Homogenization of one dimensional elliptic system

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Homogenization of one dimensional elliptic system

Paweł Mitkowski1, Wojciech Mitkowski2

1Faculty of Electrical Engineering, Automatics, Electronics and Computer Science, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland.
2Department of Automatics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland.

DOI:

https://doi.org/10.7494/cmms.2008.3.0197

Abstract:

The work presents problem of homogenization of one-dimenional mediums of periodic micrsotructure, and more precisely homogenization of one-dimensional elliptic system of layered periodic micrsotructure. The example of suitable parametrized periodic micrstructure, where parameters of homogenized system can be determine, is given. Next, the following inverse problem is considered: in what proportions components should be mix, to obtain homogenized material of given properties.

Cite as:

Mitkowski, P., & Mitkowski, W. (2008). Homogenization of one dimensional elliptic system. Computer Methods in Materials Science, 8(3), 160 – 164. https://doi.org/10.7494/cmms.2008.3.0197

Article (PDF):

Keywords:

Homogenization, Elliptic system, Layered materials, Inverse problem

References:

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Mityushev, V., 2001, Transport properties of doubly periodic arrays of circular cylinders and optimal design problems, Applied Mathematics & Optimization, 44, 17-31.

Berlyand, L., Mityushev, V., 2005, Increase and decrease of the effective conductivity of two phase composites due to polydispersity, Journal of Statistical Physics, 118, ¾, 481-509.

Mitkowski, P., Mitkowski, W., 2008, Homogenization of layered materials, Proc. 15th Conf. Infomatyka w Technologii Metali, KomPlasTech 2008, eds. Grosman, F., Hyrcza-Michalska, M., Korbielów, Publisher Akapit, Kraków, 99-106.