Two-point Padé approximants to Stieltjes series representation of bulk moduli of regular composites

Authors

  • Stanisław Tokarzewski Institute of Fundamental Technological Research Polish Academy of Sciences
    Poland
  • Józef Joachim Telega Institute of Fundamental Technological Research Polish Academy of Sciences
    Poland

Abstract

The aim of this contribution is to present two-point Padé approximants method for the determination of upper and lower estimates on the effective transport coefficients of two-phase composite materials. The obtained formulae improve the corresponding one-point Padé approximants bounds [1,2,4,14,23] . As an example, a set of narrowing bounds for the overall conductivity of a square array of cylinders has been evaluated.

References

[1] G.A. Baker. Essentials of Padé Approximants. Acad. Press, London, 1975.
[2] G.A. Baker, P. Graves-Morris. Padé Approximants. Part I: Basic Theory. Encyclopedia of Mathematics and its Applications, 13, Addison- Wesley Publ. Co., London, 1981.
[3] G.A. Baker, P. Graves-Morris. Pade Approximants, Part II: Extensions and Applications. Encyclopedia of Mathematics and its Applications, 14, Addison-Wesley Publ. Co., London, 1981.
[4] D.J . Bergman. The dielectric constant of a composite material - A problem in classical physics, Phys. Report., C 43: 377- 407, 1978.
[5] A. Bultheel. Laurent Series and their Padé Approximants. Birkhäuser-Verlag, Basel, 1987.

Downloads

Published

2023-07-14

Issue

Vol. 3 No. 2 (1996)
pp. 121-132

Section

Articles

License

Copyright © The Author(s).

This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.

How to Cite

Tokarzewski, S., & Telega, J. J. (2023). Two-point Padé approximants to Stieltjes series representation of bulk moduli of regular composites. Computer Assisted Methods in Engineering and Science, 3(2), 121-132. https://cames3.ippt.pan.pl/index.php/cames/article/view/1450