Topics in the Mathematical Modelling of Composite Materials. 1st ed. 2018

種類:

電子ブック

責任表示:

edited by Andrej V. Cherkaev, Robert Kohn

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2018

著者名:

• Cherkaev, Andrej V.
• Kohn, Robert.
• SpringerLink (Online service)

シリーズ名:

Modern Birkhäuser Classics ;

ISBN:

9783319971841 [3319971840]    

注記:

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.
Over the past several decades, we have witnessed a renaissance of theoretical work on the macroscopic behavior of microscopically heterogeneous materials. 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 "compensated 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 ph

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