Generalized Beams and Continua. Dynamics of Reticulated Structures

Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 21)

Abstract

This paper deals with the dynamic behavior of periodic reticulated beams and materials. Through the homogenization method of periodic discrete media the macro-behavior is derived at the leading order. With a systematic use of scaling, the analysis is performed on the archetypical case of symmetric unbraced framed cells. Such cells can present a high contrast between shear and compression deformability, conversely to “massive” media. This opens the possibility of enriched local kinematics involving phenomena of global rotation, inner deformation or inner resonance, according to studied configuration and frequency range.

Keywords

Anisotropy Foam 

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References

  1. 1.
    Boutin, C., Hans, S., Homogenisation of periodic discrete medium: application to dynamics of framed structures. Comput. Geotech. 30(4), 303–320 (2003) CrossRefGoogle Scholar
  2. 2.
    Boutin, C., Hans, S., Ibraim, E., Roussillon, P.: In situ experiments and seismic analysis of existing buildings—Part II. Earthquake Eng. Struct. Dyn. 34, 1531–1546 (2005) CrossRefGoogle Scholar
  3. 3.
    Caillerie, D., Trompette, P., Verna, P.: Homogenisation of periodic trusses. In: Congres IASS, Madrid, pp. 7139–7180 (1989) Google Scholar
  4. 4.
    Chesnais, C., Hans, S., Boutin, C.: Wave propagation and diffraction in discrete structures—effect of anisotropy and internal resonance. In: ICIAM, Zurich, 16–20 July 2007 Google Scholar
  5. 5.
    Cioranescu, D., Saint Jean Paulin, J.: Homogenization of Reticulated Structures. Applied Mathematical Sciences, vol. 136. Springer, Berlin (1999) MATHGoogle Scholar
  6. 6.
    Eringen, A.C.: Mechanics of micromorphic continua. In: IUTAM Symposium on the Generalized Cosserat Continuum and the Continuum Theory of Dislocations with Applications, pp. 18–35. Springer, Berlin (1968) Google Scholar
  7. 7.
    Hans, S., Boutin, C.: Dynamics of discrete framed structures: a unified homogenized description. J. Mech. Mater. Struct. 3(9), 1709–1739 (2008) CrossRefGoogle Scholar
  8. 8.
    Kerr, A.D., Accorsi, M.L.: Generalization of the equations for frame-type structures—a variational approach. Acta Mech. 56(1–2), 55–73 (1985) MATHCrossRefGoogle Scholar
  9. 9.
    Moreau, G. and Caillerie, D.: Continuum modeling of lattice structures in large displacement applications to buckling analysis. Comput. Struct. 68(1–3), 181–189 (1998) MATHCrossRefGoogle Scholar
  10. 10.
    Noor, A.K.: Continuum modeling for repetitive lattice structures. Appl. Mech. Rev. 41(7), 285–296 (1988) CrossRefGoogle Scholar
  11. 11.
    Sanchez-Palencia E.: Non-Homogeneous Media and Vibration Theory. Lecture Note in Physics, vol. 127. Springer, Berlin (1980) MATHGoogle Scholar
  12. 12.
    Tollenaere, H., Caillerie, D.: Continuum modeling of lattice structures by homogenization. Adv. Eng. Softw. 29(7–9), 699–705 (1998) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Claude Boutin
    • 1
  • Stéphane Hans
    • 1
  • Céline Chesnais
    • 1
  1. 1.DGCB, FRE CNRS 3237, Ecole Nationale des Travaux Publics de l’EtatUniversité de LyonLyonFrance

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