Analogy between micropolar continuum and grid frameworks under initial stress

Z. P. Bažant*, M. Christensen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

144 Scopus citations


It is shown that the micropolar medium is a continuum approximation to large grid frameworks under initial axial forces. The strain energy, equilibrium conditions and boundary conditions are formulated, and some inconsistencies in the previous attempts of derivation of the micropolar analogy for gridworks are pointed out. The finite difference method, which is one possible means for the analysis of the overall behavior of a large framework, is investigated and found, by means of numerical examples, to give rather accurate results using much fewer unknowns than the exact analysis. The method is also applicable to problems of overall buckling. It is shown further that the so-called substitute frame in general does not exist, although the finite difference method serves the same purpose. Finally, it is demonstrated that in micropolar continua there exist certain boundary disturbances which rapidly decay with distance from the boundary. A simplified treatment of such disturbances is proposed.

Original languageEnglish (US)
Pages (from-to)327-346
Number of pages20
JournalInternational Journal of Solids and Structures
Issue number3
StatePublished - Mar 1972

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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