A new model for thin plates with rapidly varying thickness

Robert V. Kohn, Michael Vogelius

Research output: Contribution to journalArticlepeer-review

Abstract

We study the bending of a thin plate with rapidly varying thickness, for example one with rib-like stiffeners or perforated by small holes. We obtain a fourth-order equation for the midplanc displacement, using an asymptotic analysis based on three-dimensional linear elasticity. The coefficients of this equation represent the constitutive law relating bending moments to midplane curvature; they are explicitly determined by the plate geometry. Our analysis distinguishes between three different cases, in which the thickness varies on a length scale longer than, on the order of, or shorter than the mean thickness.

Original languageEnglish (US)
Pages (from-to)333-350
Number of pages18
JournalInternational Journal of Solids and Structures
Volume20
Issue number4
DOIs
StatePublished - 1984

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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