Homogenization procedure and Pade approximations in the theory of composite materials with parallelepiped inclusions

International Journal of Heat and Mass Transfer

Volumn 41, Issue 1, 1998, Pages 175-181

  Andrianov, I V ^a   Starushenko, G A ^b   Tokarzewski, S ^c  

^a PRYDNIPROVSKA STATE ACADEMY OF CIVIL ENGINEERING AND ARCHITECTURE   (Ukraine)

^b UKRAINIAN STATE UNIVERSITY OF CHEMICAL TECHNOLOGY   (Ukraine)

^c INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

COMPOSITE; DISPERSION; HEAT TRANSFER; HOMOGENIZATION;

EID: 0031985582     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0017-9310(97)00118-X     Document Type: Article

References (21)

1. Batchelor, G., Transport properties of two-phase materials with random structures. Annual Review of Fluid Mechanics, 1974, 6, 227-255.
2. Maxwell, J. C., A Treatise on Electricity and Magnetism. Oxford University Press, Oxford, 1904.
3. Rayleigh, J. W., On the influence of obstacles arranged in rectangular order on the properties of the medium. Philosophical Magazine Series, 1892, 5(34), 481-502.
4. Torquato, S., Random heterogeneous media : microstructure and improved bounds on effective properties. Applied Mechanics Review, 1991, 44, 37-76.
5. Nitham, B. W. and Sammut, R. A., Refractive index of array of spheres and cylinders. Journal of Theoretical Biology, 1976, 56, 125-149.
6. McPhedran, R. C. and McKenzie, D. R., Electrostatic and optical resonances of arrays of cylinders. Applied Physics, 1980, 23, 223-235.
7. Perrinns, W. T., McPhedran, R. C. and McKenzie, D. R., Transport properties of regular arrays of cylinders. Proceedings of the Royal Society of London, 1979, A369, 207-225.
8. McPhedran, R. C., Poladin, L. and Milton, G. W., Asymptotic studies of closely spaced, highly conducting cylinders. Proceedings of the Royal Society of London, 1988, A415, 185-196.
9. Kohanenko, Yu., Study of the composites, reinforced by rectangular fibers, by nets method. Doklady NAN Ukraine, Mathematics, Natural and Technical Sciences, 1993, 9, 60-64 (in Russian).
10. Bourgat, J., Numerical experiments of the homogenization method for operators with periodic coefficients. In Lectures Notes in Maths, 1979, 704, 330-356.
11. Baklvalov, N. and Panasenko, G., Averaging Processes in Periodic Media. Mathematical Problem in Mechanics of Composite Materials. Kluwer Academic Publishers, Dordrecht, 1989.
12. Kerner, E. H., The elastic and thermoelastic properties of composite media. Proceedings of the Physics Society, 1956, 69, 808-820.
13. Van der Pol, C., On the rheology of concentrated dispersions. Rheohgy Acta, 1958, 1, 198-211.
14. Christensen, R., Mechanics of Composite Materials, Wiley, New York, 1979.
15. May, S., Tokarzewski, S., Zachara, A. and Cichocki, B., Continued fraction representation for the effective thermal conductivity coefficient of a regular two-component composite. International Journal of Heat and Mass Transfer, 1994, 37(4), 2165-2173.
16. Andrianov, I., Blawzdziewicz, J. and Tokarzewski, S., Effective conductivity for densely parked highly condensed cylinders. Applied Physics A, 1994, 59, 601-604.
17. Bensoussan, A., Lions, J.-L. and Papanicolaou, G., Asymptotic Methods in Periodic Structures, North-Holland, New York, 1978.
18. Andrianov, I. V., Shevchenko, V. V. and Kholod, E. G., Asymptotic methods in the statics and dynamics of perforated plates and shells with periodic structures. Technische Mechanik, 1995, 15(2), 141-157.
19. Baker, G. and Graves-Morris, P., Pade approximants. Part II. Extensions and Applications. Addison-Wesley, London. 1981.
20. Andrianov, I. V. and Starushenko, G. A., Asymptotic methods in the theory of perforated membranes of non-homogeneous structures. Engineering Transction, 1995, 43(1-2), 5-18.
21. Kantorovich, L. V. and Krylov, V. I., Approximate Methods of Higher Analysis. Fizmatgiz, Moscow, 1962.