A new model for thin plates with rapidly varying thickness

Robert Kohn, Michael Vogelius

Research output: Contribution to journalArticle

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

Fingerprint

Asymptotic analysis
thin plates
Thin Plate
Bending moments
Elasticity
Geometry
bending moments
Fourth-order Equations
Constitutive Law
Linear Elasticity
Asymptotic Analysis
Length Scale
elastic properties
Curvature
curvature
Vary
Model
Moment
Three-dimensional
Coefficient

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials

Cite this

A new model for thin plates with rapidly varying thickness. / Kohn, Robert; Vogelius, Michael.

In: International Journal of Solids and Structures, Vol. 20, No. 4, 1984, p. 333-350.

Research output: Contribution to journalArticle

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