Fredholm Integral Equation Solution for Rectangular Plate with Moment Singularity
Article Sidebar
Main Article Content
Abstract
This paper presents the finite Hankel transform method for a problem of rectangular plate clamped on the two opposite edges and simply supported on the remaining edges with an internal line support located along the center under uniformly distributed load. The proper singularity in the order of square root in moment is introduced at the tips of the internal support. The problem formulation is reduced to an inhomogeneous Fredholm integral equation of the second kind in term of an unknown auxiliary function which can be transformed to a set of algebraic simultaneous equations by using Simpson’s rule. The solution results provide the unknown auxiliary function of the problem and the physical quantities, namely the deflection and bending moment of the plate with various lengths of internal line support.
Keywords: Fredholm Integral Equation/ Hankel Transform/ Rectangular Plate/ Singularity
Corresponding author: E-mail: [email protected]
Article Details
Copyright Transfer Statement
The copyright of this article is transferred to Current Applied Science and Technology journal with effect if and when the article is accepted for publication. The copyright transfer covers the exclusive right to reproduce and distribute the article, including reprints, translations, photographic reproductions, electronic form (offline, online) or any other reproductions of similar nature.
The author warrants that this contribution is original and that he/she has full power to make this grant. The author signs for and accepts responsibility for releasing this material on behalf of any and all co-authors.
Here is the link for download: Copyright transfer form.pdf
References
[2] Williams, M.L. 1952 Surface Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates under Bending. Proceedings of the First U.S. National Congress of Applied Mechanics, Chicago, 1, pp. 325-329.
[3] Stahl, B. and Keer, L.M. 1972 Vibration and Stability of Cracked Rectangular Plates, International Journal of Solids and Structures, 8, 69-91.
[4] Stahl, B. and Keer, L.M. 1972 Vibration and Buckling of a Rectangular plate with an Internal Support, Quarterly Journal of Mechanics and Applied Mathematics, 25, 467-478.
[5] Keer, L.M. and Stahl, B. 1972 Eigenvalue Problems of Rectangular Plates with Mixed Edge Conditions, Journal of Applied Mechanics, 39, 513-520.
[6] Kiattikomol, K., Keer, L.M. and Dundurs, J. 1974 Application of Dual Series to Rectangular Plates, Journal of the Engineering Mechanics Division, 100(EM2), 433-443.
[7] Kiattikomol, K. and Sriswasdi, V. 1988 Bending of a Uniformly Loaded Annular Plate with Mixed Boundary Conditions. AIAA Journal, 26(4), 487-492.