Topics in the Mathematical Modelling of Composite Materials -

Topics in the Mathematical Modelling of Composite Materials

Buch | Softcover
321 Seiten
2012 | Softcover reprint of the original 1st ed. 1997
Springer-Verlag New York Inc.
978-1-4612-7390-5 (ISBN)
213,99 inkl. MwSt
This work has implications for many physical problems involving optimal design, composite materials, and coherent phase transitions. Still other work was published in standard books or journals, but written in Russian or French.
Andrej V. Cherkaev and Robert V. Kohn In the past twenty years we have witnessed a renaissance of theoretical work on the macroscopic behavior of microscopically heterogeneous mate­ rials. This activity brings together a number of related themes, including: ( 1) the use of weak convergence as a rigorous yet general language for the discussion of macroscopic behavior; (2) interest in new types of questions, particularly the "G-closure problem," motivated in large part by applications of optimal control theory to structural optimization; (3) the introduction of new methods for bounding effective moduli, including one based on "com­ pensated compactness"; and (4) the identification of deep links between the analysis of microstructures and the multidimensional calculus of variations. This work has implications for many physical problems involving optimal design, composite materials, and coherent phase transitions. As a result it has received attention and support from numerous scientific communities, including engineering, materials science, and physics as well as mathematics. There is by now an extensive literature in this area. But for various reasons certain fundamental papers were never properly published, circu­ lating instead as mimeographed notes or preprints. Other work appeared in poorly distributed conference proceedings volumes. Still other work was published in standard books or journals, but written in Russian or French. The net effect is a sort of "gap" in the literature, which has made the subject unnecessarily difficult for newcomers to penetrate.

1. On the Control of Coefficients in Partial Differential Equations.- 2. Estimations of Homogenized Coefficients.- 3. H- Convergence.- 4. A Strange Term Coming from Nowhere.- 5. Design of Composite Plates of Extremal Rigidity.- 6. Calculus of Variations and Homogenization.- 7. Effective Characteristics of Composite Materials and the Optimal Design of Structural Elements.- Appendix: Local distribution of a MHD Channel in the case of optimal distribution of the resistivity of the working medium.- 8. Microstructures of Composites of Extremal Rigidity and Exact Bounds on the Associated Energy Density. 

Reihe/Serie Progress in Nonlinear Differential Equations and Their Applications ; 31
Zusatzinfo XIV, 321 p.
Verlagsort New York
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Informatik Theorie / Studium
Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Technik Maschinenbau
ISBN-10 1-4612-7390-0 / 1461273900
ISBN-13 978-1-4612-7390-5 / 9781461273905
Zustand Neuware
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