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.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Boutin, C., Hans, S., Homogenisation of periodic discrete medium: application to dynamics of framed structures. Comput. Geotech. 30(4), 303–320 (2003)
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)
Caillerie, D., Trompette, P., Verna, P.: Homogenisation of periodic trusses. In: Congres IASS, Madrid, pp. 7139–7180 (1989)
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
Cioranescu, D., Saint Jean Paulin, J.: Homogenization of Reticulated Structures. Applied Mathematical Sciences, vol. 136. Springer, Berlin (1999)
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)
Hans, S., Boutin, C.: Dynamics of discrete framed structures: a unified homogenized description. J. Mech. Mater. Struct. 3(9), 1709–1739 (2008)
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)
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)
Noor, A.K.: Continuum modeling for repetitive lattice structures. Appl. Mech. Rev. 41(7), 285–296 (1988)
Sanchez-Palencia E.: Non-Homogeneous Media and Vibration Theory. Lecture Note in Physics, vol. 127. Springer, Berlin (1980)
Tollenaere, H., Caillerie, D.: Continuum modeling of lattice structures by homogenization. Adv. Eng. Softw. 29(7–9), 699–705 (1998)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Boutin, C., Hans, S., Chesnais, C. (2010). Generalized Beams and Continua. Dynamics of Reticulated Structures. In: Maugin, G., Metrikine, A. (eds) Mechanics of Generalized Continua. Advances in Mechanics and Mathematics, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5695-8_14
Download citation
DOI: https://doi.org/10.1007/978-1-4419-5695-8_14
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-5694-1
Online ISBN: 978-1-4419-5695-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)