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The theory of composites /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	620.1/18
書名/作者:	The theory of composites // Graeme W. Milton.
作者:	Milton, Graeme Walter,
面頁冊數:	1 online resource (xxviii, 719 pages) : : digital, PDF file(s).
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Composite materials.
標題:	Differential equations, Partial.
標題:	Homogenization (Differential equations)
ISBN:	9780511613357 (ebook)
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1017/CBO9780511613357

The theory of composites /
Milton, Graeme Walter,1956-

The theory of composites /Graeme W. Milton. - 1 online resource (xxviii, 719 pages) :digital, PDF file(s). - Cambridge monographs on applied and computational mathematics ;6. - Cambridge monographs on applied and computational mathematics ;14..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Introduction --1.

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.

ISBN: 9780511613357 (ebook)Subjects--Topical Terms:

380703
Composite materials.

LC Class. No.: TA418.9.C6 / M58 2002

Dewey Class. No.: 620.1/18

The theory of composites /
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505 0 0 $g 1. $t Introduction -- $g 2. $t Some equations of interest and numerical approaches to solving them -- $g 3. $t Duality transformations in two-dimensional media -- $g 4. $t Translations and equivalent media -- $g 5. $t Some microstructure-independent exact relations -- $g 6. $t Exact relations for coupled equations -- $g 7. $t Assemblages of spheres, ellipsoids, and other neutral inclusions -- $g 8. $t Tricks for generating other exactly solvable microgeometries -- $g 9. $t Laminate materials -- $g 10. $t Approximations and asymptotic formulas -- $g 11. $t Wave propagation in the quasistatic limit -- $g 12. $t Reformulating the problem of finding effective tensors -- $g 13. $t Variational principles and inequalities -- $g 14. $t Series expansions for the fields and effective tensors.
520 $a 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.
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650 0 $a Differential equations, Partial. $3 389324
650 0 $a Homogenization (Differential equations) $3 395299
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