UID:
almafu_9958062331302883
Format:
1 online resource (xxviii, 719 pages) :
,
digital, PDF file(s).
ISBN:
1-107-12029-2
,
1-280-42974-7
,
9786610429745
,
0-511-17599-X
,
0-511-15669-3
,
0-511-32935-0
,
0-511-61335-0
,
0-511-04598-0
Series Statement:
Cambridge monographs on applied and computational mathematics ; 6
Content:
Some of the greatest scientists including Poisson, Faraday, Maxwell, Rayleigh, and Einstein have contributed to the theory of composite materials. Mathematically, it is the study of partial differential equations with rapid oscillations in their coefficients. Although extensively studied for more than a hundred years, an explosion of ideas in the last five decades (and particularly in the last three decades) has dramatically increased our understanding of the relationship between the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective (electrical, thermal, elastic) moduli which govern the macroscopic behavior. This renaissance has been fueled by the technological need for improving our knowledge base of composites, by the advance of the underlying mathematical theory of homogenization, by the discovery of new variational principles, by the recognition of how important the subject is to solving structural optimization problems, and by the realization of the connection with the mathematical problem of quasiconvexification. This 2002 book surveys these exciting developments at the frontier of mathematics.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Introduction --
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Some equations of interest and numerical approaches to solving them --
,
Duality transformations in two-dimensional media --
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Translations and equivalent media --
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Some microstructure-independent exact relations --
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Exact relations for coupled equations --
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Assemblages of spheres, ellipsoids, and other neutral inclusions --
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Tricks for generating other exactly solvable microgeometries --
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Laminate materials --
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Approximations and asymptotic formulas --
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Wave propagation in the quasistatic limit --
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Reformulating the problem of finding effective tensors --
,
Variational principles and inequalities --
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Series expansions for the fields and effective tensors.
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English
Additional Edition:
ISBN 0-521-78125-6
Language:
English
