PreprintArticleVersion 2Preserved in Portico This version is not peer-reviewed
Analysis of Arbitrarily Loaded Rectangular Thin Plates with Two Opposite Edges Supported, One or Both of them Clamped, Using the Flexibility Method and a Modified Lévy Solution
Version 1
: Received: 29 May 2023 / Approved: 30 May 2023 / Online: 30 May 2023 (11:12:26 CEST)
Version 2
: Received: 12 June 2023 / Approved: 12 June 2023 / Online: 12 June 2023 (13:53:59 CEST)
How to cite:
Fogang, V. Analysis of Arbitrarily Loaded Rectangular Thin Plates with Two Opposite Edges Supported, One or Both of them Clamped, Using the Flexibility Method and a Modified Lévy Solution. Preprints2023, 2023052121. https://doi.org/10.20944/preprints202305.2121.v2
Fogang, V. Analysis of Arbitrarily Loaded Rectangular Thin Plates with Two Opposite Edges Supported, One or Both of them Clamped, Using the Flexibility Method and a Modified Lévy Solution. Preprints 2023, 2023052121. https://doi.org/10.20944/preprints202305.2121.v2
Fogang, V. Analysis of Arbitrarily Loaded Rectangular Thin Plates with Two Opposite Edges Supported, One or Both of them Clamped, Using the Flexibility Method and a Modified Lévy Solution. Preprints2023, 2023052121. https://doi.org/10.20944/preprints202305.2121.v2
APA Style
Fogang, V. (2023). Analysis of Arbitrarily Loaded Rectangular Thin Plates with Two Opposite Edges Supported, One or Both of them Clamped, Using the Flexibility Method and a Modified Lévy Solution. Preprints. https://doi.org/10.20944/preprints202305.2121.v2
Chicago/Turabian Style
Fogang, V. 2023 "Analysis of Arbitrarily Loaded Rectangular Thin Plates with Two Opposite Edges Supported, One or Both of them Clamped, Using the Flexibility Method and a Modified Lévy Solution" Preprints. https://doi.org/10.20944/preprints202305.2121.v2
Abstract
This paper aims to analyze arbitrarily loaded isotropic rectangular thin plates with two opposite edges supported (simply supported or clamped), from which one or both are clamped, and the other edges have arbitrary support conditions. Rectangular thin plates with two opposite edges simply supported are routinely analyzed using for the deflection the simple trigonometric series of Lévy or the double trigonometric series of Navier, while the loads are expanded in Fourier series. In this paper the flexibility method (or force method) of the linear beam theory was applied whereby the unknowns were the bending moments along the opposite edges; in this regard, the primary system was the plate simply supported along the above-mentioned opposite edges and subjected to the external loads, system solved using the Lévy solution, and the redundant system was the plate simply supported along the opposite edges and subjected to bending moments along those edges. In the redundant system, a modified Lévy solution was introduced to account for the edge moments. The compatibility equations (vanishing of the slopes at selected positions of the opposite edges) were set to determine the unknowns and so the efforts in the plate. The results obtained were in good agreement with the exact results.
Keywords
Isotropic rectangular Kirchhoff plate; opposite edges clamped; flexibility method; force method; Lévy solution; Fourier sine series
Subject
Engineering, Civil Engineering
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Commenter: Valentin Fogang
Commenter's Conflict of Interests: Author
Figures 2, 4, and 6 added
Results section: 3.4 added
Graphical abstract