Bending Analysis of Isotropic Rectangular Kirchhoff Plates Subjected to a Thermal Gradient Using the Fourier Transform Method<strong> </strong>

Abstract

The object of this paper is the bending analysis of isotropic rectangular Kirchhoff plates subjected to a thermal gradient (TG) 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 TG; these derivatives are zero by constant value of the TG, which leads to the absence of the TG in the governing equation. This paper presented an approach by which Fourier sine transform was utilized to describe the TG, while the double trigonometric series of Navier and the simple trigonometric series of L&amp;eacute;vy were utilized to describe the deflection. Thus, the TG 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).

Kirchhoff-Love Plate Theory: First-Order Analysis, Second-Order Analysis, Plate Buckling Analysis, and Vibration Analysis Using the Finite Difference Method

“…Detailed analysis and results are presented in Appendix C and in the Supplementary Material "Rectangular plate simply supported along all edges and subjected to a non-uniform heating." Table 3 lists the results obtained by Fogang [14] using the solution by Lévy [5] and the Fourier sine transform method, and those obtained in the present study.…”