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Poisson Theory of Isotropic Plates in Bending

Vijayakumar, K and Ramaiah, GK (2021) Poisson Theory of Isotropic Plates in Bending. [Book Chapter]

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Official URL: https://doi.org/10.1007/978-981-33-4210-1_1


Analysis of primary bending problems of homogeneous isotropic square plates is presented. Kirchhoff's theory and well-known shear deformation theories are briefly reviewed. The concept of lateral displacements as a face variable is introduced so that it is uncoupled from the determination of in-plane displacements. Poisson-Kirchhoff boundary conditions paradox is resolved through the newly proposed and developed Poisson theory. Supplementary problem based on fifteen decades old Levy's work is used to distinguish between neutral and face plane deflections. New primary problems are defined with zero transverse normal strain edge conditions. A highly accurate solution of a simple textbook problem of a simply supported plate under doubly sinusoidal vertical load is presented to show the utility of Poisson theory even for thick plates with one term representation of displacements. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Item Type: Book Chapter
Publication: Springer Tracts in Mechanical Engineering
Series.: Springer Tracts in Mechanical Engineering
Publisher: Springer Science and Business Media Deutschland GmbH
Additional Information: The copyright of this article belongs to Springer Science and Business Media Deutschland GmbH
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 16 Mar 2021 07:48
Last Modified: 16 Mar 2021 07:48
URI: http://eprints.iisc.ac.in/id/eprint/68229

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