Languages : en
Pages : 309

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Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Author: V.V. Jikov
Publisher: Springer Science & Business Media
ISBN: 3642846599
Category : Mathematics
Languages : en
Pages : 583

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Book Description
It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.

Author: Doïna Cioranescu
Publisher: Oxford University Press on Demand
ISBN: 9780198565543
Category : Mathematics
Languages : en
Pages : 262

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Book Description
Composite materials are widely used in industry: well-known examples of this are the superconducting multi-filamentary composites which are used in the composition of optical fibres. Such materials are complicated to model, as different points in the material will have different properties. The mathematical theory of homogenization is designed to deal with this problem, and hence is used to model the behaviour of these important materials. This book provides a self-contained and authoritative introduction to the subject for graduates and researchers in the field.

Author: O. A. Oleĭnik
Publisher: Cambridge University Press
ISBN: 9780521485371
Category : Mathematics
Languages : en
Pages : 218

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Book Description
In 1993, Professor Oleinik was invited to give a series of lectures about her work in the area of partial differential equations. This book contains those lectures, and more.

Author: Vladimir A. Marchenko
Publisher: Springer Science & Business Media
ISBN: 0817644687
Category : Mathematics
Languages : en
Pages : 407

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Book Description
A comprehensive study of homogenized problems, focusing on the construction of nonstandard models Details a method for modeling processes in microinhomogeneous media (radiophysics, filtration theory, rheology, elasticity theory, and other domains) Complete proofs of all main results, numerous examples Classroom text or comprehensive reference for graduate students, applied mathematicians, physicists, and engineers

Author: Doina Cioranescu
Publisher: Springer Science & Business Media
ISBN: 1461221587
Category : Mathematics
Languages : en
Pages : 367

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Book Description
Materials science is an area of growing research as composite materials become widely used in such areas as civil engineering, electrotechnics, and the aerospace industry. This mathematically rigorous treatment of lattice-type structures will appeal to both applied mathematicians, as well as engineers looking for a solid mathematical foundation of the methodology.