Thick rectangular plates-I. The generalized Navier solution

Mark Levinson, David W Cooke

Research output: Contribution to journalArticle

Abstract

Navier's classical solution for the problem of a statically loaded, rectangular plate which is simply-supported on all edges is generalized so as to provide a solution for the problem when transverse shear deformations are taken into account. Such solutions are provided for both Mindlin's plate theory and a new plate theory, recently published, which allows for warping of transverse sections of the plate. The results of the analyses are simple expressions for the Fourier coefficients in the expansions representing the transverse deflection and rotations of normals to the plate midsurface. Although both theories predict the same transverse deflection, the rotations and inplane stresses are different for the two theories. Some observations and comments concerning the effects of transverse shears on the deflections of plates and inplane stresses are made.

Original languageEnglish (US)
Pages (from-to)199-205
Number of pages7
JournalInternational Journal of Mechanical Sciences
Volume25
Issue number3
DOIs
StatePublished - 1983
Externally publishedYes

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rectangular plates
deflection
Mindlin plates
Shear deformation
shear
plate theory
expansion
coefficients

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

Thick rectangular plates-I. The generalized Navier solution. / Levinson, Mark; Cooke, David W.

In: International Journal of Mechanical Sciences, Vol. 25, No. 3, 1983, p. 199-205.

Research output: Contribution to journalArticle

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