Homogenization Techniques and Estimation of Material Parameters in Distributed Structures

  • H. T. Banks
  • R. E. Miller
  • D. Cioranescu
  • A. Das
  • D. A. Rebnord
Part of the Progress in Systems and Control Theory book series (PSCT, volume 11)


We report here on a part of our continuing efforts on the development of high fidelity dynamic models for composite material structures. The focus of our investigations has been on models to be used in estimation and control of large flexible structures mainly intended for use in space (e.g., antennas, platforms, solar panels, experimental arRays, etc.). At present there is a reasonably adequate understanding of the dynamics of beams and plates made from known materials such as aLuminum alloys. Our recent efforts (see [3] and the references therein) involved models and methods to determine material parameters in composite material structures with simple geometry (beams with attached solid bodies or solid plates). These result in inverse problems that are computationally tractable as long as the physical geometry is relatively simple. However, substantial difficulties arise in cases involving more complex geometries such as grids (which may be viewed as plates with many holes) and trusses (solid coLumns from which most of the material is removed in some periodic, regular fashion). In these cases the difficulties associated with unknown composite material characteristics such as stiffness and internal damping are combined with severe difficulties related to computational grid selection for a domain that is mostly holes or perforations.


Grid Structure Distribute Parameter System Parameter Estimation Problem Homogenization Technique Perforated Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. T. Banks, On a variational approach to some parameter estimation problems, Distributed Parameter Systems, Springer Lec. Notes in Control and Info. Sci., 75 (1985), p. 1–23.Google Scholar
  2. 2.
    H. T. Banks, D. Cioranescu, and D. A. Rebnord, Homogenization models for 2-D grid structures, to appear.Google Scholar
  3. 3.
    H. T. Banks and D. J. Inman, On damping mechanisms in beams, CAMS Rep. No. 89–3 (USC, Sept, 1989); ASME Journal of Applied Mechanics, to appear.Google Scholar
  4. 4.
    H. T. Banks and K. Ito, A unified framework for approximation in inverse problems for distributed parameter systems, Control-Theory and Adv. Tech., 4 (1988), p. 73–90.Google Scholar
  5. 5.
    H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhäuser Boston, 1989.CrossRefGoogle Scholar
  6. 6.
    H. T. Banks and D. A. Rebnord, Analytic semigroups: applications to inverse problems for flexible structures, CAMS Rep. No. 90–3, Proc. Intl. Conf. in Differential Eqns. and Applications, (Retzhof, June 18–24, 1989), Lec. Notes in Pure and Applied Mathematics, Marcel Dekker, to appear.Google Scholar
  7. 7.
    H. T. Banks and D. A. Rebnord, Estimation of material parameters for grid structures, J. Math. Systems, Estimation, and Control, 1 (1991), p. 107–130.Google Scholar
  8. 8.
    H. T. Banks and J. G. Wade, A convergence framework for approximation methods for DPS estimation problems, Proc. Intl. Symp. on Inverse Problems in Engineering Sciences, (Osaka, Aug. 19–20, 1990), to appear.Google Scholar
  9. 9.
    A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North Holland, Amsterdam, 1978.Google Scholar
  10. 10.
    D. Cioranescu and P. Donato, Exact internal controllability in perforated domains, J. Math. Pures et Appl., 68 (1989), p. 185–213.Google Scholar
  11. 11.
    D. Cioranescu and J. Saint Jean Paulin, Asymptotic analysis of elastic wireworks, preprint.Google Scholar
  12. 12.
    D. J. Gorman, Free Vibration Analysis of Rectangular Plates, Elsevier, 1982.Google Scholar
  13. 13.
    A. W. Leissa, Vibration of Plates, NASA SP-160, 1969.Google Scholar
  14. 14.
    D. A. Rebnord, Parameter Estimation for Two-Dimensional Grid Structures, PhD. Thesis, Brown University, 1989.Google Scholar
  15. 15.
    E. Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics, 127, Springer-Verlag, New York, 1980.Google Scholar
  16. 16.
    J. Wloka, Partial Differential Equations, Cambridge, 1987.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • H. T. Banks
    • 1
  • R. E. Miller
    • 1
  • D. Cioranescu
    • 2
  • A. Das
    • 3
  • D. A. Rebnord
    • 4
  1. 1.Center for Applied Mathematical Sciences University of Southern California Los AngelesCalifornia
  2. 2.Laboratoire d’Analyse Numérique Université Pierre et Marie CurieParisFrance
  3. 3.Phillips Laboratory Edwards Air Force BaseUSA
  4. 4.Department of Mathematics Syracuse University SyracuseNew York

Personalised recommendations