Version 1
: Received: 29 June 2023 / Approved: 30 June 2023 / Online: 3 July 2023 (14:32:25 CEST)
Version 2
: Received: 19 July 2023 / Approved: 20 July 2023 / Online: 21 July 2023 (12:53:46 CEST)
How to cite:
Fogang, V. Another Approach to the Analysis of Isotropic Rectangular Thin Plates Subjected to External Bending Moments Using the Fourier Series. Preprints2023, 2023070112. https://doi.org/10.20944/preprints202307.0112.v2
Fogang, V. Another Approach to the Analysis of Isotropic Rectangular Thin Plates Subjected to External Bending Moments Using the Fourier Series. Preprints 2023, 2023070112. https://doi.org/10.20944/preprints202307.0112.v2
Fogang, V. Another Approach to the Analysis of Isotropic Rectangular Thin Plates Subjected to External Bending Moments Using the Fourier Series. Preprints2023, 2023070112. https://doi.org/10.20944/preprints202307.0112.v2
APA Style
Fogang, V. (2023). Another Approach to the Analysis of Isotropic Rectangular Thin Plates Subjected to External Bending Moments Using the Fourier Series. Preprints. https://doi.org/10.20944/preprints202307.0112.v2
Chicago/Turabian Style
Fogang, V. 2023 "Another Approach to the Analysis of Isotropic Rectangular Thin Plates Subjected to External Bending Moments Using the Fourier Series" Preprints. https://doi.org/10.20944/preprints202307.0112.v2
Abstract
The object of this paper is the analysis of isotropic rectangular thin plates supported (simply supported or clamped) along two opposite edges whereby the other edges have arbitrary support conditions; the plates are subjected to external bending moments, concentrated or distributed, and perpendicular to the supported edges. The standard approach to this problem is to replace the bending moment with a couple of forces infinitely close and to use the known expressions of efforts and deformations for the plate subjected to concentrated forces; the results are then related to the first derivatives of those efforts and deformations with respect to the position of application of the load. In this study, the external bending moment was expanded into a Fourier series, leading to a distributed external bending moment, and the boundary conditions and continuity equations were applied. Various types of rectangular plates were analyzed, as well as plates of infinite length whose results were identical to those in the literature. In addition, results for cantilever plates of infinite length were presented.
Keywords
Isotropic rectangular thin plate; concentrated/distributed bending moment; plates of infinite length; 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.
Received:
21 July 2023
Commenter:
Valentin Fogang
Commenter's Conflict of Interests:
Author
Comment:
Title Abstract Materials and Methods: Section 2.2.2: two load cases were added Section 2.2.4 was added Results and Discussion: 3.3, 3.4, and 3.5 were added Four supplementary files were added
Commenter: Valentin Fogang
Commenter's Conflict of Interests: Author
Abstract
Materials and Methods: Section 2.2.2: two load cases were added
Section 2.2.4 was added
Results and Discussion: 3.3, 3.4, and 3.5 were added
Four supplementary files were added