[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

Modelling Torsional Properties of Human Bones by Multipoint Padé Approximants

  • Conference paper
  • First Online:
Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

Included in the following conference series:

  • 1268 Accesses

Abstract

The macroscopic modelling of the macroscopic behaviour of inhomegeneous media requires evaluation of the effective moduli. In the relevant literature, many papers were concerned with estimating of macroscopic moduli λe(x)) for two-phase materials. The main aim of this paper is to find the best estimation of λe(x)) from a given finite number of coefficients of power expansions of λe(x) at x = xi, i = 1, 2, ...,N,N +1, and apply them to model a torsional behaviour of a human cancellous bone filled with marrow. Errors of numerical evaluations are calculated and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
GBP 19.95
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
GBP 87.50
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
GBP 109.99
Price includes VAT (United Kingdom)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. I. Andrianov, G. Starushenko, V. Danishevsky, S. Tokarzewski, Homogenization procedure and Pad`e approximants for effective heat conductivity of composite materials with cylindrical inclusions having square cross-section, Proc. R. Soc. Lond. A, 455, 3401–3413, 1999.

    Google Scholar 

  2. G. A. Baker, P. Graves-Morris, Padé Approximants, Second Edition, in:Gian-Carlo Rota, Ed., Encyclopedia of Mathematics and its Applications, 59, Cambridge University Press 1996.

    Google Scholar 

  3. Christensen R. M., Mechanics of composite materials, John Wiley&Sons, New York, 1979.

    Google Scholar 

  4. Gibson J. L., Ashby M. F., Cellular Solids: Structure and Properties, Pergamon Press, 1988.

    Google Scholar 

  5. K. Golden and G. Papanicolaou, Bounds for effective parameters of heterogeneous media by analytic continuation, Comm.Math.Phys., 90, 473–491, 1983.

    Article  MathSciNet  Google Scholar 

  6. W. T. Perrins, D. R. McKenzie, R. C. Mc Phedran, Transport properties of regular array of cylinders, Proc. R. Soc. Lond. A 369, 207-225, 1979.

    Google Scholar 

  7. R. C. McPhedran, G. W. Milton, Bounds and exact theories for the transport properties of inhomogeneous media, Appl. Phys.A 26, 207–220, 1981.

    Article  Google Scholar 

  8. S. Tokarzewski, A. GaIlka, I. Andrianov, Bounds on the effective transport coefficients of two-p hase media from discrete theoretical and experimental data, Comp. Assis. Mech. and Eng. Sc., 4, 229–241, 1997.

    MATH  Google Scholar 

  9. S. Tokarzewski, J. J. Telega, Bounds on effective moduli by analytical continuation of the Stieltjes function expanded at zero and infinity, Z. angew. Math. Phys. 48, 1–20, 1997.

    Article  MathSciNet  Google Scholar 

  10. S. Tokarzewski, J. J. Telega, Inequalities for two-point Padè approximants to the expansions of Stieltjes functions in a real domain, Acta Applicandae Mathematicae, 48, 285–297, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  11. S. Tokarzewski, J. J. Telega, A. GaIlka, Torsional rigidities of cancellous bone filled with marrow: The application of multipoint Padé approximants, Engineering Trasaction, (in press).

    Google Scholar 

  12. S. Tokarzewski, J. J. Telega, A. GaIlka, General inequalities for multipoint Padè approximants, (in preparation)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Telega, J.J., Tokarzewski, S., Galka, A. (2001). Modelling Torsional Properties of Human Bones by Multipoint Padé Approximants. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_87

Download citation

  • DOI: https://doi.org/10.1007/3-540-45262-1_87

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics