Статті КТ

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Browsing Статті КТ by Author "Andrianov, Igor I."

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    Refinement of the Maxwell Formula for Composite Reinforced by Circular Cross-Section Fibers. Part I: Using the Schwarz Alternating Method
    (Springer Link, 2020) Andrianov, Igor I.; Awrejcewicz, Jan; Starushenko, Galina A.; Gabrinets, Vladimir A.
    EN: The effective properties of the fiber-reinforced composite materials with fibers of circular cross section are investigated. The novel estimation for the effective coefficient of thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic homogenization is used. For analytical solution of the periodically repeated cell problem, the Schwarz alternating process is employed. The principal term of the refined formula coincides with the classical Maxwell formula. On the other hand, the refined formula can be used far beyond the area of applicability of the Maxwell formula. It can be used for dilute and non-dilute composites. It is confirmed by comparison with known numerical and asymptotic results.
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    Refinement of the Maxwell Formula for Composite Reinforced by Circular Cross-Section Fibers. Part II: Using Padé Approximants
    (Springer Link, 2020) Andrianov, Igor I.; Awrejcewicz, Jan; Starushenko, Galina A.; Gabrinets, Vladimir A.
    EN: The effective properties of the fiber-reinforced composite materials with fibers of circle cross section are investigated. The novel estimation for the effective coefficient of thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic homogenization is used. For an analytical solution of the periodically repeated cell problem the Schwarz alternating process (SAP) was employed. Convergence of this method was proved by S. Mikhlin, S. Sobolev, V. Mityushev. Unfortunately, the rate of the convergence is often slow, especially for nondilute high-contrast composite materials. For improving this drawback we used Padé approximations for various forms of SAP solutions with the following additive matching of obtained expressions. As a result, the solutions in our paper are obtained in a fairly simple and convenient form. They can be used even for a volume fraction of inclusion very near the physically possible maximum value as well as for high-contrast composite constituents. The results are confirmed by comparison with known numerical and asymptotic results.