Uniformly Loaded Square Plate with Partially Simply Supported at the Middle Edges and Point-Column Supported at the Corners: I – Theoretical Formulation
Yos Sompornjaroensuk* and Prasert Ratchatasakron
Department of Civil Engineering, Faculty of Engineering
Mahanakorn University of Technology, Bangkok 10530, Thailand
*Email: This email address is being protected from spambots. You need JavaScript enabled to view it. (corresponding author)

Manuscript received January 2, 2017
Revised March 31, 2017

The objective of the present paper is to present an efficient theoretical method to solve the bending problem of uniformly loaded square plate in which the plate is point-column supported at all corners and partially simply supported at all central portion edges. The solution can first be set up by using the Lévy-Nádai’s approach and the mixed boundary conditions are then written in the form of dual-series equations. By making use of the proper finite Hankel integral transform, the dual-series equations can further finally be reduced to an inhomogeneous Fredholm integral equation of the second kind. Importantly, the highlight of the problem is that the analytical formulation explicitly considers the moment singularities existed at the ends of partial simple supports.

Keywords: Dual-series equations, Fredholm integral equation, Hankel integral transform, Mixed boundary conditions, Singularities, Square plate.

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