Version 1
: Received: 17 June 2021 / Approved: 18 June 2021 / Online: 18 June 2021 (12:52:52 CEST)
Version 2
: Received: 10 December 2021 / Approved: 10 December 2021 / Online: 10 December 2021 (13:50:59 CET)
How to cite:
Fogang, V. Bending Analysis of Isotropic Rectangular Kirchhoff Plates Subjected to Non-Uniform Heating Using the Fourier Transform Method. Preprints2021, 2021060479. https://doi.org/10.20944/preprints202106.0479.v2
Fogang, V. Bending Analysis of Isotropic Rectangular Kirchhoff Plates Subjected to Non-Uniform Heating Using the Fourier Transform Method . Preprints 2021, 2021060479. https://doi.org/10.20944/preprints202106.0479.v2
Fogang, V. Bending Analysis of Isotropic Rectangular Kirchhoff Plates Subjected to Non-Uniform Heating Using the Fourier Transform Method. Preprints2021, 2021060479. https://doi.org/10.20944/preprints202106.0479.v2
APA Style
Fogang, V. (2021). Bending Analysis of Isotropic Rectangular Kirchhoff Plates Subjected to Non-Uniform Heating Using the Fourier Transform Method<strong> </strong>. Preprints. https://doi.org/10.20944/preprints202106.0479.v2
Chicago/Turabian Style
Fogang, V. 2021 "Bending Analysis of Isotropic Rectangular Kirchhoff Plates Subjected to Non-Uniform Heating Using the Fourier Transform Method<strong> </strong>" Preprints. https://doi.org/10.20944/preprints202106.0479.v2
Abstract
The object of this paper is the bending analysis of isotropic rectangular Kirchhoff plates subjected to non-uniform heating (NUH) using the Fourier transform method. The bottom and top surfaces of the plate are assumed to have different changes in temperature, whereas the change in temperature of the mid-surface is zero. According to classical plate theory, the governing equation of the plate contains second derivatives of the NUH; these derivatives are zero by constant value of the NUH, which leads to its absence in the governing equation. This paper presented an approach by which Fourier sine transform was utilized to describe the NUH, while the double trigonometric series of Navier and the simple trigonometric series of Lévy were utilized to describe the deflection curve. Thus, the NUH appeared in the governing equation, which simplified the analysis. Rectangular plates simply supported along all edges were analyzed, bending moments, twisting moments, and deflections being determined. In addition, rectangular plates simply supported along two opposite edges were analyzed; the other edges having various support conditions (free, simply supported, and fixed).
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
The term " thermal gradient" replaced by " non-uniform heating" throughout the article