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Homogenization of Corrugated Plates Based on the Dimension Reduction for the Periodicity Cell Problem

  • Boris D. Annin
  • Alexander G. Kolpakov
  • Sergei I. Rakin
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 46)

Abstract

It is demonstrated that for corrugated plates, more generally, for plates that are cylinders from geometric point of view, three-dimensional periodicity cell problem of the homoge-nization theory can be reduced to two-dimensional problem on the cross section of the periodicity cell. The transition to two-dimensional problem significantly simplifies the numerical analysis of corrugated plates (other, non-numerical methods, are not effective if plate is thick). Significant simplification of the problem takes place in the case of the coincidence of Poisson’s ratios of the plate components, in particular, for a plate made of single homogeneous material. We present results of numerical analysis of a plate with a sinusoidal corrugation, both thin and thick plates. For thin plates, our results demonstrate good agreement with the results present in the recent paper (Ye et al, 2014).

Keywords

Corrugated plate Elasticity theory Homogenization Periodicity cell Dimension reduction Effective stiffnesses Local stress/strain state Universal relations 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Boris D. Annin
    • 1
  • Alexander G. Kolpakov
    • 2
  • Sergei I. Rakin
    • 3
  1. 1.Lavrentyev Institute of Hydrodynamics of Siberian Branch of the RASNovosibirskRussia
  2. 2.Siberian State University of Telecommunications and InformaticsNovosibirskRussia
  3. 3.Siberian State Transport UniversityNovosibirskRussia

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